Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | #include <stdio.h> #include <stdlib.h> #include <assert.h> #include <math.h> int** rref(int** matrix, int rows, int cols, int graphlen) { const int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(rows * sizeof(int)); int** used_for_row = malloc(rows * sizeof(int*)); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(cols * sizeof(int)); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + extra], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i] != 0) { other = i; break; } } if (other == -1) { extra++; continue; } if (other < col) { extra++; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j]; matrix[i][j] %= PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * used_for_row[i][cols - 1] + 1); used_for_row[i][used_for_row[i][cols - 1] + 1] = 0; qsort(used_for_row[i], used_for_row[i][cols - 1] + 1, sizeof(int), (int (*)(const void*, const void*))strcmp); } return used_for_row; } |
I extracted the following code from that output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | #include <stdio.h> #include <stdlib.h> #include <assert.h> #include <math.h> int** rref(int** matrix, int rows, int cols, int graphlen) { const int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(rows * sizeof(int)); int** used_for_row = malloc(rows * sizeof(int*)); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(cols * sizeof(int)); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + extra], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i] != 0) { other = i; break; } } if (other == -1) { extra++; continue; } if (other < col) { extra++; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j]; matrix[i][j] %= PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * used_for_row[i][cols - 1] + 1); used_for_row[i][used_for_row[i][cols - 1] + 1] = 0; qsort(used_for_row[i], used_for_row[i][cols - 1] + 1, sizeof(int), (int (*)(const void*, const void*))strcmp); } return used_for_row; } |
Running the following program:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 | #include <stdio.h> #include <stdlib.h> #include <assert.h> #include <math.h> int** rref(int** matrix, int rows, int cols, int graphlen) { const int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(rows * sizeof(int)); int** used_for_row = malloc(rows * sizeof(int*)); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(cols * sizeof(int)); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + extra], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i] != 0) { other = i; break; } } if (other == -1) { extra++; continue; } if (other < col) { extra++; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j]; matrix[i][j] %= PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * used_for_row[i][cols - 1] + 1); used_for_row[i][used_for_row[i][cols - 1] + 1] = 0; qsort(used_for_row[i], used_for_row[i][cols - 1] + 1, sizeof(int), (int (*)(const void*, const void*))strcmp); } return used_for_row; } #include<stdio.h> #include<stdlib.h> int main() { int arr0[] = {1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr1[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr2[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr3[] = {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr4[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr5[] = {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr6[] = {0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0}; int arr7[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30}; int arr8[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr9[] = {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20}; int arr10[] = {1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr11[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr12[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr13[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14}; int arr14[] = {0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr15[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30}; int arr16[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr17[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr18[] = {0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr19[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr20[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr21[] = {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr22[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20}; int arr23[] = {0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr24[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr25[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr26[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr27[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr28[] = {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr29[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr30[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr31[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr32[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10}; int arr33[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr34[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr35[] = {0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9}; int arr36[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20}; int arr37[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40}; int arr38[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int* arr[] = {arr0, arr1, arr2, arr3, arr4, arr5, arr6, arr7, arr8, arr9, arr10, arr11, arr12, arr13, arr14, arr15, arr16, arr17, arr18, arr19, arr20, arr21, arr22, arr23, arr24, arr25, arr26, arr27, arr28, arr29, arr30, arr31, arr32, arr33, arr34, arr35, arr36, arr37, arr38}; int** got = rref(arr, 39, 49, 37); int answer = got[3][0]+got[3][1]+got[3][2]+got[3][3]+got[3][4]+got[3][5]+got[3][6]; int expected = 146; if (answer != expected) { printf("Wrong answer; got %d instead of %d.\n", answer, expected); exit(1); } printf("All tests passed\n"); } |
main.c: In function 'rref':
main.c:30:18: warning: implicit declaration of function 'memcmp' [-Wimplicit-function-declaration]
30 | if (!memcmp(matrix[col], matrix[col + extra], cols * sizeof(int))) {
| ^~~~~~
main.c:6:1: note: include '<string.h>' or provide a declaration of 'memcmp'
5 | #include <math.h>
+++ |+#include <string.h>
6 |
main.c:110:111: error: 'strcmp' undeclared (first use in this function)
110 | qsort(used_for_row[i], used_for_row[i][cols - 1] + 1, sizeof(int), (int (*)(const void*, const void*))strcmp);
| ^~~~~~
main.c:110:111: note: 'strcmp' is defined in header '<string.h>'; did you forget to '#include <string.h>'?
main.c:110:111: note: each undeclared identifier is reported only once for each function it appears in
main.sh: line 2: ./a.out: No such file or directory
Testing if the previous output contains the string All tests passed
: False
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | #include <stdio.h> #include <stdlib.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!matrix[col][col + extra] && !matrix[col]) { extra += 1; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i]) { other = i; break; } } if (other < col) { extra += 1; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } |
I extracted the following code from that output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | #include <stdio.h> #include <stdlib.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!matrix[col][col + extra] && !matrix[col]) { extra += 1; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i]) { other = i; break; } } if (other < col) { extra += 1; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } |
Running the following program:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 | #include <stdio.h> #include <stdlib.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!matrix[col][col + extra] && !matrix[col]) { extra += 1; continue; } int other = -1; for (int i = col + extra + 1; i < cols; i++) { if (matrix[col][i]) { other = i; break; } } if (other < col) { extra += 1; continue; } int* temp = matrix[col]; matrix[col] = matrix[other]; matrix[other] = temp; int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } #include<stdio.h> #include<stdlib.h> int main() { int arr0[] = {1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr1[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr2[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr3[] = {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr4[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr5[] = {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr6[] = {0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0}; int arr7[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30}; int arr8[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr9[] = {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20}; int arr10[] = {1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr11[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr12[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr13[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14}; int arr14[] = {0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr15[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30}; int arr16[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr17[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr18[] = {0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr19[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr20[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr21[] = {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr22[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20}; int arr23[] = {0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr24[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr25[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr26[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr27[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr28[] = {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr29[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr30[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr31[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr32[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10}; int arr33[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr34[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr35[] = {0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9}; int arr36[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20}; int arr37[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40}; int arr38[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int* arr[] = {arr0, arr1, arr2, arr3, arr4, arr5, arr6, arr7, arr8, arr9, arr10, arr11, arr12, arr13, arr14, arr15, arr16, arr17, arr18, arr19, arr20, arr21, arr22, arr23, arr24, arr25, arr26, arr27, arr28, arr29, arr30, arr31, arr32, arr33, arr34, arr35, arr36, arr37, arr38}; int** got = rref(arr, 39, 49, 37); int answer = got[3][0]+got[3][1]+got[3][2]+got[3][3]+got[3][4]+got[3][5]+got[3][6]; int expected = 146; if (answer != expected) { printf("Wrong answer; got %d instead of %d.\n", answer, expected); exit(1); } printf("All tests passed\n"); } |
main.c: In function 'rref':
main.c:55:13: warning: implicit declaration of function 'assert' [-Wimplicit-function-declaration]
55 | assert(pivot == 1 || pivot == PH - 1);
| ^~~~~~
main.c:4:1: note: 'assert' is defined in header '<assert.h>'; did you forget to '#include <assert.h>'?
3 | #include <stdlib.h>
+++ |+#include <assert.h>
4 |
/usr/bin/ld: /tmp/ccFWbrhp.o: in function `rref':
main.c:(.text+0x3d2): undefined reference to `assert'
/usr/bin/ld: main.c:(.text+0x3fd): undefined reference to `assert'
collect2: error: ld returned 1 exit status
main.sh: line 2: ./a.out: No such file or directory
Testing if the previous output contains the string All tests passed
: False
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 | #include <stdlib.h> #include <stdio.h> #include <assert.h> // PH is the prime modulus used for arithmetic #define PH 16 // rref performs row reduction on the given matrix and returns the used_for_row array int** rref(int** matrix, int rows, int cols, int graphlen) { // extra is the number of extra columns that have been added to the matrix int extra = 0; // col is the current column being processed int col = 0; // pivots is the list of pivot columns int* pivots = malloc(sizeof(int) * rows); // used_for_row is the array that will store the set of rows that each row is used in int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); used_for_row[i][0] = i; } // Convert the matrix to mod PH for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Perform row reduction while (col + extra < cols - 1 && col < rows) { // If the current element is 0, find a non-zero element in the same column and swap the rows if (matrix[col][col + extra] == 0) { if (all_zeros(matrix, rows, cols, col)) { extra++; continue; } int other = find_non_zero(matrix, rows, cols, col, extra); if (other < col) { extra++; continue; } swap_rows(matrix, used_for_row, rows, col, other); } // Add the current column to the list of pivots pivots[col] = col + extra; // Normalize the current row int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } // Subtract multiples of the current row from the other rows for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { if (matrix[i][col + extra] != 0) { used_for_row[i] |= used_for_row[col]; if (col < graphlen) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; } else { while (matrix[i][col + extra] != 0) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } matrix[i][j] %= PH; } } } col++; } // Convert the matrix back to normal for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Return the used_for_row array return used_for_row; } // all_zeros checks if all the elements in the given column are 0 int all_zeros(int** matrix, int rows, int cols, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } // find_non_zero finds the first non-zero element in the given column below the given row int find_non_zero(int** matrix, int rows, int cols, int row, int extra) { for (int i = row + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } // swap_rows swaps the two given rows in the matrix and the used_for_row array void swap_rows(int** matrix, int** used_for_row, int rows, int row1, int row2) { int* temp1 = matrix[row1]; int* temp2 = matrix[row2]; matrix[row1] = temp2; matrix[row2] = temp1; int* temp3 = used_for_row[row1]; int* temp4 = used_for_row[row2]; used_for_row[row1] = temp4; used_for_row[row2] = temp3; } |
I extracted the following code from that output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 | #include <stdlib.h> #include <stdio.h> #include <assert.h> // PH is the prime modulus used for arithmetic #define PH 16 // rref performs row reduction on the given matrix and returns the used_for_row array int** rref(int** matrix, int rows, int cols, int graphlen) { // extra is the number of extra columns that have been added to the matrix int extra = 0; // col is the current column being processed int col = 0; // pivots is the list of pivot columns int* pivots = malloc(sizeof(int) * rows); // used_for_row is the array that will store the set of rows that each row is used in int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); used_for_row[i][0] = i; } // Convert the matrix to mod PH for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Perform row reduction while (col + extra < cols - 1 && col < rows) { // If the current element is 0, find a non-zero element in the same column and swap the rows if (matrix[col][col + extra] == 0) { if (all_zeros(matrix, rows, cols, col)) { extra++; continue; } int other = find_non_zero(matrix, rows, cols, col, extra); if (other < col) { extra++; continue; } swap_rows(matrix, used_for_row, rows, col, other); } // Add the current column to the list of pivots pivots[col] = col + extra; // Normalize the current row int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } // Subtract multiples of the current row from the other rows for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { if (matrix[i][col + extra] != 0) { used_for_row[i] |= used_for_row[col]; if (col < graphlen) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; } else { while (matrix[i][col + extra] != 0) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } matrix[i][j] %= PH; } } } col++; } // Convert the matrix back to normal for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Return the used_for_row array return used_for_row; } // all_zeros checks if all the elements in the given column are 0 int all_zeros(int** matrix, int rows, int cols, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } // find_non_zero finds the first non-zero element in the given column below the given row int find_non_zero(int** matrix, int rows, int cols, int row, int extra) { for (int i = row + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } // swap_rows swaps the two given rows in the matrix and the used_for_row array void swap_rows(int** matrix, int** used_for_row, int rows, int row1, int row2) { int* temp1 = matrix[row1]; int* temp2 = matrix[row2]; matrix[row1] = temp2; matrix[row2] = temp1; int* temp3 = used_for_row[row1]; int* temp4 = used_for_row[row2]; used_for_row[row1] = temp4; used_for_row[row2] = temp3; } |
Running the following program:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 | #include <stdlib.h> #include <stdio.h> #include <assert.h> // PH is the prime modulus used for arithmetic #define PH 16 // rref performs row reduction on the given matrix and returns the used_for_row array int** rref(int** matrix, int rows, int cols, int graphlen) { // extra is the number of extra columns that have been added to the matrix int extra = 0; // col is the current column being processed int col = 0; // pivots is the list of pivot columns int* pivots = malloc(sizeof(int) * rows); // used_for_row is the array that will store the set of rows that each row is used in int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); used_for_row[i][0] = i; } // Convert the matrix to mod PH for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Perform row reduction while (col + extra < cols - 1 && col < rows) { // If the current element is 0, find a non-zero element in the same column and swap the rows if (matrix[col][col + extra] == 0) { if (all_zeros(matrix, rows, cols, col)) { extra++; continue; } int other = find_non_zero(matrix, rows, cols, col, extra); if (other < col) { extra++; continue; } swap_rows(matrix, used_for_row, rows, col, other); } // Add the current column to the list of pivots pivots[col] = col + extra; // Normalize the current row int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } // Subtract multiples of the current row from the other rows for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { if (matrix[i][col + extra] != 0) { used_for_row[i] |= used_for_row[col]; if (col < graphlen) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; } else { while (matrix[i][col + extra] != 0) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } matrix[i][j] %= PH; } } } col++; } // Convert the matrix back to normal for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } // Return the used_for_row array return used_for_row; } // all_zeros checks if all the elements in the given column are 0 int all_zeros(int** matrix, int rows, int cols, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } // find_non_zero finds the first non-zero element in the given column below the given row int find_non_zero(int** matrix, int rows, int cols, int row, int extra) { for (int i = row + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } // swap_rows swaps the two given rows in the matrix and the used_for_row array void swap_rows(int** matrix, int** used_for_row, int rows, int row1, int row2) { int* temp1 = matrix[row1]; int* temp2 = matrix[row2]; matrix[row1] = temp2; matrix[row2] = temp1; int* temp3 = used_for_row[row1]; int* temp4 = used_for_row[row2]; used_for_row[row1] = temp4; used_for_row[row2] = temp3; } #include<stdio.h> #include<stdlib.h> int main() { int arr0[] = {1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr1[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr2[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr3[] = {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr4[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr5[] = {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr6[] = {0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0}; int arr7[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30}; int arr8[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr9[] = {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20}; int arr10[] = {1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr11[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr12[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr13[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14}; int arr14[] = {0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr15[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30}; int arr16[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr17[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr18[] = {0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr19[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr20[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr21[] = {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr22[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20}; int arr23[] = {0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr24[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr25[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr26[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr27[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr28[] = {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr29[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr30[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr31[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr32[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10}; int arr33[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr34[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr35[] = {0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9}; int arr36[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20}; int arr37[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40}; int arr38[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int* arr[] = {arr0, arr1, arr2, arr3, arr4, arr5, arr6, arr7, arr8, arr9, arr10, arr11, arr12, arr13, arr14, arr15, arr16, arr17, arr18, arr19, arr20, arr21, arr22, arr23, arr24, arr25, arr26, arr27, arr28, arr29, arr30, arr31, arr32, arr33, arr34, arr35, arr36, arr37, arr38}; int** got = rref(arr, 39, 49, 37); int answer = got[3][0]+got[3][1]+got[3][2]+got[3][3]+got[3][4]+got[3][5]+got[3][6]; int expected = 146; if (answer != expected) { printf("Wrong answer; got %d instead of %d.\n", answer, expected); exit(1); } printf("All tests passed\n"); } |
main.c: In function 'rref':
main.c:36:17: warning: implicit declaration of function 'all_zeros' [-Wimplicit-function-declaration]
36 | if (all_zeros(matrix, rows, cols, col)) {
| ^~~~~~~~~
main.c:40:25: warning: implicit declaration of function 'find_non_zero' [-Wimplicit-function-declaration]
40 | int other = find_non_zero(matrix, rows, cols, col, extra);
| ^~~~~~~~~~~~~
main.c:46:13: warning: implicit declaration of function 'swap_rows' [-Wimplicit-function-declaration]
46 | swap_rows(matrix, used_for_row, rows, col, other);
| ^~~~~~~~~
main.c:70:37: error: invalid operands to binary | (have 'int *' and 'int *')
70 | used_for_row[i] |= used_for_row[col];
| ^~ ~~~~~~~~~~~~~~~~~
| |
| int *
main.c: In function 'find_non_zero':
main.c:110:23: error: 'col' undeclared (first use in this function); did you mean 'cols'?
110 | if (matrix[i][col + extra] != 0) {
| ^~~
| cols
main.c:110:23: note: each undeclared identifier is reported only once for each function it appears in
main.c: At top level:
main.c:118:6: warning: conflicting types for 'swap_rows'; have 'void(int **, int **, int, int, int)'
118 | void swap_rows(int** matrix, int** used_for_row, int rows, int row1, int row2) {
| ^~~~~~~~~
main.c:46:13: note: previous implicit declaration of 'swap_rows' with type 'void(int **, int **, int, int, int)'
46 | swap_rows(matrix, used_for_row, rows, col, other);
| ^~~~~~~~~
main.sh: line 2: ./a.out: No such file or directory
Testing if the previous output contains the string All tests passed
: False
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + 1], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { other = i; break; } } if (other < col) { extra++; continue; } int temp; for (int i = 0; i < cols; i++) { temp = matrix[col][i]; matrix[col][i] = matrix[other][i]; matrix[other][i] = temp; } int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * (cols + 1)); used_for_row[i][cols] = -1; } return used_for_row; } |
I extracted the following code from that output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + 1], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { other = i; break; } } if (other < col) { extra++; continue; } int temp; for (int i = 0; i < cols; i++) { temp = matrix[col][i]; matrix[col][i] = matrix[other][i]; matrix[other][i] = temp; } int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * (cols + 1)); used_for_row[i][cols] = -1; } return used_for_row; } |
Running the following program:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int) * cols); for (int j = 0; j < cols; j++) { used_for_row[i][j] = i; } } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (!memcmp(matrix[col], matrix[col + 1], cols * sizeof(int))) { extra++; continue; } int other = -1; for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { other = i; break; } } if (other < col) { extra++; continue; } int temp; for (int i = 0; i < cols; i++) { temp = matrix[col][i]; matrix[col][i] = matrix[other][i]; matrix[other][i] = temp; } int* temp2 = used_for_row[col]; used_for_row[col] = used_for_row[other]; used_for_row[other] = temp2; } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(pivot == 1 || pivot == PH - 1); } else { assert(pivot == 2 || pivot == PH - 2); pivot /= 2; } for (int i = 0; i < cols; i++) { matrix[col][i] *= pivot; matrix[col][i] %= PH; } for (int i = 0; i < rows; i++) { if (i == col) continue; for (int j = 0; j < cols; j++) { used_for_row[i][j] |= used_for_row[col][j]; } if (col < graphlen) { for (int j = 0; j < cols; j++) { matrix[i][j] -= matrix[col][j] * matrix[i][col + extra]; matrix[i][j] %= PH; } } else { while (matrix[i][col + extra] != 0) { for (int j = 0; j < cols; j++) { matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH; } } } } col++; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } for (int i = 0; i < rows; i++) { used_for_row[i] = realloc(used_for_row[i], sizeof(int) * (cols + 1)); used_for_row[i][cols] = -1; } return used_for_row; } #include<stdio.h> #include<stdlib.h> int main() { int arr0[] = {1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr1[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr2[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr3[] = {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr4[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr5[] = {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr6[] = {0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0}; int arr7[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30}; int arr8[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr9[] = {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20}; int arr10[] = {1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr11[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr12[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr13[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14}; int arr14[] = {0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr15[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30}; int arr16[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr17[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr18[] = {0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr19[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr20[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr21[] = {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr22[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20}; int arr23[] = {0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr24[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr25[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr26[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr27[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr28[] = {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr29[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr30[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr31[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr32[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10}; int arr33[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr34[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr35[] = {0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9}; int arr36[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20}; int arr37[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40}; int arr38[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int* arr[] = {arr0, arr1, arr2, arr3, arr4, arr5, arr6, arr7, arr8, arr9, arr10, arr11, arr12, arr13, arr14, arr15, arr16, arr17, arr18, arr19, arr20, arr21, arr22, arr23, arr24, arr25, arr26, arr27, arr28, arr29, arr30, arr31, arr32, arr33, arr34, arr35, arr36, arr37, arr38}; int** got = rref(arr, 39, 49, 37); int answer = got[3][0]+got[3][1]+got[3][2]+got[3][3]+got[3][4]+got[3][5]+got[3][6]; int expected = 146; if (answer != expected) { printf("Wrong answer; got %d instead of %d.\n", answer, expected); exit(1); } printf("All tests passed\n"); } |
main.c: In function 'rref':
main.c:29:18: warning: implicit declaration of function 'memcmp' [-Wimplicit-function-declaration]
29 | if (!memcmp(matrix[col], matrix[col + 1], cols * sizeof(int))) {
| ^~~~~~
main.c:5:1: note: include '<string.h>' or provide a declaration of 'memcmp'
4 | #include <assert.h>
+++ |+#include <string.h>
5 |
a.out: main.c:59: rref: Assertion `pivot == 1 || pivot == PH - 1' failed.
main.sh: line 2: 16 Aborted (core dumped) ./a.out
Testing if the previous output contains the string All tests passed
: False
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
Rewrite this function in C. You can assume that the input is a 2d matrix correctly formatted. Call it rref(int** matrix, int rows, int cols, int graphlen) where the size is matrix[rows][cols]. Return an int** of used_for_row. def rref(matrix, graphlen): PH = 16 extra = 0 col = 0 pivots = [] used_for_row = [set([i]) for i in range(matrix.shape[0])] matrix = matrix%PH while col+extra < matrix.shape[1]-1 and col < matrix.shape[0]: if matrix[col,col+extra] == 0: if np.all(matrix[:,col] == 0): extra += 1 continue other = np.argwhere(matrix[:,col+extra] != 0).flatten()[-1] if other < col: extra += 1 continue matrix[col], matrix[other] = list(matrix[other]), list(matrix[col]) used_for_row[col], used_for_row[other] = used_for_row[other], used_for_row[col] pivots.append(col+extra) pivot = matrix[col,col+extra] if col+extra < graphlen: assert np.abs(pivot) == 1 or np.abs(pivot) == PH-1 else: assert np.abs(pivot) == 2 or np.abs(pivot) == PH-2 pivot //= 2 matrix[col] *= pivot matrix[col] %= PH others = np.argwhere(matrix[:,col+extra]).flatten() for i in others: if i == col: continue used_for_row[i] |= used_for_row[col] if col < graphlen: matrix[i] -= matrix[col]*matrix[i,col+extra] else: while matrix[i,col+extra] != 0: matrix[i] = (matrix[i]-matrix[col])%PH matrix[i] %= PH col += 1 matrix = np.array(matrix)%PH return [sorted(x) for x in used_for_row]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); *used_for_row[i] = i; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (all_zero(matrix, col)) { extra += 1; continue; } int other = find_nonzero(matrix, col, extra); if (other < col) { extra += 1; continue; } swap_rows(matrix, col, other); swap_sets(used_for_row, col, other); } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } scale_row(matrix, col, pivot); int* others = find_nonzero_cols(matrix, col, extra); for (int i = 0; i < rows; i++) { if (i == col) continue; union_sets(used_for_row[i], used_for_row[col]); if (col < graphlen) { subtract_rows(matrix, i, col, matrix[i][col + extra]); } else { while (matrix[i][col + extra] != 0) { subtract_rows(matrix, i, col, 1); } } matrix[i][col + extra] %= PH; } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } int all_zero(int** matrix, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } int find_nonzero(int** matrix, int col, int extra) { for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } void swap_rows(int** matrix, int row1, int row2) { int* temp = matrix[row1]; matrix[row1] = matrix[row2]; matrix[row2] = temp; } void swap_sets(int** sets, int set1, int set2) { int* temp = sets[set1]; sets[set1] = sets[set2]; sets[set2] = temp; } void scale_row(int** matrix, int row, int factor) { for (int i = 0; i < cols; i++) { matrix[row][i] *= factor; matrix[row][i] %= PH; } } int* find_nonzero_cols(int** matrix, int col, int extra) { int* others = malloc(sizeof(int) * rows); int count = 0; for (int i = 0; i < rows; i++) { if (matrix[i][col + extra] != 0) { others[count] = i; count++; } } return others; } void union_sets(int* set1, int* set2) { for (int i = 0; i < *set2; i++) { set1[*set1 + i] = set2[i]; } *set1 += *set2; } void subtract_rows(int** matrix, int row1, int row2, int factor) { for (int i = 0; i < cols; i++) { matrix[row1][i] -= matrix[row2][i] * factor; matrix[row1][i] %= PH; } } |
I extracted the following code from that output:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); *used_for_row[i] = i; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (all_zero(matrix, col)) { extra += 1; continue; } int other = find_nonzero(matrix, col, extra); if (other < col) { extra += 1; continue; } swap_rows(matrix, col, other); swap_sets(used_for_row, col, other); } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } scale_row(matrix, col, pivot); int* others = find_nonzero_cols(matrix, col, extra); for (int i = 0; i < rows; i++) { if (i == col) continue; union_sets(used_for_row[i], used_for_row[col]); if (col < graphlen) { subtract_rows(matrix, i, col, matrix[i][col + extra]); } else { while (matrix[i][col + extra] != 0) { subtract_rows(matrix, i, col, 1); } } matrix[i][col + extra] %= PH; } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } int all_zero(int** matrix, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } int find_nonzero(int** matrix, int col, int extra) { for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } void swap_rows(int** matrix, int row1, int row2) { int* temp = matrix[row1]; matrix[row1] = matrix[row2]; matrix[row2] = temp; } void swap_sets(int** sets, int set1, int set2) { int* temp = sets[set1]; sets[set1] = sets[set2]; sets[set2] = temp; } void scale_row(int** matrix, int row, int factor) { for (int i = 0; i < cols; i++) { matrix[row][i] *= factor; matrix[row][i] %= PH; } } int* find_nonzero_cols(int** matrix, int col, int extra) { int* others = malloc(sizeof(int) * rows); int count = 0; for (int i = 0; i < rows; i++) { if (matrix[i][col + extra] != 0) { others[count] = i; count++; } } return others; } void union_sets(int* set1, int* set2) { for (int i = 0; i < *set2; i++) { set1[*set1 + i] = set2[i]; } *set1 += *set2; } void subtract_rows(int** matrix, int row1, int row2, int factor) { for (int i = 0; i < cols; i++) { matrix[row1][i] -= matrix[row2][i] * factor; matrix[row1][i] %= PH; } } |
Running the following program:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 | #include <stdio.h> #include <stdlib.h> #include <assert.h> int** rref(int** matrix, int rows, int cols, int graphlen) { int PH = 16; int extra = 0; int col = 0; int* pivots = malloc(sizeof(int) * rows); int** used_for_row = malloc(sizeof(int*) * rows); for (int i = 0; i < rows; i++) { used_for_row[i] = malloc(sizeof(int)); *used_for_row[i] = i; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } while (col + extra < cols - 1 && col < rows) { if (matrix[col][col + extra] == 0) { if (all_zero(matrix, col)) { extra += 1; continue; } int other = find_nonzero(matrix, col, extra); if (other < col) { extra += 1; continue; } swap_rows(matrix, col, other); swap_sets(used_for_row, col, other); } pivots[col] = col + extra; int pivot = matrix[col][col + extra]; if (col + extra < graphlen) { assert(abs(pivot) == 1 || abs(pivot) == PH - 1); } else { assert(abs(pivot) == 2 || abs(pivot) == PH - 2); pivot /= 2; } scale_row(matrix, col, pivot); int* others = find_nonzero_cols(matrix, col, extra); for (int i = 0; i < rows; i++) { if (i == col) continue; union_sets(used_for_row[i], used_for_row[col]); if (col < graphlen) { subtract_rows(matrix, i, col, matrix[i][col + extra]); } else { while (matrix[i][col + extra] != 0) { subtract_rows(matrix, i, col, 1); } } matrix[i][col + extra] %= PH; } col += 1; } for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { matrix[i][j] %= PH; } } return used_for_row; } int all_zero(int** matrix, int col) { for (int i = 0; i < rows; i++) { if (matrix[i][col] != 0) { return 0; } } return 1; } int find_nonzero(int** matrix, int col, int extra) { for (int i = col + 1; i < rows; i++) { if (matrix[i][col + extra] != 0) { return i; } } return -1; } void swap_rows(int** matrix, int row1, int row2) { int* temp = matrix[row1]; matrix[row1] = matrix[row2]; matrix[row2] = temp; } void swap_sets(int** sets, int set1, int set2) { int* temp = sets[set1]; sets[set1] = sets[set2]; sets[set2] = temp; } void scale_row(int** matrix, int row, int factor) { for (int i = 0; i < cols; i++) { matrix[row][i] *= factor; matrix[row][i] %= PH; } } int* find_nonzero_cols(int** matrix, int col, int extra) { int* others = malloc(sizeof(int) * rows); int count = 0; for (int i = 0; i < rows; i++) { if (matrix[i][col + extra] != 0) { others[count] = i; count++; } } return others; } void union_sets(int* set1, int* set2) { for (int i = 0; i < *set2; i++) { set1[*set1 + i] = set2[i]; } *set1 += *set2; } void subtract_rows(int** matrix, int row1, int row2, int factor) { for (int i = 0; i < cols; i++) { matrix[row1][i] -= matrix[row2][i] * factor; matrix[row1][i] %= PH; } } #include<stdio.h> #include<stdlib.h> int main() { int arr0[] = {1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr1[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr2[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr3[] = {0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20}; int arr4[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr5[] = {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr6[] = {0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0}; int arr7[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -30}; int arr8[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr9[] = {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -20}; int arr10[] = {1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}; int arr11[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr12[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr13[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14}; int arr14[] = {0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr15[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -30}; int arr16[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr17[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr18[] = {0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr19[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr20[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr21[] = {0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr22[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -20}; int arr23[] = {0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10}; int arr24[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr25[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr26[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr27[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr28[] = {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr29[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr30[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int arr31[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr32[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -10}; int arr33[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13}; int arr34[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11}; int arr35[] = {0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9}; int arr36[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20}; int arr37[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -40}; int arr38[] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; int* arr[] = {arr0, arr1, arr2, arr3, arr4, arr5, arr6, arr7, arr8, arr9, arr10, arr11, arr12, arr13, arr14, arr15, arr16, arr17, arr18, arr19, arr20, arr21, arr22, arr23, arr24, arr25, arr26, arr27, arr28, arr29, arr30, arr31, arr32, arr33, arr34, arr35, arr36, arr37, arr38}; int** got = rref(arr, 39, 49, 37); int answer = got[3][0]+got[3][1]+got[3][2]+got[3][3]+got[3][4]+got[3][5]+got[3][6]; int expected = 146; if (answer != expected) { printf("Wrong answer; got %d instead of %d.\n", answer, expected); exit(1); } printf("All tests passed\n"); } |
main.c: In function 'rref':
main.c:27:17: warning: implicit declaration of function 'all_zero' [-Wimplicit-function-declaration]
27 | if (all_zero(matrix, col)) {
| ^~~~~~~~
main.c:31:25: warning: implicit declaration of function 'find_nonzero' [-Wimplicit-function-declaration]
31 | int other = find_nonzero(matrix, col, extra);
| ^~~~~~~~~~~~
main.c:37:13: warning: implicit declaration of function 'swap_rows' [-Wimplicit-function-declaration]
37 | swap_rows(matrix, col, other);
| ^~~~~~~~~
main.c:38:13: warning: implicit declaration of function 'swap_sets' [-Wimplicit-function-declaration]
38 | swap_sets(used_for_row, col, other);
| ^~~~~~~~~
main.c:49:9: warning: implicit declaration of function 'scale_row' [-Wimplicit-function-declaration]
49 | scale_row(matrix, col, pivot);
| ^~~~~~~~~
main.c:51:23: warning: implicit declaration of function 'find_nonzero_cols' [-Wimplicit-function-declaration]
51 | int* others = find_nonzero_cols(matrix, col, extra);
| ^~~~~~~~~~~~~~~~~
main.c:51:23: warning: initialization of 'int *' from 'int' makes pointer from integer without a cast [-Wint-conversion]
main.c:55:13: warning: implicit declaration of function 'union_sets' [-Wimplicit-function-declaration]
55 | union_sets(used_for_row[i], used_for_row[col]);
| ^~~~~~~~~~
main.c:57:17: warning: implicit declaration of function 'subtract_rows' [-Wimplicit-function-declaration]
57 | subtract_rows(matrix, i, col, matrix[i][col + extra]);
| ^~~~~~~~~~~~~
main.c: In function 'all_zero':
main.c:79:25: error: 'rows' undeclared (first use in this function)
79 | for (int i = 0; i < rows; i++) {
| ^~~~
main.c:79:25: note: each undeclared identifier is reported only once for each function it appears in
main.c: In function 'find_nonzero':
main.c:88:31: error: 'rows' undeclared (first use in this function)
88 | for (int i = col + 1; i < rows; i++) {
| ^~~~
main.c: At top level:
main.c:96:6: warning: conflicting types for 'swap_rows'; have 'void(int **, int, int)'
96 | void swap_rows(int** matrix, int row1, int row2) {
| ^~~~~~~~~
main.c:37:13: note: previous implicit declaration of 'swap_rows' with type 'void(int **, int, int)'
37 | swap_rows(matrix, col, other);
| ^~~~~~~~~
main.c:102:6: warning: conflicting types for 'swap_sets'; have 'void(int **, int, int)'
102 | void swap_sets(int** sets, int set1, int set2) {
| ^~~~~~~~~
main.c:38:13: note: previous implicit declaration of 'swap_sets' with type 'void(int **, int, int)'
38 | swap_sets(used_for_row, col, other);
| ^~~~~~~~~
main.c:108:6: warning: conflicting types for 'scale_row'; have 'void(int **, int, int)'
108 | void scale_row(int** matrix, int row, int factor) {
| ^~~~~~~~~
main.c:49:9: note: previous implicit declaration of 'scale_row' with type 'void(int **, int, int)'
49 | scale_row(matrix, col, pivot);
| ^~~~~~~~~
main.c: In function 'scale_row':
main.c:109:25: error: 'cols' undeclared (first use in this function)
109 | for (int i = 0; i < cols; i++) {
| ^~~~
main.c:111:27: error: 'PH' undeclared (first use in this function)
111 | matrix[row][i] %= PH;
| ^~
main.c: At top level:
main.c:115:6: error: conflicting types for 'find_nonzero_cols'; have 'int *(int **, int, int)'
115 | int* find_nonzero_cols(int** matrix, int col, int extra) {
| ^~~~~~~~~~~~~~~~~
main.c:51:23: note: previous implicit declaration of 'find_nonzero_cols' with type 'int()'
51 | int* others = find_nonzero_cols(matrix, col, extra);
| ^~~~~~~~~~~~~~~~~
main.c: In function 'find_nonzero_cols':
main.c:116:40: error: 'rows' undeclared (first use in this function)
116 | int* others = malloc(sizeof(int) * rows);
| ^~~~
main.c: At top level:
main.c:127:6: warning: conflicting types for 'union_sets'; have 'void(int *, int *)'
127 | void union_sets(int* set1, int* set2) {
| ^~~~~~~~~~
main.c:55:13: note: previous implicit declaration of 'union_sets' with type 'void(int *, int *)'
55 | union_sets(used_for_row[i], used_for_row[col]);
| ^~~~~~~~~~
main.c:134:6: warning: conflicting types for 'subtract_rows'; have 'void(int **, int, int, int)'
134 | void subtract_rows(int** matrix, int row1, int row2, int factor) {
| ^~~~~~~~~~~~~
main.c:57:17: note: previous implicit declaration of 'subtract_rows' with type 'void(int **, int, int, int)'
57 | subtract_rows(matrix, i, col, matrix[i][col + extra]);
| ^~~~~~~~~~~~~
main.c: In function 'subtract_rows':
main.c:135:25: error: 'cols' undeclared (first use in this function)
135 | for (int i = 0; i < cols; i++) {
| ^~~~
main.c:137:28: error: 'PH' undeclared (first use in this function)
137 | matrix[row1][i] %= PH;
| ^~
main.sh: line 2: ./a.out: No such file or directory
Testing if the previous output contains the string All tests passed
: False