Initial Query

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]

LLM Generation

Query

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]

Output

Certainly! Below is the C implementation of the `rref` function based on your provided Python code. This function performs the Reduced Row Echelon Form (RREF) transformation on a given 2D matrix modulo `PH = 16`. It also tracks the rows used to form each pivot row and returns this information as an array of integer arrays. ### Explanation: 1. **Function Signature:** 

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   int** rref(int** matrix, int rows, int cols, int graphlen);
- `matrix`: A pointer to a 2D array representing the matrix. - `rows`: Number of rows in the matrix. - `cols`: Number of columns in the matrix. - `graphlen`: An integer used in pivot assertions. 2. **Used for Row Tracking:** - `used_for_row` is an array of integer arrays where each sub-array contains the indices of the original rows that contribute to the current pivot row. - Each sub-array is sorted and terminated with `-1` to indicate the end. 3. **Process Overview:** - The matrix is first reduced modulo `PH = 16`. - The algorithm iterates through each column, attempting to create pivots. - If a pivot is found, it normalizes the pivot row and eliminates the corresponding column elements in other rows. - It also updates the `used_for_row` to keep track of row dependencies. - Finally, the function returns the `used_for_row` array. 4. **Memory Management:** - Memory is dynamically allocated for the `used_for_row` arrays. - Each sub-array in `used_for_row` can hold up to `rows + 1` integers to accommodate all possible row indices plus the sentinel `-1`. Here is the complete C implementation: 
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#include <stdio.h>
#include <stdlib.h>
#include <string.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;

    // Allocate memory for used_for_row
    // Each row can have up to 'rows' elements plus a sentinel -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    if (used_for_row == NULL) {
        fprintf(stderr, "Memory allocation failed for used_for_row.\n");
        exit(EXIT_FAILURE);
    }
    for(int i = 0; i < rows; i++) {
        used_for_row[i] = (int*)malloc((rows + 1) * sizeof(int));
        if (used_for_row[i] == NULL) {
            fprintf(stderr, "Memory allocation failed for used_for_row[%d].\n", i);
            exit(EXIT_FAILURE);
        }
        used_for_row[i][0] = i;      // Initialize with the row itself
        used_for_row[i][1] = -1;     // Sentinel to mark end
    }

    // Apply modulo PH to all elements in the matrix
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                matrix[i][j] += PH;
            }
        }
    }

    // Main loop to perform RREF
    while((col + extra < cols - 1) && (col < rows)) {
        if(matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if(all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero element in the current column
            int other = -1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col + extra] != 0) {
                    other = i;
                }
            }
            if(other == -1) {
                extra += 1;
                continue;
            }

            if(other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            int* temp_row = matrix[col];
            matrix[col] = matrix[other];
            matrix[other] = temp_row;

            // Swap the used_for_row sets accordingly
            int* temp_set = used_for_row[col];
            used_for_row[col] = used_for_row[other];
            used_for_row[other] = temp_set;
        }

        // Identify the pivot
        int pivot = matrix[col][col + extra];
        if(col + extra < graphlen) {
            // Ensure pivot is 1 or PH-1
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        } else {
            // Ensure pivot is 2 or PH-2 and adjust
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Normalize the pivot row
        for(int j = 0; j < cols; j++) {
            matrix[col][j] = (matrix[col][j] * pivot) % PH;
            if(matrix[col][j] < 0) {
                matrix[col][j] += PH;
            }
        }

        // Eliminate the current column in all other rows
        for(int i = 0; i < rows; i++) {
            if(matrix[i][col + extra] == 0 || i == col) {
                continue;
            }

            // Merge used_for_row[i] and used_for_row[col]
            int* set_i = used_for_row[i];
            int* set_col = used_for_row[col];
            int new_set[rows];
            int idx1 = 0, idx2 = 0, idx = 0;

            while(set_i[idx1] != -1 && set_col[idx2] != -1) {
                if(set_i[idx1] < set_col[idx2]) {
                    new_set[idx++] = set_i[idx1++];
                }
                else if(set_i[idx1] > set_col[idx2]) {
                    new_set[idx++] = set_col[idx2++];
                }
                else {
                    new_set[idx++] = set_i[idx1++];
                    idx2++;
                }
            }
            while(set_i[idx1] != -1) {
                new_set[idx++] = set_i[idx1++];
            }
            while(set_col[idx2] != -1) {
                new_set[idx++] = set_col[idx2++];
            }
            new_set[idx] = -1; // Sentinel

            // Update used_for_row[i] with the merged set
            for(int k = 0; k <= idx; k++) {
                used_for_row[i][k] = new_set[k];
            }

            // Perform row elimination
            if(col < graphlen) {
                int factor = matrix[i][col + extra];
                for(int j = 0; j < cols; j++) {
                    matrix[i][j] -= matrix[col][j] * factor;
                    matrix[i][j] %= PH;
                    if(matrix[i][j] < 0) {
                        matrix[i][j] += PH;
                    }
                }
            } else {
                // Iterative elimination for non-graph columns
                while(matrix[i][col + extra] != 0) {
                    for(int j = 0; j < cols; j++) {
                        matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH;
                        if(matrix[i][j] < 0) {
                            matrix[i][j] += PH;
                        }
                    }
                }
            }
        }

        col += 1;
    }

    // Ensure all matrix elements are within 0 to PH-1
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                matrix[i][j] += PH;
            }
        }
    }

    return used_for_row;
}

// Example usage
int main() {
    int rows = 3;
    int cols = 4;
    int graphlen = 2;
    
    // Example matrix
    int** matrix = (int**)malloc(rows * sizeof(int*));
    for(int i = 0; i < rows; i++) {
        matrix[i] = (int*)malloc(cols * sizeof(int));
    }
    
    // Initialize the matrix with some values
    matrix[0][0] = 2; matrix[0][1] = 4; matrix[0][2] = 6; matrix[0][3] = 8;
    matrix[1][0] = 1; matrix[1][1] = 3; matrix[1][2] = 5; matrix[1][3] = 7;
    matrix[2][0] = 0; matrix[2][1] = 2; matrix[2][2] = 4; matrix[2][3] = 6;

    // Call the rref function
    int** result = rref(matrix, rows, cols, graphlen);

    // Print the used_for_row sets
    printf("Used for each row:\n");
    for(int i = 0; i < rows; i++) {
        printf("Row %d: ", i);
        int j = 0;
        while(result[i][j] != -1) {
            printf("%d ", result[i][j]);
            j++;
        }
        printf("\n");
    }

    // Free allocated memory
    for(int i = 0; i < rows; i++) {
        free(matrix[i]);
        free(result[i]);
    }
    free(matrix);
    free(result);
    
    return 0;
}
### Notes: - **Memory Allocation:** - The `used_for_row` array is dynamically allocated, and each sub-array is designed to hold up to `rows + 1` integers to include all possible row indices plus a sentinel `-1`. - Ensure that the input `matrix` is properly allocated and populated before calling the `rref` function. - **Error Handling:** - The function includes basic error handling for memory allocation failures using `fprintf` and `exit`. Depending on your application, you might want to handle these errors differently. - **Assertions:** - The `assert` statements ensure that the pivot elements meet the required conditions. If an assertion fails, the program will terminate, indicating a logical error in the matrix. - **Example Usage:** - The `main` function provides an example of how to use the `rref` function. It initializes a sample matrix, calls the function, and prints the resulting `used_for_row` sets. - Make sure to replace the example matrix with your actual data as needed. - **Memory Cleanup:** - It's crucial to free all dynamically allocated memory to avoid memory leaks. The example `main` function demonstrates how to free the memory allocated for both the matrix and the `used_for_row` arrays. This implementation closely follows the logic of your Python function and should work efficiently for correctly formatted input matrices.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>
#include <stdlib.h>
#include <string.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;

    // Allocate memory for used_for_row
    // Each row can have up to 'rows' elements plus a sentinel -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    if (used_for_row == NULL) {
        fprintf(stderr, "Memory allocation failed for used_for_row.\n");
        exit(EXIT_FAILURE);
    }
    for(int i = 0; i < rows; i++) {
        used_for_row[i] = (int*)malloc((rows + 1) * sizeof(int));
        if (used_for_row[i] == NULL) {
            fprintf(stderr, "Memory allocation failed for used_for_row[%d].\n", i);
            exit(EXIT_FAILURE);
        }
        used_for_row[i][0] = i;      // Initialize with the row itself
        used_for_row[i][1] = -1;     // Sentinel to mark end
    }

    // Apply modulo PH to all elements in the matrix
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                matrix[i][j] += PH;
            }
        }
    }

    // Main loop to perform RREF
    while((col + extra < cols - 1) && (col < rows)) {
        if(matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if(all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero element in the current column
            int other = -1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col + extra] != 0) {
                    other = i;
                }
            }
            if(other == -1) {
                extra += 1;
                continue;
            }

            if(other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            int* temp_row = matrix[col];
            matrix[col] = matrix[other];
            matrix[other] = temp_row;

            // Swap the used_for_row sets accordingly
            int* temp_set = used_for_row[col];
            used_for_row[col] = used_for_row[other];
            used_for_row[other] = temp_set;
        }

        // Identify the pivot
        int pivot = matrix[col][col + extra];
        if(col + extra < graphlen) {
            // Ensure pivot is 1 or PH-1
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        } else {
            // Ensure pivot is 2 or PH-2 and adjust
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Normalize the pivot row
        for(int j = 0; j < cols; j++) {
            matrix[col][j] = (matrix[col][j] * pivot) % PH;
            if(matrix[col][j] < 0) {
                matrix[col][j] += PH;
            }
        }

        // Eliminate the current column in all other rows
        for(int i = 0; i < rows; i++) {
            if(matrix[i][col + extra] == 0 || i == col) {
                continue;
            }

            // Merge used_for_row[i] and used_for_row[col]
            int* set_i = used_for_row[i];
            int* set_col = used_for_row[col];
            int new_set[rows];
            int idx1 = 0, idx2 = 0, idx = 0;

            while(set_i[idx1] != -1 && set_col[idx2] != -1) {
                if(set_i[idx1] < set_col[idx2]) {
                    new_set[idx++] = set_i[idx1++];
                }
                else if(set_i[idx1] > set_col[idx2]) {
                    new_set[idx++] = set_col[idx2++];
                }
                else {
                    new_set[idx++] = set_i[idx1++];
                    idx2++;
                }
            }
            while(set_i[idx1] != -1) {
                new_set[idx++] = set_i[idx1++];
            }
            while(set_col[idx2] != -1) {
                new_set[idx++] = set_col[idx2++];
            }
            new_set[idx] = -1; // Sentinel

            // Update used_for_row[i] with the merged set
            for(int k = 0; k <= idx; k++) {
                used_for_row[i][k] = new_set[k];
            }

            // Perform row elimination
            if(col < graphlen) {
                int factor = matrix[i][col + extra];
                for(int j = 0; j < cols; j++) {
                    matrix[i][j] -= matrix[col][j] * factor;
                    matrix[i][j] %= PH;
                    if(matrix[i][j] < 0) {
                        matrix[i][j] += PH;
                    }
                }
            } else {
                // Iterative elimination for non-graph columns
                while(matrix[i][col + extra] != 0) {
                    for(int j = 0; j < cols; j++) {
                        matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH;
                        if(matrix[i][j] < 0) {
                            matrix[i][j] += PH;
                        }
                    }
                }
            }
        }

        col += 1;
    }

    // Ensure all matrix elements are within 0 to PH-1
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                matrix[i][j] += PH;
            }
        }
    }

    return used_for_row;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>
#include <stdlib.h>
#include <string.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;

    // Allocate memory for used_for_row
    // Each row can have up to 'rows' elements plus a sentinel -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    if (used_for_row == NULL) {
        fprintf(stderr, "Memory allocation failed for used_for_row.\n");
        exit(EXIT_FAILURE);
    }
    for(int i = 0; i < rows; i++) {
        used_for_row[i] = (int*)malloc((rows + 1) * sizeof(int));
        if (used_for_row[i] == NULL) {
            fprintf(stderr, "Memory allocation failed for used_for_row[%d].\n", i);
            exit(EXIT_FAILURE);
        }
        used_for_row[i][0] = i;      // Initialize with the row itself
        used_for_row[i][1] = -1;     // Sentinel to mark end
    }

    // Apply modulo PH to all elements in the matrix
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                matrix[i][j] += PH;
            }
        }
    }

    // Main loop to perform RREF
    while((col + extra < cols - 1) && (col < rows)) {
        if(matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if(all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero element in the current column
            int other = -1;
            for(int i = 0; i < rows; i++) {
                if(matrix[i][col + extra] != 0) {
                    other = i;
                }
            }
            if(other == -1) {
                extra += 1;
                continue;
            }

            if(other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            int* temp_row = matrix[col];
            matrix[col] = matrix[other];
            matrix[other] = temp_row;

            // Swap the used_for_row sets accordingly
            int* temp_set = used_for_row[col];
            used_for_row[col] = used_for_row[other];
            used_for_row[other] = temp_set;
        }

        // Identify the pivot
        int pivot = matrix[col][col + extra];
        if(col + extra < graphlen) {
            // Ensure pivot is 1 or PH-1
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        } else {
            // Ensure pivot is 2 or PH-2 and adjust
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Normalize the pivot row
        for(int j = 0; j < cols; j++) {
            matrix[col][j] = (matrix[col][j] * pivot) % PH;
            if(matrix[col][j] < 0) {
                matrix[col][j] += PH;
            }
        }

        // Eliminate the current column in all other rows
        for(int i = 0; i < rows; i++) {
            if(matrix[i][col + extra] == 0 || i == col) {
                continue;
            }

            // Merge used_for_row[i] and used_for_row[col]
            int* set_i = used_for_row[i];
            int* set_col = used_for_row[col];
            int new_set[rows];
            int idx1 = 0, idx2 = 0, idx = 0;

            while(set_i[idx1] != -1 && set_col[idx2] != -1) {
                if(set_i[idx1] < set_col[idx2]) {
                    new_set[idx++] = set_i[idx1++];
                }
                else if(set_i[idx1] > set_col[idx2]) {
                    new_set[idx++] = set_col[idx2++];
                }
                else {
                    new_set[idx++] = set_i[idx1++];
                    idx2++;
                }
            }
            while(set_i[idx1] != -1) {
                new_set[idx++] = set_i[idx1++];
            }
            while(set_col[idx2] != -1) {
                new_set[idx++] = set_col[idx2++];
            }
            new_set[idx] = -1; // Sentinel

            // Update used_for_row[i] with the merged set
            for(int k = 0; k <= idx; k++) {
                used_for_row[i][k] = new_set[k];
            }

            // Perform row elimination
            if(col < graphlen) {
                int factor = matrix[i][col + extra];
                for(int j = 0; j < cols; j++) {
                    matrix[i][j] -= matrix[col][j] * factor;
                    matrix[i][j] %= PH;
                    if(matrix[i][j] < 0) {
                        matrix[i][j] += PH;
                    }
                }
            } else {
                // Iterative elimination for non-graph columns
                while(matrix[i][col + extra] != 0) {
                    for(int j = 0; j < cols; j++) {
                        matrix[i][j] = (matrix[i][j] - matrix[col][j]) % PH;
                        if(matrix[i][j] < 0) {
                            matrix[i][j] += PH;
                        }
                    }
                }
            }
        }

        col += 1;
    }

    // Ensure all matrix elements are within 0 to PH-1
    for(int i = 0; i < rows; i++) {
        for(int j = 0; j < cols; j++) {
            matrix[i][j] %= PH;
            if(matrix[i][j] < 0) {
                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");
}
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True

Initial Query

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]

LLM Generation

Query

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]

Output

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>

#define PH 16

// Helper function to swap two rows in the matrix
void swap_rows(int** matrix, int row1, int row2, int cols) {
    int* temp = matrix[row1];
    matrix[row1] = matrix[row2];
    matrix[row2] = temp;
    // Swap elements in all columns if necessary
    // Not needed here as we are swapping row pointers
}

// Helper function to swap two used_for_row sets
void swap_used_for_row(int** used_for_row, int row1, int row2) {
    int* temp = used_for_row[row1];
    used_for_row[row1] = used_for_row[row2];
    used_for_row[row2] = temp;
}

// Helper function to merge two sorted sets without duplicates
void union_rows(int* set1, int* set2, int rows) {
    int temp_size = 0;
    int temp[rows + 1]; // Temporary array to hold merged set
    int i = 0, j = 0;

    // Merge set1 and set2 into temp
    while (set1[i] != -1 && set2[j] != -1) {
        if (set1[i] < set2[j]) {
            temp[temp_size++] = set1[i++];
        }
        else if (set1[i] > set2[j]) {
            temp[temp_size++] = set2[j++];
        }
        else {
            temp[temp_size++] = set1[i];
            i++;
            j++;
        }
    }

    while (set1[i] != -1) {
        temp[temp_size++] = set1[i++];
    }

    while (set2[j] != -1) {
        temp[temp_size++] = set2[j++];
    }

    temp[temp_size++] = -1; // Terminate the merged set

    // Copy the merged set back to set1
    for (int k = 0; k < temp_size; k++) {
        set1[k] = temp[k];
    }
    // Fill the rest with -1 if needed
    for (int k = temp_size; k <= rows; k++) {
        set1[k] = -1;
    }
}

// Function to perform row reduction to row-echelon form (RREF)
int** rref(int** matrix, int rows, int cols, int graphlen) {
    // Initialize used_for_row as an array of sorted sets
    // Each set is represented as an array terminated with -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    for (int r = 0; r < rows; r++) {
        used_for_row[r] = (int*)malloc((rows + 1) * sizeof(int));
        used_for_row[r][0] = r;
        used_for_row[r][1] = -1;
    }

    // Apply matrix modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    int extra = 0;
    int col = 0;

    while ((col + extra < cols - 1) && (col < rows)) {
        if (matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for (int r = 0; r < rows; r++) {
                if (matrix[r][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if (all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero entry in the current pivot column
            int other = -1;
            for (int r = rows - 1; r >= 0; r--) {
                if (matrix[r][col + extra] != 0) {
                    other = r;
                    break;
                }
            }

            if (other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            swap_rows(matrix, col, other, cols);
            swap_used_for_row(used_for_row, col, other);
        }

        // Record the pivot column (optional, not used further here)
        // pivots.append(col + extra);

        int pivot = matrix[col][col + extra];

        // Assertions based on the pivot position
        if (col + extra < graphlen) {
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        }
        else {
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Multiply the pivot row by the pivot value and take modulo PH
        for (int c = 0; c < cols; c++) {
            matrix[col][c] = (matrix[col][c] * pivot) % PH;
            if (matrix[col][c] < 0) matrix[col][c] += PH; // Ensure non-negative
        }

        // Find all rows that have a non-zero entry in the pivot column
        int others_count = 0;
        int* others = (int*)malloc(rows * sizeof(int));
        for (int r = 0; r < rows; r++) {
            if (matrix[r][col + extra] != 0) {
                others[others_count++] = r;
            }
        }

        // Perform row operations on the other rows
        for (int i = 0; i < others_count; i++) {
            int r = others[i];
            if (r == col) continue;

            // Union the used_for_row sets
            union_rows(used_for_row[r], used_for_row[col], rows);

            if (col < graphlen) {
                // matrix[r] -= matrix[col] * matrix[r][col + extra]
                int factor = matrix[r][col + extra];
                for (int c = 0; c < cols; c++) {
                    matrix[r][c] = (matrix[r][c] - (matrix[col][c] * factor)) % PH;
                    if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                }
            }
            else {
                // While matrix[r][col + extra] != 0, perform row subtraction
                while (matrix[r][col + extra] != 0) {
                    for (int c = 0; c < cols; c++) {
                        matrix[r][c] = (matrix[r][c] - matrix[col][c]) % PH;
                        if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                    }
                }
            }
        }

        free(others);
        col += 1;
    }

    // Ensure all matrix elements are modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    // Sort each used_for_row set (already sorted through union_rows)
    // If additional sorting is needed, implement it here using qsort

    return used_for_row;
}

// Example usage:
// int main() {
//     // Example matrix setup
//     int rows = 3, cols = 4, graphlen = 2;
//     int** matrix = (int**)malloc(rows * sizeof(int*));
//     for(int i = 0; i < rows; i++) {
//         matrix[i] = (int*)malloc(cols * sizeof(int));
//         for(int j = 0; j < cols; j++) {
//             matrix[i][j] = /* initialize with your values */ 0;
//         }
//     }

//     // Initialize your matrix values here

//     // Perform RREF
//     int** used_for_row = rref(matrix, rows, cols, graphlen);

//     // Print used_for_row
//     for(int r = 0; r < rows; r++) {
//         printf("Row %d used for rows: ", r);
//         int c = 0;
//         while(used_for_row[r][c] != -1) {
//             printf("%d ", used_for_row[r][c]);
//             c++;
//         }
//         printf("\n");
//     }

//     // Free allocated memory
//     for(int i = 0; i < rows; i++) {
//         free(matrix[i]);
//         free(used_for_row[i]);
//     }
//     free(matrix);
//     free(used_for_row);

//     return 0;
// }

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>

#define PH 16

// Helper function to swap two rows in the matrix
void swap_rows(int** matrix, int row1, int row2, int cols) {
    int* temp = matrix[row1];
    matrix[row1] = matrix[row2];
    matrix[row2] = temp;
    // Swap elements in all columns if necessary
    // Not needed here as we are swapping row pointers
}

// Helper function to swap two used_for_row sets
void swap_used_for_row(int** used_for_row, int row1, int row2) {
    int* temp = used_for_row[row1];
    used_for_row[row1] = used_for_row[row2];
    used_for_row[row2] = temp;
}

// Helper function to merge two sorted sets without duplicates
void union_rows(int* set1, int* set2, int rows) {
    int temp_size = 0;
    int temp[rows + 1]; // Temporary array to hold merged set
    int i = 0, j = 0;

    // Merge set1 and set2 into temp
    while (set1[i] != -1 && set2[j] != -1) {
        if (set1[i] < set2[j]) {
            temp[temp_size++] = set1[i++];
        }
        else if (set1[i] > set2[j]) {
            temp[temp_size++] = set2[j++];
        }
        else {
            temp[temp_size++] = set1[i];
            i++;
            j++;
        }
    }

    while (set1[i] != -1) {
        temp[temp_size++] = set1[i++];
    }

    while (set2[j] != -1) {
        temp[temp_size++] = set2[j++];
    }

    temp[temp_size++] = -1; // Terminate the merged set

    // Copy the merged set back to set1
    for (int k = 0; k < temp_size; k++) {
        set1[k] = temp[k];
    }
    // Fill the rest with -1 if needed
    for (int k = temp_size; k <= rows; k++) {
        set1[k] = -1;
    }
}

// Function to perform row reduction to row-echelon form (RREF)
int** rref(int** matrix, int rows, int cols, int graphlen) {
    // Initialize used_for_row as an array of sorted sets
    // Each set is represented as an array terminated with -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    for (int r = 0; r < rows; r++) {
        used_for_row[r] = (int*)malloc((rows + 1) * sizeof(int));
        used_for_row[r][0] = r;
        used_for_row[r][1] = -1;
    }

    // Apply matrix modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    int extra = 0;
    int col = 0;

    while ((col + extra < cols - 1) && (col < rows)) {
        if (matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for (int r = 0; r < rows; r++) {
                if (matrix[r][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if (all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero entry in the current pivot column
            int other = -1;
            for (int r = rows - 1; r >= 0; r--) {
                if (matrix[r][col + extra] != 0) {
                    other = r;
                    break;
                }
            }

            if (other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            swap_rows(matrix, col, other, cols);
            swap_used_for_row(used_for_row, col, other);
        }

        // Record the pivot column (optional, not used further here)
        // pivots.append(col + extra);

        int pivot = matrix[col][col + extra];

        // Assertions based on the pivot position
        if (col + extra < graphlen) {
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        }
        else {
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Multiply the pivot row by the pivot value and take modulo PH
        for (int c = 0; c < cols; c++) {
            matrix[col][c] = (matrix[col][c] * pivot) % PH;
            if (matrix[col][c] < 0) matrix[col][c] += PH; // Ensure non-negative
        }

        // Find all rows that have a non-zero entry in the pivot column
        int others_count = 0;
        int* others = (int*)malloc(rows * sizeof(int));
        for (int r = 0; r < rows; r++) {
            if (matrix[r][col + extra] != 0) {
                others[others_count++] = r;
            }
        }

        // Perform row operations on the other rows
        for (int i = 0; i < others_count; i++) {
            int r = others[i];
            if (r == col) continue;

            // Union the used_for_row sets
            union_rows(used_for_row[r], used_for_row[col], rows);

            if (col < graphlen) {
                // matrix[r] -= matrix[col] * matrix[r][col + extra]
                int factor = matrix[r][col + extra];
                for (int c = 0; c < cols; c++) {
                    matrix[r][c] = (matrix[r][c] - (matrix[col][c] * factor)) % PH;
                    if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                }
            }
            else {
                // While matrix[r][col + extra] != 0, perform row subtraction
                while (matrix[r][col + extra] != 0) {
                    for (int c = 0; c < cols; c++) {
                        matrix[r][c] = (matrix[r][c] - matrix[col][c]) % PH;
                        if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                    }
                }
            }
        }

        free(others);
        col += 1;
    }

    // Ensure all matrix elements are modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    // Sort each used_for_row set (already sorted through union_rows)
    // If additional sorting is needed, implement it here using qsort

    return used_for_row;
}

// Example usage:
// int main() {
//     // Example matrix setup
//     int rows = 3, cols = 4, graphlen = 2;
//     int** matrix = (int**)malloc(rows * sizeof(int*));
//     for(int i = 0; i < rows; i++) {
//         matrix[i] = (int*)malloc(cols * sizeof(int));
//         for(int j = 0; j < cols; j++) {
//             matrix[i][j] = /* initialize with your values */ 0;
//         }
//     }

//     // Initialize your matrix values here

//     // Perform RREF
//     int** used_for_row = rref(matrix, rows, cols, graphlen);

//     // Print used_for_row
//     for(int r = 0; r < rows; r++) {
//         printf("Row %d used for rows: ", r);
//         int c = 0;
//         while(used_for_row[r][c] != -1) {
//             printf("%d ", used_for_row[r][c]);
//             c++;
//         }
//         printf("\n");
//     }

//     // Free allocated memory
//     for(int i = 0; i < rows; i++) {
//         free(matrix[i]);
//         free(used_for_row[i]);
//     }
//     free(matrix);
//     free(used_for_row);

//     return 0;
// }

Run Code Interpreter

Running the following program: 

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>

#define PH 16

// Helper function to swap two rows in the matrix
void swap_rows(int** matrix, int row1, int row2, int cols) {
    int* temp = matrix[row1];
    matrix[row1] = matrix[row2];
    matrix[row2] = temp;
    // Swap elements in all columns if necessary
    // Not needed here as we are swapping row pointers
}

// Helper function to swap two used_for_row sets
void swap_used_for_row(int** used_for_row, int row1, int row2) {
    int* temp = used_for_row[row1];
    used_for_row[row1] = used_for_row[row2];
    used_for_row[row2] = temp;
}

// Helper function to merge two sorted sets without duplicates
void union_rows(int* set1, int* set2, int rows) {
    int temp_size = 0;
    int temp[rows + 1]; // Temporary array to hold merged set
    int i = 0, j = 0;

    // Merge set1 and set2 into temp
    while (set1[i] != -1 && set2[j] != -1) {
        if (set1[i] < set2[j]) {
            temp[temp_size++] = set1[i++];
        }
        else if (set1[i] > set2[j]) {
            temp[temp_size++] = set2[j++];
        }
        else {
            temp[temp_size++] = set1[i];
            i++;
            j++;
        }
    }

    while (set1[i] != -1) {
        temp[temp_size++] = set1[i++];
    }

    while (set2[j] != -1) {
        temp[temp_size++] = set2[j++];
    }

    temp[temp_size++] = -1; // Terminate the merged set

    // Copy the merged set back to set1
    for (int k = 0; k < temp_size; k++) {
        set1[k] = temp[k];
    }
    // Fill the rest with -1 if needed
    for (int k = temp_size; k <= rows; k++) {
        set1[k] = -1;
    }
}

// Function to perform row reduction to row-echelon form (RREF)
int** rref(int** matrix, int rows, int cols, int graphlen) {
    // Initialize used_for_row as an array of sorted sets
    // Each set is represented as an array terminated with -1
    int** used_for_row = (int**)malloc(rows * sizeof(int*));
    for (int r = 0; r < rows; r++) {
        used_for_row[r] = (int*)malloc((rows + 1) * sizeof(int));
        used_for_row[r][0] = r;
        used_for_row[r][1] = -1;
    }

    // Apply matrix modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    int extra = 0;
    int col = 0;

    while ((col + extra < cols - 1) && (col < rows)) {
        if (matrix[col][col + extra] == 0) {
            // Check if all elements in the current column are zero
            int all_zero = 1;
            for (int r = 0; r < rows; r++) {
                if (matrix[r][col] != 0) {
                    all_zero = 0;
                    break;
                }
            }
            if (all_zero) {
                extra += 1;
                continue;
            }

            // Find the last row with a non-zero entry in the current pivot column
            int other = -1;
            for (int r = rows - 1; r >= 0; r--) {
                if (matrix[r][col + extra] != 0) {
                    other = r;
                    break;
                }
            }

            if (other < col) {
                extra += 1;
                continue;
            }

            // Swap the current row with the 'other' row
            swap_rows(matrix, col, other, cols);
            swap_used_for_row(used_for_row, col, other);
        }

        // Record the pivot column (optional, not used further here)
        // pivots.append(col + extra);

        int pivot = matrix[col][col + extra];

        // Assertions based on the pivot position
        if (col + extra < graphlen) {
            assert(abs(pivot) == 1 || abs(pivot) == PH - 1);
        }
        else {
            assert(abs(pivot) == 2 || abs(pivot) == PH - 2);
            pivot /= 2;
        }

        // Multiply the pivot row by the pivot value and take modulo PH
        for (int c = 0; c < cols; c++) {
            matrix[col][c] = (matrix[col][c] * pivot) % PH;
            if (matrix[col][c] < 0) matrix[col][c] += PH; // Ensure non-negative
        }

        // Find all rows that have a non-zero entry in the pivot column
        int others_count = 0;
        int* others = (int*)malloc(rows * sizeof(int));
        for (int r = 0; r < rows; r++) {
            if (matrix[r][col + extra] != 0) {
                others[others_count++] = r;
            }
        }

        // Perform row operations on the other rows
        for (int i = 0; i < others_count; i++) {
            int r = others[i];
            if (r == col) continue;

            // Union the used_for_row sets
            union_rows(used_for_row[r], used_for_row[col], rows);

            if (col < graphlen) {
                // matrix[r] -= matrix[col] * matrix[r][col + extra]
                int factor = matrix[r][col + extra];
                for (int c = 0; c < cols; c++) {
                    matrix[r][c] = (matrix[r][c] - (matrix[col][c] * factor)) % PH;
                    if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                }
            }
            else {
                // While matrix[r][col + extra] != 0, perform row subtraction
                while (matrix[r][col + extra] != 0) {
                    for (int c = 0; c < cols; c++) {
                        matrix[r][c] = (matrix[r][c] - matrix[col][c]) % PH;
                        if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
                    }
                }
            }
        }

        free(others);
        col += 1;
    }

    // Ensure all matrix elements are modulo PH
    for (int r = 0; r < rows; r++) {
        for (int c = 0; c < cols; c++) {
            matrix[r][c] %= PH;
            if (matrix[r][c] < 0) matrix[r][c] += PH; // Ensure non-negative
        }
    }

    // Sort each used_for_row set (already sorted through union_rows)
    // If additional sorting is needed, implement it here using qsort

    return used_for_row;
}

// Example usage:
// int __delete_this__main() {
//     // Example matrix setup
//     int rows = 3, cols = 4, graphlen = 2;
//     int** matrix = (int**)malloc(rows * sizeof(int*));
//     for(int i = 0; i < rows; i++) {
//         matrix[i] = (int*)malloc(cols * sizeof(int));
//         for(int j = 0; j < cols; j++) {
//             matrix[i][j] = /* initialize with your values */ 0;
//         }
//     }

//     // Initialize your matrix values here

//     // Perform RREF
//     int** used_for_row = rref(matrix, rows, cols, graphlen);

//     // Print used_for_row
//     for(int r = 0; r < rows; r++) {
//         printf("Row %d used for rows: ", r);
//         int c = 0;
//         while(used_for_row[r][c] != -1) {
//             printf("%d ", used_for_row[r][c]);
//             c++;
//         }
//         printf("\n");
//     }

//     // Free allocated memory
//     for(int i = 0; i < rows; i++) {
//         free(matrix[i]);
//         free(used_for_row[i]);
//     }
//     free(matrix);
//     free(used_for_row);

//     return 0;
// }



#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");
}
And got the output: All tests passed

Substring Evaluation

Testing if the previous output contains the string All tests passed: True