Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

Output

Plan for the program: 1. Define a function is_unholy that takes an unsigned long representing an 8x8 matrix and returns 1 if the matrix is unholy and 0 otherwise. 2. Use bit arithmetic to check for isolated 1s in the matrix. 3. Write a dynamic programming function count_unholy_matrices that takes the number of rows left to process and the previous two rows as input. 4. Recurse on the number of rows left, generating all possible combinations of the next two rows and counting the number of unholy matrices. 5. Initialize the count with the base cases of 1 row and 2 rows. 6. Output the total count of unholy matrices. Implementation in C: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix >> (i * 8 + j)) & 1) {
                // Check for isolated 1s
                if ((i == 0 || ((matrix >> ((i - 1) * 8 + j)) & 1) == 0) &&
                    (i == 7 || ((matrix >> ((i + 1) * 8 + j)) & 1) == 0) &&
                    (j == 0 || ((matrix >> (i * 8 + j - 1)) & 1) == 0) &&
                    (j == 7 || ((matrix >> (i * 8 + j + 1)) & 1) == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

unsigned long count_unholy_matrices(int rows_left, unsigned long row1, unsigned long row2) {
    if (rows_left == 0) {
        return 1;
    }

    unsigned long count = 0;

    for (unsigned long next_rows = 0; next_rows < (1 << 16); next_rows++) {
        if (is_unholy(next_rows << 16 | row2)) {
            count += count_unholy_matrices(rows_left - 1, row2, next_rows);
        }
    }

    return count;
}

int main() {
    unsigned long count = count_unholy_matrices(6, 0, 0);
    printf("Total number of unholy 8x8 matrices: %lu\n", count);

    return 0;
}
This C program implements the plan described above to count the total number of unholy 8x8 matrices using bit arithmetic and dynamic programming.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix >> (i * 8 + j)) & 1) {
                // Check for isolated 1s
                if ((i == 0 || ((matrix >> ((i - 1) * 8 + j)) & 1) == 0) &&
                    (i == 7 || ((matrix >> ((i + 1) * 8 + j)) & 1) == 0) &&
                    (j == 0 || ((matrix >> (i * 8 + j - 1)) & 1) == 0) &&
                    (j == 7 || ((matrix >> (i * 8 + j + 1)) & 1) == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

unsigned long count_unholy_matrices(int rows_left, unsigned long row1, unsigned long row2) {
    if (rows_left == 0) {
        return 1;
    }

    unsigned long count = 0;

    for (unsigned long next_rows = 0; next_rows < (1 << 16); next_rows++) {
        if (is_unholy(next_rows << 16 | row2)) {
            count += count_unholy_matrices(rows_left - 1, row2, next_rows);
        }
    }

    return count;
}

int main() {
    unsigned long count = count_unholy_matrices(6, 0, 0);
    printf("Total number of unholy 8x8 matrices: %lu\n", count);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix >> (i * 8 + j)) & 1) {
                // Check for isolated 1s
                if ((i == 0 || ((matrix >> ((i - 1) * 8 + j)) & 1) == 0) &&
                    (i == 7 || ((matrix >> ((i + 1) * 8 + j)) & 1) == 0) &&
                    (j == 0 || ((matrix >> (i * 8 + j - 1)) & 1) == 0) &&
                    (j == 7 || ((matrix >> (i * 8 + j + 1)) & 1) == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

unsigned long count_unholy_matrices(int rows_left, unsigned long row1, unsigned long row2) {
    if (rows_left == 0) {
        return 1;
    }

    unsigned long count = 0;

    for (unsigned long next_rows = 0; next_rows < (1 << 16); next_rows++) {
        if (is_unholy(next_rows << 16 | row2)) {
            count += count_unholy_matrices(rows_left - 1, row2, next_rows);
        }
    }

    return count;
}

int main() {
    unsigned long count = count_unholy_matrices(6, 0, 0);
    printf("Total number of unholy 8x8 matrices: %lu\n", count);

    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

Output

Plan: 1. Define a function is_unholy that takes in an unsigned long representing an 8x8 matrix and returns 1 if the matrix is unholy, 0 otherwise. 2. Implement the is_unholy function by iterating through each cell of the matrix and checking if it is isolated. 3. Define a recursive function count_unholy that takes in the current row and the current matrix state as parameters and returns the total number of unholy matrices. 4. In the count_unholy function, iterate through all possible combinations of the next two rows and recursively call count_unholy with the updated matrix state. 5. Initialize the count_unholy function with the first row and an empty matrix state to start the recursion. 6. Print out the total number of unholy matrices found. 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if (i % 8 > 0 && (matrix >> (i-1)) & 1) {
                return 0;
            }
            if (i % 8 < 7 && (matrix >> (i+1)) & 1) {
                return 0;
            }
            if (i >= 8 && (matrix >> (i-8)) & 1) {
                return 0;
            }
            if (i < 56 && (matrix >> (i+8)) & 1) {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy(int row, unsigned long matrix) {
    if (row == 8) {
        return is_unholy(matrix);
    }
    
    int totalCount = 0;
    for (int i = 0; i < 256; i++) {
        unsigned long nextRow = i << (row * 8);
        totalCount += count_unholy(row+1, matrix | nextRow);
    }
    
    return totalCount;
}

int main() {
    int totalUnholy = count_unholy(0, 0);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholy);

    return 0;
}

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if (i % 8 > 0 && (matrix >> (i-1)) & 1) {
                return 0;
            }
            if (i % 8 < 7 && (matrix >> (i+1)) & 1) {
                return 0;
            }
            if (i >= 8 && (matrix >> (i-8)) & 1) {
                return 0;
            }
            if (i < 56 && (matrix >> (i+8)) & 1) {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy(int row, unsigned long matrix) {
    if (row == 8) {
        return is_unholy(matrix);
    }
    
    int totalCount = 0;
    for (int i = 0; i < 256; i++) {
        unsigned long nextRow = i << (row * 8);
        totalCount += count_unholy(row+1, matrix | nextRow);
    }
    
    return totalCount;
}

int main() {
    int totalUnholy = count_unholy(0, 0);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholy);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if (i % 8 > 0 && (matrix >> (i-1)) & 1) {
                return 0;
            }
            if (i % 8 < 7 && (matrix >> (i+1)) & 1) {
                return 0;
            }
            if (i >= 8 && (matrix >> (i-8)) & 1) {
                return 0;
            }
            if (i < 56 && (matrix >> (i+8)) & 1) {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy(int row, unsigned long matrix) {
    if (row == 8) {
        return is_unholy(matrix);
    }
    
    int totalCount = 0;
    for (int i = 0; i < 256; i++) {
        unsigned long nextRow = i << (row * 8);
        totalCount += count_unholy(row+1, matrix | nextRow);
    }
    
    return totalCount;
}

int main() {
    int totalUnholy = count_unholy(0, 0);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholy);

    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

Output

Plan: 1. Define a function is_unholy that takes an unsigned long representing an 8x8 matrix and returns 1 if the matrix is unholy and 0 otherwise. 2. Implement the is_unholy function by iterating through each cell in the matrix and checking if it is isolated. 3. Define a recursive function count_unholy_matrices that takes the current row, current mask, and current count of unholy matrices as parameters. 4. In the count_unholy_matrices function, iterate through all possible next two rows (2^16 combinations) and recursively call the function with updated parameters. 5. In the main function, initialize the count of unholy matrices to 0 and call the count_unholy_matrices function with initial parameters. 6. Print out the total number of unholy matrices. 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix & (1UL << (i*8 + j))) {
                if (i > 0 && (matrix & (1UL << ((i-1)*8 + j))))
                    return 0;
                if (i < 7 && (matrix & (1UL << ((i+1)*8 + j))))
                    return 0;
                if (j > 0 && (matrix & (1UL << (i*8 + j-1))))
                    return 0;
                if (j < 7 && (matrix & (1UL << (i*8 + j+1))))
                    return 0;
            }
        }
    }
    return 1;
}

void count_unholy_matrices(int row, unsigned long mask, int count) {
    if (row == 8) {
        if (mask == 0xFFFF) // All rows are filled
            count++;
        return;
    }
    
    for (int i = 0; i < 0xFFFF; i++) { // Iterate through all possible next two rows
        if ((i & mask) == 0) {
            count_unholy_matrices(row+1, i, count);
        }
    }
}

int main() {
    int count = 0;
    count_unholy_matrices(0, 0, count);
    printf("Total number of unholy matrices: %d\n", count);
    
    return 0;
}

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix & (1UL << (i*8 + j))) {
                if (i > 0 && (matrix & (1UL << ((i-1)*8 + j))))
                    return 0;
                if (i < 7 && (matrix & (1UL << ((i+1)*8 + j))))
                    return 0;
                if (j > 0 && (matrix & (1UL << (i*8 + j-1))))
                    return 0;
                if (j < 7 && (matrix & (1UL << (i*8 + j+1))))
                    return 0;
            }
        }
    }
    return 1;
}

void count_unholy_matrices(int row, unsigned long mask, int count) {
    if (row == 8) {
        if (mask == 0xFFFF) // All rows are filled
            count++;
        return;
    }
    
    for (int i = 0; i < 0xFFFF; i++) { // Iterate through all possible next two rows
        if ((i & mask) == 0) {
            count_unholy_matrices(row+1, i, count);
        }
    }
}

int main() {
    int count = 0;
    count_unholy_matrices(0, 0, count);
    printf("Total number of unholy matrices: %d\n", count);
    
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix & (1UL << (i*8 + j))) {
                if (i > 0 && (matrix & (1UL << ((i-1)*8 + j))))
                    return 0;
                if (i < 7 && (matrix & (1UL << ((i+1)*8 + j))))
                    return 0;
                if (j > 0 && (matrix & (1UL << (i*8 + j-1))))
                    return 0;
                if (j < 7 && (matrix & (1UL << (i*8 + j+1))))
                    return 0;
            }
        }
    }
    return 1;
}

void count_unholy_matrices(int row, unsigned long mask, int count) {
    if (row == 8) {
        if (mask == 0xFFFF) // All rows are filled
            count++;
        return;
    }
    
    for (int i = 0; i < 0xFFFF; i++) { // Iterate through all possible next two rows
        if ((i & mask) == 0) {
            count_unholy_matrices(row+1, i, count);
        }
    }
}

int main() {
    int count = 0;
    count_unholy_matrices(0, 0, count);
    printf("Total number of unholy matrices: %d\n", count);
    
    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

Output

Plan: 1. Define a function 'is_unholy' that takes an unsigned long representing a 8x8 matrix and returns 1 if the matrix is unholy, 0 otherwise. 2. Use bit-shifting and masking to check if there are isolated 1s in the matrix. 3. Define a function 'count_unholy_matrices' that recursively counts the number of unholy matrices by enumerating all possible next two rows for a given set of rows. 4. Use dynamic programming to store the results of subproblems to avoid redundant calculations. 5. Initialize a counter variable to keep track of the total number of unholy matrices and return the final count. Implementation in C: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix & (1UL << (i*8 + j))) == 0) {
                continue;
            }
            if ((i > 0 && (matrix & (1UL << ((i-1)*8 + j)))) ||
                (i < 7 && (matrix & (1UL << ((i+1)*8 + j))) || 
                (j > 0 && (matrix & (1UL << (i*8 + j-1))) ||
                (j < 7 && (matrix & (1UL << (i*8 + j+1))))) {
                return 0;
            }
        }
    }
    return 1;
}

int dp[8][256][256];

int count_unholy_matrices(int row, unsigned long prev_row, unsigned long curr_row) {
    if (row == 8) {
        return is_unholy(prev_row) && is_unholy(curr_row);
    }
    if (dp[row][prev_row][curr_row] != -1) {
        return dp[row][prev_row][curr_row];
    }
    
    int count = 0;
    for (int next_row = 0; next_row < (1 << 8); next_row++) {
        count += count_unholy_matrices(row+1, curr_row, next_row);
    }
    
    dp[row][prev_row][curr_row] = count;
    return count;
}

int main() {
    memset(dp, -1, sizeof(dp));
    
    int total_count = 0;
    for (int row1 = 0; row1 < (1 << 8); row1++) {
        for (int row2 = 0; row2 < (1 << 8); row2++) {
            total_count += count_unholy_matrices(2, row1, row2);
        }
    }
    
    printf("Total number of unholy matrices: %d\n", total_count);
    
    return 0;
}
This program defines the functions 'is_unholy' to check if a matrix is unholy and 'count_unholy_matrices' to count the total number of unholy matrices using dynamic programming. The main function initializes the dynamic programming array and calculates the total count of unholy matrices.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix & (1UL << (i*8 + j))) == 0) {
                continue;
            }
            if ((i > 0 && (matrix & (1UL << ((i-1)*8 + j)))) ||
                (i < 7 && (matrix & (1UL << ((i+1)*8 + j))) || 
                (j > 0 && (matrix & (1UL << (i*8 + j-1))) ||
                (j < 7 && (matrix & (1UL << (i*8 + j+1))))) {
                return 0;
            }
        }
    }
    return 1;
}

int dp[8][256][256];

int count_unholy_matrices(int row, unsigned long prev_row, unsigned long curr_row) {
    if (row == 8) {
        return is_unholy(prev_row) && is_unholy(curr_row);
    }
    if (dp[row][prev_row][curr_row] != -1) {
        return dp[row][prev_row][curr_row];
    }
    
    int count = 0;
    for (int next_row = 0; next_row < (1 << 8); next_row++) {
        count += count_unholy_matrices(row+1, curr_row, next_row);
    }
    
    dp[row][prev_row][curr_row] = count;
    return count;
}

int main() {
    memset(dp, -1, sizeof(dp));
    
    int total_count = 0;
    for (int row1 = 0; row1 < (1 << 8); row1++) {
        for (int row2 = 0; row2 < (1 << 8); row2++) {
            total_count += count_unholy_matrices(2, row1, row2);
        }
    }
    
    printf("Total number of unholy matrices: %d\n", total_count);
    
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if ((matrix & (1UL << (i*8 + j))) == 0) {
                continue;
            }
            if ((i > 0 && (matrix & (1UL << ((i-1)*8 + j)))) ||
                (i < 7 && (matrix & (1UL << ((i+1)*8 + j))) || 
                (j > 0 && (matrix & (1UL << (i*8 + j-1))) ||
                (j < 7 && (matrix & (1UL << (i*8 + j+1))))) {
                return 0;
            }
        }
    }
    return 1;
}

int dp[8][256][256];

int count_unholy_matrices(int row, unsigned long prev_row, unsigned long curr_row) {
    if (row == 8) {
        return is_unholy(prev_row) && is_unholy(curr_row);
    }
    if (dp[row][prev_row][curr_row] != -1) {
        return dp[row][prev_row][curr_row];
    }
    
    int count = 0;
    for (int next_row = 0; next_row < (1 << 8); next_row++) {
        count += count_unholy_matrices(row+1, curr_row, next_row);
    }
    
    dp[row][prev_row][curr_row] = count;
    return count;
}

int main() {
    memset(dp, -1, sizeof(dp));
    
    int total_count = 0;
    for (int row1 = 0; row1 < (1 << 8); row1++) {
        for (int row2 = 0; row2 < (1 << 8); row2++) {
            total_count += count_unholy_matrices(2, row1, row2);
        }
    }
    
    printf("Total number of unholy matrices: %d\n", total_count);
    
    return 0;
}
And got the output: main.c: In function 'is_unholy': main.c:13:60: error: expected ')' before '{' token 13 | (j < 7 && (matrix & (1UL << (i*8 + j+1))))) { | ^~ | ) main.c:11:17: note: to match this '(' 11 | (i < 7 && (matrix & (1UL << ((i+1)*8 + j))) || | ^ main.c:15:14: error: expected ')' before '}' token 15 | } | ^ | ) 16 | } | ~ main.c:10:16: note: to match this '(' 10 | if ((i > 0 && (matrix & (1UL << ((i-1)*8 + j)))) || | ^ main.c:16:9: error: expected expression before '}' token 16 | } | ^ main.c: In function 'main': main.c:41:5: warning: implicit declaration of function 'memset' [-Wimplicit-function-declaration] 41 | memset(dp, -1, sizeof(dp)); | ^~~~~~ main.c:3:1: note: include '<string.h>' or provide a declaration of 'memset' 2 | #include <stdio.h> +++ |+#include <string.h> 3 | main.c:41:5: warning: incompatible implicit declaration of built-in function 'memset' [-Wbuiltin-declaration-mismatch] 41 | memset(dp, -1, sizeof(dp)); | ^~~~~~ main.c:41:5: note: include '<string.h>' or provide a declaration of 'memset' main.sh: line 2: ./a.out: No such file or directory

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False

Initial Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

LLM Generation

Query

A binary 8x8 matrix is 'unholy' if there are no isolated 1s. A 1 is isolated if there isn't another 1 in any of the 4 direct cardinal directions. Write a C program that counts the total number of unholy 8x8 matricies.To solve this question: - Use bit arithmetic and an unsigned long to represent the matrix. - Write a function is_unholy that tests if a matrix is unholy by bit-shifting and masking. Use a dynamic program to count the number of unholy matricies. - Recurse on the number of rows the matrix has. - Enumerate all 2^16 next two rows. This is enough to completely isolate the prior solutions from the next. Write out a plan for the program, and then implement the plan in C.

Output

Plan: 1. Define a function is_unholy that takes an unsigned long representing the 8x8 matrix and checks if it is unholy. 2. Define a recursive function count_unholy_matrices that takes the current row and column as arguments and counts the number of unholy matrices. 3. In count_unholy_matrices, use dynamic programming to calculate the total count by considering all possible next two rows and recursively calling the function. 4. Initialize a counter variable to 0 and call count_unholy_matrices with initial row and column values. 5. Print the total count of unholy matrices. Implementation in C: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if ((i % 8 != 0 && (matrix >> (i - 1)) & 1) || // check left
                (i % 8 != 7 && (matrix >> (i + 1)) & 1) || // check right
                (i >= 8 && (matrix >> (i - 8)) & 1) || // check up
                (i < 56 && (matrix >> (i + 8)) & 1)) // check down
            {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy_matrices(unsigned long current, int row, int col) {
    if (row == 8) {
        return is_unholy(current);
    }

    int count = 0;
    for (unsigned long next = 0; next < (1 << 16); next++) {
        if (is_unholy(next)) {
            count += count_unholy_matrices(current | (next << (row * 8)), row + 1, 0);
        }
    }
    return count;
}

int main() {
    int total_count = count_unholy_matrices(0, 0, 0);
    printf("Total number of unholy matrices: %d\n", total_count);
    return 0;
}
This program defines the necessary functions to check if a matrix is unholy and count the total number of unholy matrices using dynamic programming. The main function initializes the count and prints the result.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if ((i % 8 != 0 && (matrix >> (i - 1)) & 1) || // check left
                (i % 8 != 7 && (matrix >> (i + 1)) & 1) || // check right
                (i >= 8 && (matrix >> (i - 8)) & 1) || // check up
                (i < 56 && (matrix >> (i + 8)) & 1)) // check down
            {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy_matrices(unsigned long current, int row, int col) {
    if (row == 8) {
        return is_unholy(current);
    }

    int count = 0;
    for (unsigned long next = 0; next < (1 << 16); next++) {
        if (is_unholy(next)) {
            count += count_unholy_matrices(current | (next << (row * 8)), row + 1, 0);
        }
    }
    return count;
}

int main() {
    int total_count = count_unholy_matrices(0, 0, 0);
    printf("Total number of unholy matrices: %d\n", total_count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>

int is_unholy(unsigned long matrix) {
    for (int i = 0; i < 64; i++) {
        if ((matrix >> i) & 1) {
            if ((i % 8 != 0 && (matrix >> (i - 1)) & 1) || // check left
                (i % 8 != 7 && (matrix >> (i + 1)) & 1) || // check right
                (i >= 8 && (matrix >> (i - 8)) & 1) || // check up
                (i < 56 && (matrix >> (i + 8)) & 1)) // check down
            {
                return 0;
            }
        }
    }
    return 1;
}

int count_unholy_matrices(unsigned long current, int row, int col) {
    if (row == 8) {
        return is_unholy(current);
    }

    int count = 0;
    for (unsigned long next = 0; next < (1 << 16); next++) {
        if (is_unholy(next)) {
            count += count_unholy_matrices(current | (next << (row * 8)), row + 1, 0);
        }
    }
    return count;
}

int main() {
    int total_count = count_unholy_matrices(0, 0, 0);
    printf("Total number of unholy matrices: %d\n", total_count);
    return 0;
}
And got the output: Timeout: function took too long to complete

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False