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.

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.

Output

Here's a C program that counts the total number of unholy 8x8 matrices: 

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

int isIsolated(int matrix[8][8], int row, int col) {
    // Check if the given position has a 1 in any of the 4 direct cardinal directions
    if (row > 0 && matrix[row - 1][col]) return 0;
    if (row < 7 && matrix[row + 1][col]) return 0;
    if (col > 0 && matrix[row][col - 1]) return 0;
    if (col < 7 && matrix[row][col + 1]) return 0;
    return 1;
}

int isUnholy(int matrix[8][8]) {
    int isolated = 1;
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] && !isIsolated(matrix, i, j)) {
                isolated = 0;
                break;
            }
        }
    }
    return isolated;
}

int countUnholyMatrices(int n) {
    int count = 0;
    int matrix[8][8];
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        int k = 0;
        for (int j = 0; j < 8; j++) {
            for (int l = 0; l < 8; l++) {
                matrix[j][l] = (i >> k) & 1;
                k++;
            }
        }
        if (isUnholy(matrix)) {
            count++;
        }
    }
    return count;
}

int main() {
    int totalUnholyMatrices = countUnholyMatrices(8);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholyMatrices);
    return 0;
}
Here's how the program works: 1. The `isIsolated` function checks if a given position (row, col) in the matrix has a 1 in any of the 4 direct cardinal directions. If there is a 1 in any of the adjacent positions, it returns 0 (not isolated). Otherwise, it returns 1 (isolated). 2. The `isUnholy` function checks if a given matrix is unholy. It iterates through all positions in the matrix and calls the `isIsolated` function for each position with a 1. If it finds a position with an isolated 1, it returns 0 (the matrix is holy). Otherwise, it returns 1 (the matrix is unholy). 3. The `countUnholyMatrices` function generates all possible 8x8 binary matrices and counts the number of unholy matrices. It uses a nested loop to generate all possible bit combinations (2^(8*8) combinations) and stores each combination in a matrix. Then, it calls the `isUnholy` function for each matrix and increments the count if the matrix is unholy. 4. In the `main` function, we call the `countUnholyMatrices` function with the size 8 and print the result. Note that this program has an exponential time complexity due to the generation of all possible matrices. For larger matrix sizes, the program may take an impractically long time to run.

Extract Code

I extracted the following code from that output: 

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

int isIsolated(int matrix[8][8], int row, int col) {
    // Check if the given position has a 1 in any of the 4 direct cardinal directions
    if (row > 0 && matrix[row - 1][col]) return 0;
    if (row < 7 && matrix[row + 1][col]) return 0;
    if (col > 0 && matrix[row][col - 1]) return 0;
    if (col < 7 && matrix[row][col + 1]) return 0;
    return 1;
}

int isUnholy(int matrix[8][8]) {
    int isolated = 1;
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] && !isIsolated(matrix, i, j)) {
                isolated = 0;
                break;
            }
        }
    }
    return isolated;
}

int countUnholyMatrices(int n) {
    int count = 0;
    int matrix[8][8];
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        int k = 0;
        for (int j = 0; j < 8; j++) {
            for (int l = 0; l < 8; l++) {
                matrix[j][l] = (i >> k) & 1;
                k++;
            }
        }
        if (isUnholy(matrix)) {
            count++;
        }
    }
    return count;
}

int main() {
    int totalUnholyMatrices = countUnholyMatrices(8);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholyMatrices);
    return 0;
}

Run Code Interpreter

Running the following program: 

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

int isIsolated(int matrix[8][8], int row, int col) {
    // Check if the given position has a 1 in any of the 4 direct cardinal directions
    if (row > 0 && matrix[row - 1][col]) return 0;
    if (row < 7 && matrix[row + 1][col]) return 0;
    if (col > 0 && matrix[row][col - 1]) return 0;
    if (col < 7 && matrix[row][col + 1]) return 0;
    return 1;
}

int isUnholy(int matrix[8][8]) {
    int isolated = 1;
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] && !isIsolated(matrix, i, j)) {
                isolated = 0;
                break;
            }
        }
    }
    return isolated;
}

int countUnholyMatrices(int n) {
    int count = 0;
    int matrix[8][8];
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        int k = 0;
        for (int j = 0; j < 8; j++) {
            for (int l = 0; l < 8; l++) {
                matrix[j][l] = (i >> k) & 1;
                k++;
            }
        }
        if (isUnholy(matrix)) {
            count++;
        }
    }
    return count;
}

int main() {
    int totalUnholyMatrices = countUnholyMatrices(8);
    printf("Total number of unholy 8x8 matrices: %d\n", totalUnholyMatrices);
    return 0;
}
And got the output: Total number of unholy 8x8 matrices: 0 main.c: In function 'countUnholyMatrices': main.c:30:28: warning: left shift count >= width of type [-Wshift-count-overflow] 30 | for (int i = 0; i < (1 << (8 * 8)); i++) { | ^~

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.

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.

Output

Here's a C program that counts the total number of unholy 8x8 matrices: 

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

// Function to check if a matrix is unholy
int isUnholy(int matrix[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                int isolated = 1;
                // Check top
                if (i > 0 && matrix[i - 1][j] == 1) {
                    isolated = 0;
                }
                // Check bottom
                if (i < 7 && matrix[i + 1][j] == 1) {
                    isolated = 0;
                }
                // Check left
                if (j > 0 && matrix[i][j - 1] == 1) {
                    isolated = 0;
                }
                // Check right
                if (j < 7 && matrix[i][j + 1] == 1) {
                    isolated = 0;
                }
                if (isolated == 0) {
                    return 1; // Matrix is unholy
                }
            }
        }
    }
    return 0; // Matrix is holy
}

int main() {
    int count = 0;
    int matrix[8][8];

    // Generate all possible 8x8 matrices
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        // Convert the integer to a matrix
        for (int j = 0; j < 8; j++) {
            for (int k = 0; k < 8; k++) {
                matrix[j][k] = (i >> (j * 8 + k)) & 1;
            }
        }

        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}
Here's how the program works: 1. The `isUnholy` function takes an 8x8 matrix as input and checks if there are any isolated 1s in the matrix. It iterates through each element of the matrix and checks if it's a 1. If it is, it checks the neighboring elements in the four cardinal directions (top, bottom, left, and right) to see if there are any other 1s. If there are no other 1s, it means the current 1 is isolated, and the function returns 0 (holy matrix). If there is at least one non-isolated 1, the function returns 1 (unholy matrix). 2. In the `main` function, we generate all possible 8x8 matrices using a loop that iterates from 0 to (1 << (8 * 8)) - 1. This loop generates all possible combinations of 0s and 1s in an 8x8 matrix. 3. For each generated matrix, we call the `isUnholy` function to check if it's unholy. If it is, we increment the `count` variable. 4. Finally, the program prints the total number of unholy 8x8 matrices. Note that this program has a time complexity of O(N * M^2), where N is the number of possible matrices (2^(8*8)) and M is the size of the matrix (8 in this case). This is because we need to check each element of the matrix for every possible matrix combination. For larger matrix sizes, the running time will increase exponentially.

Extract Code

I extracted the following code from that output: 

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

// Function to check if a matrix is unholy
int isUnholy(int matrix[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                int isolated = 1;
                // Check top
                if (i > 0 && matrix[i - 1][j] == 1) {
                    isolated = 0;
                }
                // Check bottom
                if (i < 7 && matrix[i + 1][j] == 1) {
                    isolated = 0;
                }
                // Check left
                if (j > 0 && matrix[i][j - 1] == 1) {
                    isolated = 0;
                }
                // Check right
                if (j < 7 && matrix[i][j + 1] == 1) {
                    isolated = 0;
                }
                if (isolated == 0) {
                    return 1; // Matrix is unholy
                }
            }
        }
    }
    return 0; // Matrix is holy
}

int main() {
    int count = 0;
    int matrix[8][8];

    // Generate all possible 8x8 matrices
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        // Convert the integer to a matrix
        for (int j = 0; j < 8; j++) {
            for (int k = 0; k < 8; k++) {
                matrix[j][k] = (i >> (j * 8 + k)) & 1;
            }
        }

        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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

// Function to check if a matrix is unholy
int isUnholy(int matrix[8][8]) {
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                int isolated = 1;
                // Check top
                if (i > 0 && matrix[i - 1][j] == 1) {
                    isolated = 0;
                }
                // Check bottom
                if (i < 7 && matrix[i + 1][j] == 1) {
                    isolated = 0;
                }
                // Check left
                if (j > 0 && matrix[i][j - 1] == 1) {
                    isolated = 0;
                }
                // Check right
                if (j < 7 && matrix[i][j + 1] == 1) {
                    isolated = 0;
                }
                if (isolated == 0) {
                    return 1; // Matrix is unholy
                }
            }
        }
    }
    return 0; // Matrix is holy
}

int main() {
    int count = 0;
    int matrix[8][8];

    // Generate all possible 8x8 matrices
    for (int i = 0; i < (1 << (8 * 8)); i++) {
        // Convert the integer to a matrix
        for (int j = 0; j < 8; j++) {
            for (int k = 0; k < 8; k++) {
                matrix[j][k] = (i >> (j * 8 + k)) & 1;
            }
        }

        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}
And got the output: Total number of unholy 8x8 matrices: 0 main.c: In function 'main': main.c:42:28: warning: left shift count >= width of type [-Wshift-count-overflow] 42 | for (int i = 0; i < (1 << (8 * 8)); i++) { | ^~

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.

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.

Output

Here's a C program that counts the total number of unholy 8x8 matrices: 

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#include <stdio.h>
#include <math.h>

int isUnholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                if (
                    (i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)
                ) {
                    // This is an isolated 1, so the matrix is not unholy
                    return 0;
                }
            }
        }
    }
    // No isolated 1s were found, so the matrix is unholy
    return 1;
}

int main() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    // Iterate through all possible 8x8 matrices
    for (k = 0; k < (int)pow(2, 64); k++) {
        // Convert the integer k to a binary matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        // Check if the current matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %d\n", count);

    return 0;
}
Here's how the program works: 1. The `isUnholy` function takes an 8x8 matrix as input and checks if it is unholy or not. It iterates through all elements of the matrix and checks if there are any isolated 1s. If an isolated 1 is found, the function returns 0 (not unholy). If no isolated 1s are found, the function returns 1 (unholy). 2. The `main` function initializes a counter variable `count` to keep track of the number of unholy matrices. 3. It then iterates through all possible 8x8 matrices using a nested loop. The outer loop iterates from 0 to 2^64 - 1, which covers all possible combinations of 64 bits (8x8 matrix elements). The inner loops convert the current integer value to a binary matrix. 4. For each matrix, the `isUnholy` function is called to check if it is unholy or not. If it is unholy, the `count` variable is incremented. 5. After iterating through all possible matrices, the total count of unholy matrices is printed. Note that this program has a time complexity of O(2^64), which is extremely inefficient for large matrices. It may take an impractically long time to run for matrices larger than 8x8. For larger matrices, a more efficient algorithm would be required.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>
#include <math.h>

int isUnholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                if (
                    (i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)
                ) {
                    // This is an isolated 1, so the matrix is not unholy
                    return 0;
                }
            }
        }
    }
    // No isolated 1s were found, so the matrix is unholy
    return 1;
}

int main() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    // Iterate through all possible 8x8 matrices
    for (k = 0; k < (int)pow(2, 64); k++) {
        // Convert the integer k to a binary matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        // Check if the current matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %d\n", count);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>
#include <math.h>

int isUnholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the current 1 is isolated
                if (
                    (i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)
                ) {
                    // This is an isolated 1, so the matrix is not unholy
                    return 0;
                }
            }
        }
    }
    // No isolated 1s were found, so the matrix is unholy
    return 1;
}

int main() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    // Iterate through all possible 8x8 matrices
    for (k = 0; k < (int)pow(2, 64); k++) {
        // Convert the integer k to a binary matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        // Check if the current matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 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.

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.

Output

Here's a C program that counts the total number of unholy 8x8 matrices: 

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#include <stdio.h>
#include <stdint.h>

#define ROWS 8
#define COLS 8

int is_unholy(uint64_t matrix) {
    int i, j;
    int is_isolated;

    for (i = 0; i < ROWS; i++) {
        for (j = 0; j < COLS; j++) {
            is_isolated = 1;
            if ((matrix & (1ULL << (i * COLS + j)))) {
                // Check left
                if (j > 0 && (matrix & (1ULL << (i * COLS + j - 1)))) {
                    is_isolated = 0;
                }
                // Check right
                if (j < COLS - 1 && (matrix & (1ULL << (i * COLS + j + 1)))) {
                    is_isolated = 0;
                }
                // Check up
                if (i > 0 && (matrix & (1ULL << ((i - 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                // Check down
                if (i < ROWS - 1 && (matrix & (1ULL << ((i + 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                if (is_isolated) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int main() {
    uint64_t count = 0;
    uint64_t max_value = 1ULL << (ROWS * COLS);

    for (uint64_t matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}
Here's how the program works: 1. The `is_unholy` function checks if a given 8x8 matrix represented as a 64-bit integer is unholy or not. It iterates over each bit in the matrix and checks if the corresponding position has a 1. If it does, it checks if there are any other 1s in the four direct cardinal directions. If there is an isolated 1, the function returns 0 (not unholy). If there are no isolated 1s, the function returns 1 (unholy). 2. In the `main` function, we iterate over all possible 8x8 matrices by generating 64-bit integers from 0 to `(1ULL << (ROWS * COLS)) - 1`. For each matrix, we call the `is_unholy` function and increment the count if the matrix is unholy. 3. Finally, we print the total count of unholy 8x8 matrices. Note that this program uses a 64-bit integer to represent the 8x8 matrix, with each bit representing a cell in the matrix. This allows us to efficiently check the neighboring cells using bitwise operations.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>
#include <stdint.h>

#define ROWS 8
#define COLS 8

int is_unholy(uint64_t matrix) {
    int i, j;
    int is_isolated;

    for (i = 0; i < ROWS; i++) {
        for (j = 0; j < COLS; j++) {
            is_isolated = 1;
            if ((matrix & (1ULL << (i * COLS + j)))) {
                // Check left
                if (j > 0 && (matrix & (1ULL << (i * COLS + j - 1)))) {
                    is_isolated = 0;
                }
                // Check right
                if (j < COLS - 1 && (matrix & (1ULL << (i * COLS + j + 1)))) {
                    is_isolated = 0;
                }
                // Check up
                if (i > 0 && (matrix & (1ULL << ((i - 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                // Check down
                if (i < ROWS - 1 && (matrix & (1ULL << ((i + 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                if (is_isolated) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int main() {
    uint64_t count = 0;
    uint64_t max_value = 1ULL << (ROWS * COLS);

    for (uint64_t matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>
#include <stdint.h>

#define ROWS 8
#define COLS 8

int is_unholy(uint64_t matrix) {
    int i, j;
    int is_isolated;

    for (i = 0; i < ROWS; i++) {
        for (j = 0; j < COLS; j++) {
            is_isolated = 1;
            if ((matrix & (1ULL << (i * COLS + j)))) {
                // Check left
                if (j > 0 && (matrix & (1ULL << (i * COLS + j - 1)))) {
                    is_isolated = 0;
                }
                // Check right
                if (j < COLS - 1 && (matrix & (1ULL << (i * COLS + j + 1)))) {
                    is_isolated = 0;
                }
                // Check up
                if (i > 0 && (matrix & (1ULL << ((i - 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                // Check down
                if (i < ROWS - 1 && (matrix & (1ULL << ((i + 1) * COLS + j)))) {
                    is_isolated = 0;
                }
                if (is_isolated) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

int main() {
    uint64_t count = 0;
    uint64_t max_value = 1ULL << (ROWS * COLS);

    for (uint64_t matrix = 0; matrix < max_value; matrix++) {
        if (is_unholy(matrix)) {
            count++;
        }
    }

    printf("Total number of unholy 8x8 matrices: %llu\n", count);
    return 0;
}
And got the output: Total number of unholy 8x8 matrices: 0 main.c: In function 'main': main.c:43:31: warning: left shift count >= width of type [-Wshift-count-overflow] 43 | uint64_t max_value = 1ULL << (ROWS * COLS); | ^~ main.c:51:53: warning: format '%llu' expects argument of type 'long long unsigned int', but argument 2 has type 'uint64_t' {aka 'long unsigned int'} [-Wformat=] 51 | printf("Total number of unholy 8x8 matrices: %llu\n", count); | ~~~^ ~~~~~ | | | | | uint64_t {aka long unsigned int} | long long unsigned int | %lu

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.

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.

Output

Here's a C program that counts the total number of unholy 8x8 matrices: 

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

int is_unholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)) {
                    return 0; // Isolated 1 found, not unholy
                }
            }
        }
    }
    return 1; // No isolated 1s, it's unholy
}

int count_unholy_matrices() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    for (k = 0; k < (1 << (8*8)); k++) {
        // Generate the current matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    int num_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", num_unholy);
    return 0;
}
Here's how the program works: 1. The `is_unholy` function takes an 8x8 matrix as input and checks if it is unholy or not. It iterates through all the elements of the matrix and checks if there is any 1 that is isolated (i.e., there is no other 1 in any of the four cardinal directions). If an isolated 1 is found, it returns 0 (not unholy). If no isolated 1s are found, it returns 1 (unholy). 2. The `count_unholy_matrices` function generates all possible 8x8 matrices and counts the number of unholy matrices using the `is_unholy` function. It does this by iterating through all possible bit patterns for an 8x8 matrix (2^64 patterns in total) using a loop that increments the binary value `k` from 0 to (2^64 - 1). For each value of `k`, it generates the corresponding 8x8 matrix by extracting the bits from `k` and storing them in the `matrix` array. It then calls the `is_unholy` function to check if the matrix is unholy, and if so, increments the `count` variable. 3. In the `main` function, the `count_unholy_matrices` function is called, and the total number of unholy matrices is printed. Note that this program generates and checks all possible 8x8 matrices, which involves iterating through 2^64 bit patterns. This can be computationally expensive for larger matrix sizes.

Extract Code

I extracted the following code from that output: 

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

int is_unholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)) {
                    return 0; // Isolated 1 found, not unholy
                }
            }
        }
    }
    return 1; // No isolated 1s, it's unholy
}

int count_unholy_matrices() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    for (k = 0; k < (1 << (8*8)); k++) {
        // Generate the current matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    int num_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", num_unholy);
    return 0;
}

Run Code Interpreter

Running the following program: 

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

int is_unholy(int matrix[8][8]) {
    int i, j;
    for (i = 0; i < 8; i++) {
        for (j = 0; j < 8; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == 7 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == 7 || matrix[i][j+1] == 0)) {
                    return 0; // Isolated 1 found, not unholy
                }
            }
        }
    }
    return 1; // No isolated 1s, it's unholy
}

int count_unholy_matrices() {
    int count = 0;
    int matrix[8][8];
    int i, j, k;

    for (k = 0; k < (1 << (8*8)); k++) {
        // Generate the current matrix
        for (i = 0; i < 8; i++) {
            for (j = 0; j < 8; j++) {
                matrix[i][j] = (k >> (i*8 + j)) & 1;
            }
        }

        if (is_unholy(matrix)) {
            count++;
        }
    }

    return count;
}

int main() {
    int num_unholy = count_unholy_matrices();
    printf("Total number of unholy 8x8 matrices: %d\n", num_unholy);
    return 0;
}
And got the output: Total number of unholy 8x8 matrices: 0 main.c: In function 'count_unholy_matrices': main.c:28:24: warning: left shift count >= width of type [-Wshift-count-overflow] 28 | for (k = 0; k < (1 << (8*8)); k++) { | ^~

Substring Evaluation

Testing if the previous output contains the string 1121231537486377866: False