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 to count the total number of unholy 8x8 matrices. This program uses a recursive approach to generate all possible binary 8x8 matrices and checks each one for isolated 1s. 

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#include <stdio.h>
#include <stdbool.h>

// Structure to represent an 8x8 matrix
typedef struct {
    int matrix[8][8];
} Matrix;

// Function to check if a 1 is isolated in the given matrix
bool isIsolated(Matrix matrix, int row, int col) {
    // Check all four direct cardinal directions
    int directions[][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    for (int i = 0; i < 4; i++) {
        int newRow = row + directions[i][0];
        int newCol = col + directions[i][1];

        // Check if the new position is within the matrix bounds
        if (newRow >= 0 && newRow < 8 && newCol >= 0 && newCol < 8) {
            // If there's a 1 in any of the four directions, the 1 is not isolated
            if (matrix.matrix[newRow][newCol] == 1) {
                return false;
            }
        }
    }

    // If no 1 is found in any of the four directions, the 1 is isolated
    return true;
}

// Function to check if a matrix is unholy
bool isUnholy(Matrix matrix) {
    // Check all elements in the matrix
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            // If a 1 is isolated, the matrix is not unholy
            if (matrix.matrix[i][j] == 1 && isIsolated(matrix, i, j)) {
                return false;
            }
        }
    }

    // If no isolated 1s are found, the matrix is unholy
    return true;
}

// Function to generate all possible binary 8x8 matrices and count the unholy ones
long long countUnholyMatrices(int row, int col, Matrix matrix) {
    // Base case: if all elements have been filled
    if (row == 8) {
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            return 1;
        } else {
            return 0;
        }
    }

    // Recursive case: try both 0 and 1 for the current element
    long long count = 0;
    for (int val = 0; val <= 1; val++) {
        matrix.matrix[row][col] = val;

        // Move to the next element
        if (col == 7) {
            count += countUnholyMatrices(row + 1, 0, matrix);
        } else {
            count += countUnholyMatrices(row, col + 1, matrix);
        }
    }

    return count;
}

int main() {
    Matrix matrix;
    // Initialize all elements to 0
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            matrix.matrix[i][j] = 0;
        }
    }

    long long count = countUnholyMatrices(0, 0, matrix);
    printf("Total number of unholy 8x8 matrices: %lld\n", count);

    return 0;
}
This program uses a recursive approach to generate all possible binary 8x8 matrices. For each matrix, it checks if there are any isolated 1s by calling the `isIsolated` function. If a matrix is found to be unholy (i.e., it has no isolated 1s), it increments the count. Please note that this program may take a significant amount of time to run due to the large number of possible binary 8x8 matrices (2^64). You may want to consider running this program on a powerful machine or using a more efficient algorithm. Also, keep in mind that the result of this program is the total number of unholy 8x8 matrices, which is a very large number and may not fit in a standard `long long` variable. You may need to use a library that supports arbitrary-precision arithmetic to handle such large numbers. In the context of this program, the output will likely be a very large number that exceeds the maximum limit of `long long` data type, which will cause an overflow and result in an incorrect output. To handle such large numbers, you can use a library like the GNU Multiple Precision Arithmetic Library (GMP). Here's a modified version of the program that uses the GMP library to handle large numbers: 
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#include <stdio.h>
#include <stdbool.h>
#include <gmp.h>

// Structure to represent an 8x8 matrix
typedef struct {
    int matrix[8][8];
} Matrix;

// Function to check if a 1 is isolated in the given matrix
bool isIsolated(Matrix matrix, int row, int col) {
    // Check all four direct cardinal directions
    int directions[][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    for (int i = 0; i < 4; i++) {
        int newRow = row + directions[i][0];
        int newCol = col + directions[i][1];

        // Check if the new position is within the matrix bounds
        if (newRow >= 0 && newRow < 8 && newCol >= 0 && newCol < 8) {
            // If there's a 1 in any of the four directions, the 1 is not isolated
            if (matrix.matrix[newRow][newCol] == 1) {
                return false;
            }
        }
    }

    // If no 1 is found in any of the four directions, the 1 is isolated
    return true;
}

// Function to check if a matrix is unholy
bool isUnholy(Matrix matrix) {
    // Check all elements in the matrix
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            // If a 1 is isolated, the matrix is not unholy
            if (matrix.matrix[i][j] == 1 && isIsolated(matrix, i, j)) {
                return false;
            }
        }
    }

    // If no isolated 1s are found, the matrix is unholy
    return true;
}

// Function to generate all possible binary 8x8 matrices and count the unholy ones
void countUnholyMatrices(int row, int col, Matrix matrix, mpz_t count) {
    // Base case: if all elements have been filled
    if (row == 8) {
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            mpz_add_ui(count, count, 1);
        }
        return;
    }

    // Recursive case: try both 0 and 1 for the current element
    for (int val = 0; val <= 1; val++) {
        matrix.matrix[row][col] = val;

        // Move to the next element
        if (col == 7) {
            countUnholyMatrices(row + 1, 0, matrix, count);
        } else {
            countUnholyMatrices(row, col + 1, matrix, count);
        }
    }
}

int main() {
    Matrix matrix;
    // Initialize all elements to 0
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            matrix.matrix[i][j] = 0;
        }
    }

    mpz_t count;
    mpz_init(count);
    countUnholyMatrices(0, 0, matrix, count);

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

    mpz_clear(count);
    return 0;
}
This modified version uses the GMP library to handle large numbers. The `countUnholyMatrices` function now takes an `mpz_t` argument to store the count, and the `gmp_printf` function is used to print the result.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>
#include <stdbool.h>

// Structure to represent an 8x8 matrix
typedef struct {
    int matrix[8][8];
} Matrix;

// Function to check if a 1 is isolated in the given matrix
bool isIsolated(Matrix matrix, int row, int col) {
    // Check all four direct cardinal directions
    int directions[][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    for (int i = 0; i < 4; i++) {
        int newRow = row + directions[i][0];
        int newCol = col + directions[i][1];

        // Check if the new position is within the matrix bounds
        if (newRow >= 0 && newRow < 8 && newCol >= 0 && newCol < 8) {
            // If there's a 1 in any of the four directions, the 1 is not isolated
            if (matrix.matrix[newRow][newCol] == 1) {
                return false;
            }
        }
    }

    // If no 1 is found in any of the four directions, the 1 is isolated
    return true;
}

// Function to check if a matrix is unholy
bool isUnholy(Matrix matrix) {
    // Check all elements in the matrix
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            // If a 1 is isolated, the matrix is not unholy
            if (matrix.matrix[i][j] == 1 && isIsolated(matrix, i, j)) {
                return false;
            }
        }
    }

    // If no isolated 1s are found, the matrix is unholy
    return true;
}

// Function to generate all possible binary 8x8 matrices and count the unholy ones
long long countUnholyMatrices(int row, int col, Matrix matrix) {
    // Base case: if all elements have been filled
    if (row == 8) {
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            return 1;
        } else {
            return 0;
        }
    }

    // Recursive case: try both 0 and 1 for the current element
    long long count = 0;
    for (int val = 0; val <= 1; val++) {
        matrix.matrix[row][col] = val;

        // Move to the next element
        if (col == 7) {
            count += countUnholyMatrices(row + 1, 0, matrix);
        } else {
            count += countUnholyMatrices(row, col + 1, matrix);
        }
    }

    return count;
}

int main() {
    Matrix matrix;
    // Initialize all elements to 0
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            matrix.matrix[i][j] = 0;
        }
    }

    long long count = countUnholyMatrices(0, 0, matrix);
    printf("Total number of unholy 8x8 matrices: %lld\n", count);

    return 0;
}

Run Code Interpreter

Running the following program: 

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#include <stdio.h>
#include <stdbool.h>

// Structure to represent an 8x8 matrix
typedef struct {
    int matrix[8][8];
} Matrix;

// Function to check if a 1 is isolated in the given matrix
bool isIsolated(Matrix matrix, int row, int col) {
    // Check all four direct cardinal directions
    int directions[][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    for (int i = 0; i < 4; i++) {
        int newRow = row + directions[i][0];
        int newCol = col + directions[i][1];

        // Check if the new position is within the matrix bounds
        if (newRow >= 0 && newRow < 8 && newCol >= 0 && newCol < 8) {
            // If there's a 1 in any of the four directions, the 1 is not isolated
            if (matrix.matrix[newRow][newCol] == 1) {
                return false;
            }
        }
    }

    // If no 1 is found in any of the four directions, the 1 is isolated
    return true;
}

// Function to check if a matrix is unholy
bool isUnholy(Matrix matrix) {
    // Check all elements in the matrix
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            // If a 1 is isolated, the matrix is not unholy
            if (matrix.matrix[i][j] == 1 && isIsolated(matrix, i, j)) {
                return false;
            }
        }
    }

    // If no isolated 1s are found, the matrix is unholy
    return true;
}

// Function to generate all possible binary 8x8 matrices and count the unholy ones
long long countUnholyMatrices(int row, int col, Matrix matrix) {
    // Base case: if all elements have been filled
    if (row == 8) {
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            return 1;
        } else {
            return 0;
        }
    }

    // Recursive case: try both 0 and 1 for the current element
    long long count = 0;
    for (int val = 0; val <= 1; val++) {
        matrix.matrix[row][col] = val;

        // Move to the next element
        if (col == 7) {
            count += countUnholyMatrices(row + 1, 0, matrix);
        } else {
            count += countUnholyMatrices(row, col + 1, matrix);
        }
    }

    return count;
}

int main() {
    Matrix matrix;
    // Initialize all elements to 0
    for (int i = 0; i < 8; i++) {
        for (int j = 0; j < 8; j++) {
            matrix.matrix[i][j] = 0;
        }
    }

    long long count = countUnholyMatrices(0, 0, matrix);
    printf("Total number of unholy 8x8 matrices: %lld\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