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

To count the total number of unholy 8x8 matrices, we can use a recursive approach with backtracking. Here's a C program that solves the problem: 

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

#define ROWS 8
#define COLS 8

int count = 0;

bool isIsolated(int matrix[ROWS][COLS], int row, int col) {
    if (row > 0 && matrix[row - 1][col] == 1)
        return false;
    if (row < ROWS - 1 && matrix[row + 1][col] == 1)
        return false;
    if (col > 0 && matrix[row][col - 1] == 1)
        return false;
    if (col < COLS - 1 && matrix[row][col + 1] == 1)
        return false;
    return true;
}

bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1 && isIsolated(matrix, i, j))
                return false;
        }
    }
    return true;
}

void backtrack(int matrix[ROWS][COLS], int row, int col) {
    if (col == COLS) {
        col = 0;
        row++;
    }

    if (row == ROWS) {
        if (isUnholy(matrix))
            count++;
        return;
    }

    matrix[row][col] = 0;
    backtrack(matrix, row, col + 1);

    matrix[row][col] = 1;
    backtrack(matrix, row, col + 1);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    backtrack(matrix, 0, 0);
    printf("Total number of unholy 8x8 matrices: %d\n", count);
    return 0;
}
Explanation: 1. The `isIsolated` function checks if a given cell (row, col) in the matrix is isolated. It checks the four cardinal directions to see if there is another 1 adjacent to the current cell. If any adjacent cell is 1, it returns false; otherwise, it returns true. 2. The `isUnholy` function checks if the entire matrix is unholy. It iterates over each cell in the matrix, and if a cell is 1, it checks if it is isolated using the `isIsolated` function. If any isolated 1 is found, it returns false; otherwise, it returns true. 3. The `backtrack` function uses backtracking to generate all possible 8x8 binary matrices. It recursively fills the matrix by placing either 0 or 1 in each cell. When the entire matrix is filled (row == ROWS), it checks if the matrix is unholy using the `isUnholy` function. If the matrix is unholy, it increments the count. 4. In the `main` function, we initialize an empty matrix and call the `backtrack` function starting from the first cell (0, 0). After the backtracking is complete, it prints the total count of unholy matrices. The program will generate all possible 8x8 binary matrices and count the number of unholy matrices among them. The final count will be printed as the output. Note: This program will take a significant amount of time to run due to the large number of possible matrices (2^64). It may be more efficient to use dynamic programming or other optimization techniques for larger matrix sizes.

Extract Code

I extracted the following code from that output: 

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

#define ROWS 8
#define COLS 8

int count = 0;

bool isIsolated(int matrix[ROWS][COLS], int row, int col) {
    if (row > 0 && matrix[row - 1][col] == 1)
        return false;
    if (row < ROWS - 1 && matrix[row + 1][col] == 1)
        return false;
    if (col > 0 && matrix[row][col - 1] == 1)
        return false;
    if (col < COLS - 1 && matrix[row][col + 1] == 1)
        return false;
    return true;
}

bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1 && isIsolated(matrix, i, j))
                return false;
        }
    }
    return true;
}

void backtrack(int matrix[ROWS][COLS], int row, int col) {
    if (col == COLS) {
        col = 0;
        row++;
    }

    if (row == ROWS) {
        if (isUnholy(matrix))
            count++;
        return;
    }

    matrix[row][col] = 0;
    backtrack(matrix, row, col + 1);

    matrix[row][col] = 1;
    backtrack(matrix, row, col + 1);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    backtrack(matrix, 0, 0);
    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 <stdbool.h>

#define ROWS 8
#define COLS 8

int count = 0;

bool isIsolated(int matrix[ROWS][COLS], int row, int col) {
    if (row > 0 && matrix[row - 1][col] == 1)
        return false;
    if (row < ROWS - 1 && matrix[row + 1][col] == 1)
        return false;
    if (col > 0 && matrix[row][col - 1] == 1)
        return false;
    if (col < COLS - 1 && matrix[row][col + 1] == 1)
        return false;
    return true;
}

bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1 && isIsolated(matrix, i, j))
                return false;
        }
    }
    return true;
}

void backtrack(int matrix[ROWS][COLS], int row, int col) {
    if (col == COLS) {
        col = 0;
        row++;
    }

    if (row == ROWS) {
        if (isUnholy(matrix))
            count++;
        return;
    }

    matrix[row][col] = 0;
    backtrack(matrix, row, col + 1);

    matrix[row][col] = 1;
    backtrack(matrix, row, col + 1);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    backtrack(matrix, 0, 0);
    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>

#define SIZE 8

int is_unholy(int matrix[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (matrix[i][j] == 1) {
                int is_isolated = 1;
                if (i > 0 && matrix[i-1][j] == 1) is_isolated = 0;
                if (i < SIZE-1 && matrix[i+1][j] == 1) is_isolated = 0;
                if (j > 0 && matrix[i][j-1] == 1) is_isolated = 0;
                if (j < SIZE-1 && matrix[i][j+1] == 1) is_isolated = 0;
                if (is_isolated) return 0;
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[SIZE][SIZE], int row, int col, long long *count) {
    if (row == SIZE) {
        if (is_unholy(matrix)) (*count)++;
        return;
    }
    
    if (col == SIZE) {
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }
    
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);
    
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[SIZE][SIZE];
    long long count = 0;
    
    generate_matrices(matrix, 0, 0, &count);
    
    printf("Total number of unholy 8x8 matrices: %lld\n", count);
    
    return 0;
}
This program uses a recursive approach to generate all possible 8x8 binary matrices and counts the number of unholy matrices. The `is_unholy` function checks if a given matrix is unholy. It iterates over each cell of the matrix and checks if a 1 is isolated. If any isolated 1 is found, the function returns 0 (not unholy). If no isolated 1 is found, it returns 1 (unholy). The `generate_matrices` function generates all possible 8x8 binary matrices using recursion. It fills the matrix cell by cell, recursively generating matrices with 0 and 1 at each position. Once a complete matrix is generated, it checks if it is unholy using the `is_unholy` function and increments the count if it is. In the `main` function, we initialize the `matrix` array and the `count` variable. We then call the `generate_matrices` function to generate all possible matrices and count the unholy ones. Finally, we print the total count of unholy matrices. Note that the number of possible 8x8 binary matrices is quite large (2^64), so this program may take a significant amount of time to complete. You can optimize it further by using dynamic programming techniques or parallel processing if needed.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define SIZE 8

int is_unholy(int matrix[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (matrix[i][j] == 1) {
                int is_isolated = 1;
                if (i > 0 && matrix[i-1][j] == 1) is_isolated = 0;
                if (i < SIZE-1 && matrix[i+1][j] == 1) is_isolated = 0;
                if (j > 0 && matrix[i][j-1] == 1) is_isolated = 0;
                if (j < SIZE-1 && matrix[i][j+1] == 1) is_isolated = 0;
                if (is_isolated) return 0;
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[SIZE][SIZE], int row, int col, long long *count) {
    if (row == SIZE) {
        if (is_unholy(matrix)) (*count)++;
        return;
    }
    
    if (col == SIZE) {
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }
    
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);
    
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[SIZE][SIZE];
    long long count = 0;
    
    generate_matrices(matrix, 0, 0, &count);
    
    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>

#define SIZE 8

int is_unholy(int matrix[SIZE][SIZE]) {
    for (int i = 0; i < SIZE; i++) {
        for (int j = 0; j < SIZE; j++) {
            if (matrix[i][j] == 1) {
                int is_isolated = 1;
                if (i > 0 && matrix[i-1][j] == 1) is_isolated = 0;
                if (i < SIZE-1 && matrix[i+1][j] == 1) is_isolated = 0;
                if (j > 0 && matrix[i][j-1] == 1) is_isolated = 0;
                if (j < SIZE-1 && matrix[i][j+1] == 1) is_isolated = 0;
                if (is_isolated) return 0;
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[SIZE][SIZE], int row, int col, long long *count) {
    if (row == SIZE) {
        if (is_unholy(matrix)) (*count)++;
        return;
    }
    
    if (col == SIZE) {
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }
    
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);
    
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[SIZE][SIZE];
    long long count = 0;
    
    generate_matrices(matrix, 0, 0, &count);
    
    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

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>

#define ROWS 8
#define COLS 8

int is_unholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == ROWS-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == COLS-1 || matrix[i][j+1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[ROWS][COLS], int row, int col, int *count) {
    if (row == ROWS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    int next_row = (col == COLS - 1) ? row + 1 : row;
    int next_col = (col + 1) % COLS;

    matrix[row][col] = 0;
    generate_matrices(matrix, next_row, next_col, count);

    matrix[row][col] = 1;
    generate_matrices(matrix, next_row, next_col, count);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    int count = 0;

    generate_matrices(matrix, 0, 0, &count);

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

    return 0;
}
Explanation: 1. The `is_unholy` function checks if a given matrix is unholy. It iterates over each element of the matrix and checks if there is an isolated 1. If an isolated 1 is found, it returns 0 (indicating the matrix is not unholy). If no isolated 1 is found, it returns 1 (indicating the matrix is unholy). 2. The `generate_matrices` function generates all possible 8x8 binary matrices recursively. It starts with an empty matrix and recursively fills each position with 0 and 1. When a complete matrix is generated, it calls the `is_unholy` function to check if the matrix is unholy. If it is unholy, the count is incremented. 3. In the `main` function, we initialize an empty 8x8 matrix and a count variable to keep track of the number of unholy matrices. We then call the `generate_matrices` function to generate all possible matrices and count the unholy ones. 4. Finally, we print the total number of unholy 8x8 matrices. Note: This program uses a brute-force approach to generate all possible 8x8 binary matrices and counts the unholy ones. The time complexity of this approach is exponential (2^64) since there are 2^64 possible matrices. For larger matrix sizes, this approach may not be feasible, and more efficient algorithms or techniques would need to be employed.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define ROWS 8
#define COLS 8

int is_unholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == ROWS-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == COLS-1 || matrix[i][j+1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[ROWS][COLS], int row, int col, int *count) {
    if (row == ROWS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    int next_row = (col == COLS - 1) ? row + 1 : row;
    int next_col = (col + 1) % COLS;

    matrix[row][col] = 0;
    generate_matrices(matrix, next_row, next_col, count);

    matrix[row][col] = 1;
    generate_matrices(matrix, next_row, next_col, count);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    int count = 0;

    generate_matrices(matrix, 0, 0, &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>

#define ROWS 8
#define COLS 8

int is_unholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == ROWS-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == COLS-1 || matrix[i][j+1] == 0)) {
                    return 0;
                }
            }
        }
    }
    return 1;
}

void generate_matrices(int matrix[ROWS][COLS], int row, int col, int *count) {
    if (row == ROWS) {
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    int next_row = (col == COLS - 1) ? row + 1 : row;
    int next_col = (col + 1) % COLS;

    matrix[row][col] = 0;
    generate_matrices(matrix, next_row, next_col, count);

    matrix[row][col] = 1;
    generate_matrices(matrix, next_row, next_col, count);
}

int main() {
    int matrix[ROWS][COLS] = {0};
    int count = 0;

    generate_matrices(matrix, 0, 0, &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 <stdbool.h>

#define ROWS 8
#define COLS 8

// Function to check if a matrix is unholy
bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                bool isolated = true;
                
                // Check the four cardinal directions
                int dx[] = {-1, 0, 1, 0};
                int dy[] = {0, -1, 0, 1};
                
                for (int k = 0; k < 4; k++) {
                    int nx = i + dx[k];
                    int ny = j + dy[k];
                    
                    if (nx >= 0 && nx < ROWS && ny >= 0 && ny < COLS && matrix[nx][ny] == 1) {
                        isolated = false;
                        break;
                    }
                }
                
                if (isolated) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Function to generate and count unholy matrices
int countUnholyMatrices() {
    int count = 0;
    int matrix[ROWS][COLS];
    
    // Generate all possible matrices
    for (int i = 0; i < (1 << (ROWS * COLS)); i++) {
        for (int j = 0; j < ROWS * COLS; j++) {
            matrix[j / COLS][j % COLS] = (i >> j) & 1;
        }
        
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }
    
    return count;
}

int main() {
    int unholyCount = countUnholyMatrices();
    printf("Total number of unholy 8x8 matrices: %d\n", unholyCount);
    return 0;
}
Explanation: 1. The `isUnholy` function takes an 8x8 matrix as input and checks if it is unholy. It iterates over each element of the matrix, and if it finds a 1, it checks the four cardinal directions (up, down, left, right) to see if there is another 1. If there are no adjacent 1s, it means the 1 is isolated, and the function returns `false`. If all 1s have at least one adjacent 1, the function returns `true`. 2. The `countUnholyMatrices` function generates all possible 8x8 matrices and counts the number of unholy matrices. It uses a loop to iterate over all possible combinations of 0s and 1s in the matrix. For each combination, it constructs the matrix using bitwise operations and calls the `isUnholy` function to check if the matrix is unholy. If it is, the count is incremented. 3. In the `main` function, we call the `countUnholyMatrices` function to obtain the total count of unholy matrices and print the result. Note: The code uses bitwise operations to generate all possible matrices efficiently. It may take some time to execute due to the large number of combinations (2^64).

Extract Code

I extracted the following code from that output: 

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

#define ROWS 8
#define COLS 8

// Function to check if a matrix is unholy
bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                bool isolated = true;
                
                // Check the four cardinal directions
                int dx[] = {-1, 0, 1, 0};
                int dy[] = {0, -1, 0, 1};
                
                for (int k = 0; k < 4; k++) {
                    int nx = i + dx[k];
                    int ny = j + dy[k];
                    
                    if (nx >= 0 && nx < ROWS && ny >= 0 && ny < COLS && matrix[nx][ny] == 1) {
                        isolated = false;
                        break;
                    }
                }
                
                if (isolated) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Function to generate and count unholy matrices
int countUnholyMatrices() {
    int count = 0;
    int matrix[ROWS][COLS];
    
    // Generate all possible matrices
    for (int i = 0; i < (1 << (ROWS * COLS)); i++) {
        for (int j = 0; j < ROWS * COLS; j++) {
            matrix[j / COLS][j % COLS] = (i >> j) & 1;
        }
        
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }
    
    return count;
}

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

Run Code Interpreter

Running the following program: 

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

#define ROWS 8
#define COLS 8

// Function to check if a matrix is unholy
bool isUnholy(int matrix[ROWS][COLS]) {
    for (int i = 0; i < ROWS; i++) {
        for (int j = 0; j < COLS; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                bool isolated = true;
                
                // Check the four cardinal directions
                int dx[] = {-1, 0, 1, 0};
                int dy[] = {0, -1, 0, 1};
                
                for (int k = 0; k < 4; k++) {
                    int nx = i + dx[k];
                    int ny = j + dy[k];
                    
                    if (nx >= 0 && nx < ROWS && ny >= 0 && ny < COLS && matrix[nx][ny] == 1) {
                        isolated = false;
                        break;
                    }
                }
                
                if (isolated) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Function to generate and count unholy matrices
int countUnholyMatrices() {
    int count = 0;
    int matrix[ROWS][COLS];
    
    // Generate all possible matrices
    for (int i = 0; i < (1 << (ROWS * COLS)); i++) {
        for (int j = 0; j < ROWS * COLS; j++) {
            matrix[j / COLS][j % COLS] = (i >> j) & 1;
        }
        
        // Check if the matrix is unholy
        if (isUnholy(matrix)) {
            count++;
        }
    }
    
    return count;
}

int main() {
    int unholyCount = countUnholyMatrices();
    printf("Total number of unholy 8x8 matrices: %d\n", unholyCount);
    return 0;
}
And got the output: Total number of unholy 8x8 matrices: 0 main.c: In function 'countUnholyMatrices': main.c:45:28: warning: left shift count >= width of type [-Wshift-count-overflow] 45 | for (int i = 0; i < (1 << (ROWS * COLS)); 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>

#define N 8

int is_unholy(int matrix[N][N]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == N-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == N-1 || matrix[i][j+1] == 0)) {
                    return 0; // The matrix is not unholy
                }
            }
        }
    }
    return 1; // The matrix is unholy
}

void generate_matrices(int matrix[N][N], int row, int col, long long *count) {
    if (row == N) {
        // Matrix is complete, check if it is unholy
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    if (col == N) {
        // Move to the next row
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }

    // Fill the current cell with 0 and move to the next cell
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);

    // Fill the current cell with 1 and move to the next cell
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[N][N] = {0};
    long long count = 0;

    generate_matrices(matrix, 0, 0, &count);

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

    return 0;
}
Explanation: 1. The `is_unholy` function checks if a given matrix is unholy. It iterates over each cell of the matrix and checks if any 1 is isolated. If an isolated 1 is found, the function returns 0, indicating that the matrix is not unholy. If no isolated 1 is found, the function returns 1, indicating that the matrix is unholy. 2. The `generate_matrices` function generates all possible 8x8 binary matrices using a recursive approach. It starts with an empty matrix and fills each cell with 0 and 1, recursively generating all possible combinations. When a complete matrix is generated, it checks if the matrix is unholy using the `is_unholy` function. If the matrix is unholy, it increments the count. 3. In the `main` function, an 8x8 matrix is initialized with zeros, and a variable `count` is used to store the total number of unholy matrices. The `generate_matrices` function is called with the initial matrix, starting row and column as 0, and the address of the `count` variable. 4. Finally, the program prints the total number of unholy 8x8 matrices. Note: The program uses a long long integer (`long long`) to store the count since the number of possible matrices can be large. Please be aware that generating all possible 8x8 binary matrices is a computationally intensive task and may take a significant amount of time to complete.

Extract Code

I extracted the following code from that output: 

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#include <stdio.h>

#define N 8

int is_unholy(int matrix[N][N]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == N-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == N-1 || matrix[i][j+1] == 0)) {
                    return 0; // The matrix is not unholy
                }
            }
        }
    }
    return 1; // The matrix is unholy
}

void generate_matrices(int matrix[N][N], int row, int col, long long *count) {
    if (row == N) {
        // Matrix is complete, check if it is unholy
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    if (col == N) {
        // Move to the next row
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }

    // Fill the current cell with 0 and move to the next cell
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);

    // Fill the current cell with 1 and move to the next cell
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[N][N] = {0};
    long long count = 0;

    generate_matrices(matrix, 0, 0, &count);

    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>

#define N 8

int is_unholy(int matrix[N][N]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (matrix[i][j] == 1) {
                // Check if the 1 is isolated
                if ((i == 0 || matrix[i-1][j] == 0) &&
                    (i == N-1 || matrix[i+1][j] == 0) &&
                    (j == 0 || matrix[i][j-1] == 0) &&
                    (j == N-1 || matrix[i][j+1] == 0)) {
                    return 0; // The matrix is not unholy
                }
            }
        }
    }
    return 1; // The matrix is unholy
}

void generate_matrices(int matrix[N][N], int row, int col, long long *count) {
    if (row == N) {
        // Matrix is complete, check if it is unholy
        if (is_unholy(matrix)) {
            (*count)++;
        }
        return;
    }

    if (col == N) {
        // Move to the next row
        generate_matrices(matrix, row + 1, 0, count);
        return;
    }

    // Fill the current cell with 0 and move to the next cell
    matrix[row][col] = 0;
    generate_matrices(matrix, row, col + 1, count);

    // Fill the current cell with 1 and move to the next cell
    matrix[row][col] = 1;
    generate_matrices(matrix, row, col + 1, count);
}

int main() {
    int matrix[N][N] = {0};
    long long count = 0;

    generate_matrices(matrix, 0, 0, &count);

    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