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

**Program Plan:** ### Step 1: Represent the Matrix * Use an unsigned long to represent each row of the matrix. * Use bit arithmetic to manipulate the matrix. ### Step 2: Implement the `is_unholy` Function * Write a function `is_unholy` that takes a matrix as input and returns 1 if the matrix is unholy, 0 otherwise. * Use bit-shifting and masking to check for isolated 1s in the matrix. ### Step 3: Implement the Dynamic Programming Approach * Write a recursive function to count the number of unholy matrices with a given number of rows. * Recurse on the number of rows, starting from 1 and going up to 8. * Enumerate all 2^16 possible next two rows and check if the resulting matrix is unholy. * Use memoization to store intermediate results and avoid redundant computation. ### Step 4: Implement the Main Function * Call the recursive function with the initial number of rows (8) and print the result. **Implementation:** 

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

// Define the size of the matrix
#define MATRIX_SIZE 8

// Define the mask for the first row
#define FIRST_ROW_MASK 0xFF

// Define the mask for the second row
#define SECOND_ROW_MASK 0xFF00

// Function to check if a matrix is unholy
bool is_unholy(uint64_t matrix) {
    // Iterate over each row
    for (int i = 0; i < MATRIX_SIZE; i++) {
        // Get the current row
        uint64_t row = (matrix >> (i * 8)) & 0xFF;
        
        // Check for isolated 1s in the current row
        for (int j = 0; j < MATRIX_SIZE; j++) {
            // Check if the current bit is 1
            if ((row >> j) & 1) {
                // Check if there is no adjacent 1 in the same row or in the adjacent rows
                if (!(row >> (j + 1) & 1) && !(row >> (j - 1) & 1) &&
                     !(i > 0 && (matrix >> ((i - 1) * 8 + j)) & 1) &&
                     !(i < MATRIX_SIZE - 1 && (matrix >> ((i + 1) * 8 + j)) & 1)) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Recursive function to count the number of unholy matrices
uint64_t count_unholy_matrices(int rows, uint64_t prev_rows) {
    // Base case: if there are no more rows to add, check if the matrix is unholy
    if (rows == 0) {
        return is_unholy(prev_rows) ? 1 : 0;
    }

    // Initialize the count of unholy matrices
    uint64_t count = 0;

    // Enumerate all possible next two rows
    for (uint16_t next_two_rows = 0; next_two_rows < (1 << 16); next_two_rows++) {
        // Add the next two rows to the previous rows
        uint64_t new_rows = (prev_rows << 16) | next_two_rows;

        // Recurse on the number of rows
        count += count_unholy_matrices(rows - 2, new_rows);
    }

    return count;
}

int main() {
    // Call the recursive function with the initial number of rows and print the result
    uint64_t count = count_unholy_matrices(MATRIX_SIZE, 0);
    printf("Total number of unholy matrices: %llu\n", count);
    return 0;
}
Note: This program uses a recursive approach to count the number of unholy matrices, which may cause a stack overflow for large inputs. To avoid this, you can use a dynamic programming approach with memoization to store intermediate results.

Extract Code

I extracted the following code from that output: 

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

// Define the size of the matrix
#define MATRIX_SIZE 8

// Define the mask for the first row
#define FIRST_ROW_MASK 0xFF

// Define the mask for the second row
#define SECOND_ROW_MASK 0xFF00

// Function to check if a matrix is unholy
bool is_unholy(uint64_t matrix) {
    // Iterate over each row
    for (int i = 0; i < MATRIX_SIZE; i++) {
        // Get the current row
        uint64_t row = (matrix >> (i * 8)) & 0xFF;
        
        // Check for isolated 1s in the current row
        for (int j = 0; j < MATRIX_SIZE; j++) {
            // Check if the current bit is 1
            if ((row >> j) & 1) {
                // Check if there is no adjacent 1 in the same row or in the adjacent rows
                if (!(row >> (j + 1) & 1) && !(row >> (j - 1) & 1) &&
                     !(i > 0 && (matrix >> ((i - 1) * 8 + j)) & 1) &&
                     !(i < MATRIX_SIZE - 1 && (matrix >> ((i + 1) * 8 + j)) & 1)) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Recursive function to count the number of unholy matrices
uint64_t count_unholy_matrices(int rows, uint64_t prev_rows) {
    // Base case: if there are no more rows to add, check if the matrix is unholy
    if (rows == 0) {
        return is_unholy(prev_rows) ? 1 : 0;
    }

    // Initialize the count of unholy matrices
    uint64_t count = 0;

    // Enumerate all possible next two rows
    for (uint16_t next_two_rows = 0; next_two_rows < (1 << 16); next_two_rows++) {
        // Add the next two rows to the previous rows
        uint64_t new_rows = (prev_rows << 16) | next_two_rows;

        // Recurse on the number of rows
        count += count_unholy_matrices(rows - 2, new_rows);
    }

    return count;
}

int main() {
    // Call the recursive function with the initial number of rows and print the result
    uint64_t count = count_unholy_matrices(MATRIX_SIZE, 0);
    printf("Total number of unholy matrices: %llu\n", count);
    return 0;
}

Run Code Interpreter

Running the following program: 

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

// Define the size of the matrix
#define MATRIX_SIZE 8

// Define the mask for the first row
#define FIRST_ROW_MASK 0xFF

// Define the mask for the second row
#define SECOND_ROW_MASK 0xFF00

// Function to check if a matrix is unholy
bool is_unholy(uint64_t matrix) {
    // Iterate over each row
    for (int i = 0; i < MATRIX_SIZE; i++) {
        // Get the current row
        uint64_t row = (matrix >> (i * 8)) & 0xFF;
        
        // Check for isolated 1s in the current row
        for (int j = 0; j < MATRIX_SIZE; j++) {
            // Check if the current bit is 1
            if ((row >> j) & 1) {
                // Check if there is no adjacent 1 in the same row or in the adjacent rows
                if (!(row >> (j + 1) & 1) && !(row >> (j - 1) & 1) &&
                     !(i > 0 && (matrix >> ((i - 1) * 8 + j)) & 1) &&
                     !(i < MATRIX_SIZE - 1 && (matrix >> ((i + 1) * 8 + j)) & 1)) {
                    return false;
                }
            }
        }
    }
    return true;
}

// Recursive function to count the number of unholy matrices
uint64_t count_unholy_matrices(int rows, uint64_t prev_rows) {
    // Base case: if there are no more rows to add, check if the matrix is unholy
    if (rows == 0) {
        return is_unholy(prev_rows) ? 1 : 0;
    }

    // Initialize the count of unholy matrices
    uint64_t count = 0;

    // Enumerate all possible next two rows
    for (uint16_t next_two_rows = 0; next_two_rows < (1 << 16); next_two_rows++) {
        // Add the next two rows to the previous rows
        uint64_t new_rows = (prev_rows << 16) | next_two_rows;

        // Recurse on the number of rows
        count += count_unholy_matrices(rows - 2, new_rows);
    }

    return count;
}

int main() {
    // Call the recursive function with the initial number of rows and print the result
    uint64_t count = count_unholy_matrices(MATRIX_SIZE, 0);
    printf("Total number of unholy matrices: %llu\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