triomino拼图问题c语言

Triomino拼图问题是一个经典的计算机科学问题，它可以通过C语言来实现。简单来说，Triomino拼图问题是将一个2^n * 2^n的正方形分成L形态的三格块，然后用特定的方式填充这些块，使得整个正方形没有留下任何空白。以下是一个简单的C语言程序，用于解决Triomino拼图问题。

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

#define EMPTY -1
#define BLOCK 0
#define L_BLOCK 1

void triomino(int **board, int size, int row, int col, int missing_row, int missing_col, int type);

int main() {
    int size, row, col;
    printf("Enter the size of the board: ");
    scanf("%d", &size);
    printf("Enter the row position of the missing square: ");
    scanf("%d", &row);
    printf("Enter the column position of the missing square: ");
    scanf("%d", &col);

    int **board = (int **)malloc(size * sizeof(int *));
    for (int i = 0; i < size; i++)
        board[i] = (int *)malloc(size * sizeof(int));

    // 初始化棋盘
    for (int i = 0; i < size; i++)
        for (int j = 0; j < size; j++)
            board[i][j] = EMPTY;

    // 放置缺失的方块
    board[row][col] = BLOCK;

    // 解决问题
    triomino(board, size, 0, 0, row, col, L_BLOCK);

    // 打印解决方案
    for (int i = 0; i < size; i++) {
        for (int j = 0; j < size; j++)
            printf("%2d ", board[i][j]);
        printf("\n");
    }

    // 释放内存
    for (int i = 0; i < size; i++)
        free(board[i]);
    free(board);

    return 0;
}

void triomino(int **board, int size, int row, int col, int missing_row, int missing_col, int type) {
    if (size == 1)
        return;

    int half_size = size / 2;
    int center_row = row + half_size - 1;
    int center_col = col + half_size - 1;

    // 放置L形块
    int block_type = type;
    if (missing_row < center_row) {
        if (missing_col < center_col) {
            board[center_row][center_col + 1] = block_type;
            board[center_row + 1][center_col] = block_type;
        }
        else {
            board[center_row][center_col] = block_type;
            board[center_row + 1][center_col] = block_type;
        }
    }
    else {
        if (missing_col < center_col) {
            board[center_row][center_col + 1] = block_type;
            board[center_row][center_col] = block_type;
        }
        else {
            board[center_row + 1][center_col] = block_type;
            board[center_row][center_col] = block_type;
        }
    }

    // 递归解决四个子问题
    triomino(board, half_size, row, col, center_row, center_col, type);
    triomino(board, half_size, row, center_col + 1, center_row, center_col + 1, type);
    triomino(board, half_size, center_row + 1, col, center_row + 1, center_col, type);
    triomino(board, half_size, center_row + 1, center_col + 1, center_row + 1, center_col + 1, type);

    // 处理缺失的方块
    if (missing_row <= center_row && missing_col <= center_col)
        triomino(board, half_size, row, col, missing_row, missing_col, L_BLOCK);
    else if (missing_row <= center_row && missing_col > center_col)
        triomino(board, half_size, row, center_col + 1, missing_row, missing_col, L_BLOCK);
    else if (missing_row > center_row && missing_col <= center_col)
        triomino(board, half_size, center_row + 1, col, missing_row, missing_col, L_BLOCK);
    else
        triomino(board, half_size, center_row + 1, center_col + 1, missing_row, missing_col, L_BLOCK);
}

该程序使用递归算法来解决Triomino拼图问题。它首先初始化棋盘，并将缺失的方块放置在适当的位置。然后，它使用triomino函数来递归解决问题。该函数将棋盘分成四个子问题，并在中心处放置L形块。然后，它递归地解决四个子问题，并在必要时继续处理缺失的方块。最后，该程序打印出解决方案，并释放内存。