From Gossip@caterpillar

Algorithm Gossip: 老鼠走迷官（一）

說明

老鼠走迷宮是遞迴求解的基本題型，我們在二維陣列中使用2表示迷宮牆壁，使用1來表示老鼠的行走路徑，試以程式求出由入口至出口的路徑。

解法

老鼠的走法有上、左、下、右四個方向，在每前進一格之後就選一個方向前進，無法前進時退回選擇下一個可前進方向，如此在陣列中依序測試四個方向，直到走到出口為止，這是遞迴的基本題，請直接看程式應就可以理解。

演算法

Procedure GO(maze[]) [
    VISIT(maze, STARTI, STARTJ);
]
    
Procedure VISIT(maze[], i, j) [
    maze[i][j] = 1; 

    IF(i == ENDI AND j == ENDJ) 
        success = TRUE; 

    IF(success != TRUE AND maze[i][j+1] == 0)
        VISIT(maze, i, j+1); 
    IF(success != TRUE AND maze[i+1][j] == 0)
        VISIT(maze, i+1, j); 
    IF(success != TRUE AND maze[i][j-1] == 0)
        VISIT(maze, i, j-1); 
    if(success != TRUE AND maze[i-1][j] == 0)
        VISIT(maze, i-1, j); 

    IF(success != TRUE) 
        maze[i][j] = 0; 
]

實作

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

int visit(int, int); 

int maze[7][7] = {{2, 2, 2, 2, 2, 2, 2}, 
                  {2, 0, 0, 0, 0, 0, 2}, 
                  {2, 0, 2, 0, 2, 0, 2}, 
                  {2, 0, 0, 2, 0, 2, 2}, 
                  {2, 2, 0, 2, 0, 2, 2}, 
                  {2, 0, 0, 0, 0, 0, 2}, 
                  {2, 2, 2, 2, 2, 2, 2}}; 

int startI = 1, startJ = 1;  // 入口
int endI = 5, endJ = 5;  // 出口
int success = 0;

int main(void) { 
    int i, j; 

    printf("顯示迷宮：\n"); 
    for(i = 0; i < 7; i++) { 
        for(j = 0; j < 7; j++) 
            if(maze[i][j] == 2) 
                printf("█"); 
            else 
                printf("  "); 
        printf("\n"); 
    } 

    if(visit(startI, startJ) == 0)
        printf("\n沒有找到出口！\n"); 
    else { 
        printf("\n顯示路徑：\n"); 
        for(i = 0; i < 7; i++) { 
            for(j = 0; j < 7; j++) { 
                if(maze[i][j] == 2) 
                    printf("█"); 
                else if(maze[i][j] == 1) 
                    printf("◇"); 
                else 
                    printf("  "); 
            } 
            printf("\n"); 
        } 
    } 

    return 0; 
} 

int visit(int i, int j) { 
    maze[i][j] = 1; 

    if(i == endI && j == endJ)
        success = 1; 

    if(success != 1 && maze[i][j+1] == 0) visit(i, j+1); 
    if(success != 1 && maze[i+1][j] == 0) visit(i+1, j); 
    if(success != 1 && maze[i][j-1] == 0) visit(i, j-1); 
    if(success != 1 && maze[i-1][j] == 0) visit(i-1, j); 

    if(success != 1) 
        maze[i][j] = 0; 
    
    return success; 
}

Java

public class Mouse {
    private int startI, startJ;  // 入口 
    private int endI, endJ;  // 出口
    private boolean success = false;
    
    public static void main(String[] args) {
        int[][] maze = {{2, 2, 2, 2, 2, 2, 2}, 
                        {2, 0, 0, 0, 0, 0, 2}, 
                        {2, 0, 2, 0, 2, 0, 2}, 
                        {2, 0, 0, 2, 0, 2, 2}, 
                        {2, 2, 0, 2, 0, 2, 2}, 
                        {2, 0, 0, 0, 0, 0, 2}, 
                        {2, 2, 2, 2, 2, 2, 2}};
        
        System.out.println("顯示迷宮："); 
        for(int i = 0; i < maze.length; i++) { 
            for(int j = 0; j < maze[0].length; j++) 
                if(maze[i][j] == 2) 
                    System.out.print("█"); 
                else 
                    System.out.print("  "); 
            System.out.println(); 
        }

        Mouse mouse = new Mouse();
        mouse.setStart(1, 1);
        mouse.setEnd(5, 5);
        
        if(!mouse.go(maze)) {
            System.out.println("\n沒有找到出口！");
        }
        else {
            System.out.println("\n找到出口！");
            for(int i = 0; i < maze.length; i++) { 
                for(int j = 0; j < maze[0].length; j++) { 
                    if(maze[i][j] == 2) 
                        System.out.print("█"); 
                    else if(maze[i][j] == 1) 
                        System.out.print("◇"); 
                    else 
                        System.out.print("  "); 
                } 
                System.out.println(); 
            }            
        }
    }
    
    public void setStart(int i, int j) {
        this.startI = i;
        this.startJ = j;
    }
    
    public void setEnd(int i, int j) {
        this.endI = i;
        this.endJ = j;
    }
    
    public boolean go(int[][] maze) {
        return visit(maze, startI, startJ);
    }
    
    private boolean visit(int[][] maze, int i, int j) {
        maze[i][j] = 1; 

        if(i == endI && j == endJ) 
            success = true; 

        if(!success && maze[i][j+1] == 0) 
            visit(maze, i, j+1); 
        if(!success && maze[i+1][j] == 0)
            visit(maze, i+1, j); 
        if(!success && maze[i][j-1] == 0)
            visit(maze, i, j-1); 
        if(!success && maze[i-1][j] == 0)
            visit(maze, i-1, j); 

        if(!success) 
            maze[i][j] = 0; 
        
        return success; 
    }
}