From Gossip@caterpillar

Algorithm Gossip: 老鼠走迷官（二）

說明

由於迷宮的設計，老鼠走迷宮的入口至出口路徑可能不只一條，如何求出所有的路徑呢？

解法

求所有路徑看起來複雜但其實更簡單，只要在老鼠走至出口時顯示經過的路徑，然後退回上一格重新選擇下一個位置繼續遞迴就可以了，比求出單一路徑還簡單，我們的程式只要作一點修改就可以了。

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) [
        // FIND A ROUTE, PRINT THE ROUTE
    ]

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

    maze[i][j] = 0; 
]

實作

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

void visit(int, int);

int maze[9][9] = {{2, 2, 2, 2, 2, 2, 2, 2, 2},
                  {2, 0, 0, 0, 0, 0, 0, 0, 2},
                  {2, 0, 2, 2, 0, 2, 2, 0, 2},
                  {2, 0, 2, 0, 0, 2, 0, 0, 2},
                  {2, 0, 2, 0, 2, 0, 2, 0, 2},
                  {2, 0, 0, 0, 0, 0, 2, 0, 2},
                  {2, 2, 0, 2, 2, 0, 2, 2, 2},
                  {2, 0, 0, 0, 0, 0, 0, 0, 2},
                  {2, 2, 2, 2, 2, 2, 2, 2, 2}};

int startI = 1, startJ = 1;  // 入口
int endI = 7, endJ = 7;  // 出口

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"); 
    } 

    visit(startI, startJ);

    return 0; 
} 

void visit(int i, int j) {
    int m, n;

    maze[i][j] = 1; 

    if(i == endI && j == endJ) {
        printf("\n顯示路徑：\n");
        for(m = 0; m < 9; m++) {
            for(n = 0; n < 9; n++)
                if(maze[m][n] == 2)
                    printf("█");
                else if(maze[m][n] == 1)
                    printf("◇");
                else
                    printf("  ");
            printf("\n");
        }
    }

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

    maze[i][j] = 0;
}

Java

public class Mouse {
    private int startI, startJ;  // 入口 
    private int endI, endJ;  // 出口
    
    public static void main(String[] args) {
        int maze[][] = {{2, 2, 2, 2, 2, 2, 2, 2, 2},
                        {2, 0, 0, 0, 0, 0, 0, 0, 2},
                        {2, 0, 2, 2, 0, 2, 2, 0, 2},
                        {2, 0, 2, 0, 0, 2, 0, 0, 2},
                        {2, 0, 2, 0, 2, 0, 2, 0, 2},
                        {2, 0, 0, 0, 0, 0, 2, 0, 2},
                        {2, 2, 0, 2, 2, 0, 2, 2, 2},
                        {2, 0, 0, 0, 0, 0, 0, 0, 2},
                        {2, 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(7, 7);
        
        mouse.go(maze);
    }
    
    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 void go(int[][] maze) {
        visit(maze, startI, startJ);
    }
    
    private void visit(int[][] maze, int i, int j) {
        maze[i][j] = 1; 

        if(i == endI && j == endJ) {
            System.out.println("\n找到出口！");
            for(int m = 0; m < maze.length; m++) { 
                for(int n = 0; n < maze[0].length; n++) { 
                    if(maze[m][n] == 2) 
                        System.out.print("█"); 
                    else if(maze[m][n] == 1) 
                        System.out.print("◇"); 
                    else 
                        System.out.print("  "); 
                } 
                System.out.println();
            }
        }

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