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 < 9; i++) {
for(j = 0; j < 9; 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;
}
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;
}
}
|
|