递归问题:一穿越迷宫

迷宫问题的解决涉及到大量的试探和失败：选择一条路径，在无法前景时折回，并选择其他还未尝试过的路径。使用递归能够很好的处理这类问题。

package com.chingcloud.test01;

public class Maze {
private final int TRIED = 3 ;
private final int PATH = 7 ;
private int[][] grid = {{1,1,1,0,1,1,0,0,0,1,1,1,1},
{1,0,1,1,1,0,1,1,1,1,0,0,1},
{0,0,0,0,1,0,1,0,1,0,1,0,0},
{1,1,1,0,1,1,1,0,1,0,1,1,1},
{1,0,1,0,0,0,0,1,1,1,0,0,1},
{1,0,1,1,1,1,1,1,0,1,1,1,1},
{1,0,0,0,0,0,0,0,0,0,0,0,0},
{1,1,1,1,1,1,1,1,1,1,1,1,1}} ;

public boolean traverse(int row,int column){
boolean done = false ;
if(valid(row,column)){
grid[row][column] = TRIED ;
if(row == grid.length-1 && column == grid[0].length-1){
done = true ;
}else{
done = traverse(row+1,column) ;
if(!done){
done = traverse(row,column+1) ;
}
if(!done){
done = traverse(row-1,column) ;
}
if(!done){
done = traverse(row,column-1) ;
}
}
if(done){
grid[row][column] = PATH ;
}
}
return done ;
}
public boolean valid(int row,int column){
boolean result = false ;
if(row>=0 && row<grid.length && column>=0 && column<grid[row].length){
if(grid[row][column]==1){
result = true ;
}
}
return result ;
}
public String toString(){
String result = "\n" ;
for(int row=0;row<grid.length;row++){
for(int column=0;column<grid[row].length;column++){
result += grid[row][column] + "" ;
}
result += "\n" ;
}
return result ;
}
public static void main(String[] args) {
Maze labyrinth = new Maze() ;
System.out.println(labyrinth);
if(labyrinth.traverse(0,0)){
System.out.println("The maze was successfully traversed!");
}else{
System.out.println("There is no possible path.");
}
System.out.println(labyrinth);
}

}

result

1110110001111

1011101111001

0000101010100

1110111010111

1010000111001

1011111101111

1000000000000

1111111111111

The maze was successfully traversed!

7770110001111

3077707771001

0000707070300

7770777070333

7070000773003

7077777703333

7000000000000

7777777777777