有限网格中的路径查找

Question

我有一个 7x7 网格（一个城市）。我想从起点 (x1, y1) 到终点 (x2, y2) 并以逗号分隔的多个 (x, y) 字符串的形式将 path 显示为输出。我想使用 RECURSION 执行此操作，如果路径存在则输出 true，否则输出 false。
我该怎么做？我正在考虑制作 4 种检查 4 个方向的方法。任何意见将不胜感激。

现在，我刚刚实现了我的类的构造函数：-

    map = new boolean[row][column];

    for(int i = 0; i < 7; i++)
    {
        for(int j = 0; j < 7; j++)
        { 
            map[i][j] = false; 
        }
    }

Answer 1

import java.io.PrintStream;

/**
 * Dev Parzival
 * Date : 27/10/2020 Time : 18:28
 * I have a confidence about my life that comes from standing tall on my own two feet.
 */

public class Path {
    static PrintStream out=System.out;
    static boolean pathfound=false;
    //////////Main/////////
    public static void main(String $[]){
        boolean arr[][]=new boolean[5][5];
        for(int i=0;i<arr.length;i++)
            for(int j=0;j<arr[0].length;j++) {
                if (i==0)
                    arr[i][j] = true;
                if(j==arr[0].length-1)
                    arr[i][j]=true;
            }
        travel(arr,0,0,arr.length-1,arr[0].length-1);
        if(pathfound)
            out.println("Path is found");
        else
            out.println("Path is not found");
    }
    
    static boolean travel(boolean a[][],int r,int c,int targetR,int targetC){
    //Target is found
    if(r==targetR && c==targetC){
        pathfound=true;
    }
    //South
    if(!pathfound && r+1<a.length)
        if(a[r+1][c]){
            a[r+1][c]=false;
            pathfound=travel(a,r+1,c,targetR,targetC);
        }
    //North
    if(!pathfound && r-1>=0)
        if(a[r-1][c]){
            a[r-1][c]=false;
            pathfound=travel(a,r-1,c,targetR,targetC);
        }
    //East
    if(!pathfound && c+1<a[0].length)
        if(a[r][c+1]){
            a[r][c+1]=false;
            pathfound=travel(a,r,c+1,targetR,targetC);
        }
    //West
    if(!pathfound && c-1>=0)
        if(a[r][c-1]){
            a[r][c-1]=false;
            pathfound=travel(a,r,c-1,targetR,targetC);
        }
        if(pathfound)
            out.println(r+" "+c);
        return pathfound;
    }
}

我会建议复制原始数组，这样值就不会被修改。 我已经测试了上面的代码工作正常。这种方法被称为flood fill。在graph.中搜索更多关于depth first search的信息

Answer 2

import java.io.PrintStream;

/**
 * Dev Parzival
 * Date : 27/10/2020 Time : 18:28
 * I have a confidence about my life that comes from standing tall on my own two feet.
 */

public class Path {
    static PrintStream out=System.out;
    static boolean pathfound=false;
    //////////Main/////////
    public static void main(String $[]){
        boolean arr[][]=new boolean[5][5];
        for(int i=0;i<arr.length;i++)
            for(int j=0;j<arr[0].length;j++) {
                if (i==j)
                    arr[i][j] = true;
//                if(j==arr[0].length-1)
//                    arr[i][j]=true;
            }
        travel(arr,0,0,arr.length-1,arr[0].length-1);
        if(pathfound)
            out.println("Path is found");
        else
            out.println("Path is not found");
    }

    static boolean travel(boolean a[][],int r,int c,int targetR,int targetC){

        //Target is found
        if(r==targetR && c==targetC){
            pathfound=true;
        }
        //South
        if(!pathfound && r+1<a.length)
            if(a[r+1][c]){
                a[r+1][c]=false;
                pathfound=travel(a,r+1,c,targetR,targetC);
            }
        //North
        if(!pathfound && r-1>=0)
            if(a[r-1][c]){
                a[r-1][c]=false;
                pathfound=travel(a,r-1,c,targetR,targetC);
            }
        //East
        if(!pathfound && c+1<a[0].length)
            if(a[r][c+1]){
                a[r][c+1]=false;
                pathfound=travel(a,r,c+1,targetR,targetC);
            }
        //West
        if(!pathfound && c-1>=0)
            if(a[r][c-1]){
                a[r][c-1]=false;
                pathfound=travel(a,r,c-1,targetR,targetC);
            }
        //North-West
        if(!pathfound && c-1>=0 && r-1>=0)
            if(a[r-1][c-1]){
                a[r-1][c-1]=false;
                pathfound=travel(a,r-1,c-1,targetR,targetC);
            }
        //Noth-East
        if(!pathfound && c+1<a[0].length && r-1>=0)
            if(a[r-1][c+1]){
                a[r-1][c+1]=false;
                pathfound=travel(a,r-1,c+1,targetR,targetC);
            }
        //South-East
        if(!pathfound && c+1<a[0].length && r+1<a.length)
            if(a[r+1][c+1]){
                a[r+1][c+1]=false;
                pathfound=travel(a,r+1,c+1,targetR,targetC);
            }
        //South-West
        if(!pathfound && c-1>=0 && r+1<a.length)
            if(a[r+1][c-1]){
                a[r+1][c-1]=false;
                pathfound=travel(a,r+1,c-1,targetR,targetC);
            }
        //Print the cell position
        if(pathfound)
            out.println(r+" "+c);
        return pathfound;
    }
}

如果路径存在，上述代码将在起始单元格和目标单元格之间找到路径。

它生成的输出：

4 4
3 3
2 2
1 1
0 0
Path is found