蓝桥杯：迷宫

水深无声 2024-03-25 22:24 12阅读 0赞

#### **题目描述** ####

**本题为填空题，只需要算出结果后，在代码中使用输出语句将所填结果输出即可。**

下图给出了一个迷宫的平面图，其中标记为 11 的为障碍，标记为 00 的为可以通行的地方。

010000
    000100
    001001
    110000

迷宫的入口为左上角，出口为右下角，在迷宫中，只能从一个位置走到这 个它的上、下、左、右四个方向之一。

对于上面的迷宫，从入口开始，可以按 DRRURRDDDR 的顺序通过迷宫， 一共 1010 步。其中 �、�、�、�*D*、*U*、*L*、*R* 分别表示向下、向上、向左、向右走。 对于下面这个更复杂的迷宫（3030 行 5050 列），请找出一种通过迷宫的方式，其使用的步数最少，在步数最少的前提下，请找出字典序最小的一个作为答案。

请注意在字典序中 �<�<�<�*D*<*L*<*R*<*U*。

01010101001011001001010110010110100100001000101010
    00001000100000101010010000100000001001100110100101
    01111011010010001000001101001011100011000000010000
    01000000001010100011010000101000001010101011001011
    00011111000000101000010010100010100000101100000000
    11001000110101000010101100011010011010101011110111
    00011011010101001001001010000001000101001110000000
    10100000101000100110101010111110011000010000111010
    00111000001010100001100010000001000101001100001001
    11000110100001110010001001010101010101010001101000
    00010000100100000101001010101110100010101010000101
    11100100101001001000010000010101010100100100010100
    00000010000000101011001111010001100000101010100011
    10101010011100001000011000010110011110110100001000
    10101010100001101010100101000010100000111011101001
    10000000101100010000101100101101001011100000000100
    10101001000000010100100001000100000100011110101001
    00101001010101101001010100011010101101110000110101
    11001010000100001100000010100101000001000111000010
    00001000110000110101101000000100101001001000011101
    10100101000101000000001110110010110101101010100001
    00101000010000110101010000100010001001000100010101
    10100001000110010001000010101001010101011111010010
    00000100101000000110010100101001000001000000000010
    11010000001001110111001001000011101001011011101000
    00000110100010001000100000001000011101000000110011
    10101000101000100010001111100010101001010000001000
    10000010100101001010110000000100101010001011101000
    00111100001000010000000110111000000001000000001011
    10000001100111010111010001000110111010101101111000

**解题思路：BFS+记录路径**

当找到终点时，便停止搜索。

import java.util.LinkedList;
    import java.util.Queue;
    import java.util.Scanner;
    
    public class P3 {
        public static void main(String[] args) {
            Scanner sc=new Scanner(System.in);
            char [][]map=new char[30][50];
            for (int i=0;i<30;i++){
                map[i]=sc.nextLine().toCharArray();
            }
            sc.close();
            
            int[] dx = {1,0,0,-1};
            int[] dy = {0,-1,1,0};
           String []path={"D","L","R","U"};//注意，一定要和x、y的值相匹配
            Queue<Node>queue=new LinkedList<>();
            boolean [][]mark=new boolean[30][50];
            queue.add(new Node(0,0,""));
            mark[0][0]=true;
            while(!queue.isEmpty()){
                Node poll = queue.poll();
                mark[poll.x][poll.y]=true;
    
    
                if(poll.x==29&&poll.y==49){//找到终点
                    System.out.println(poll.s);
                    break;
                }
    
                for (int i = 0; i < 4; i++) {
                    int new_x= poll.x+dx[i];
                    int new_y= poll.y+dy[i];
                    if(new_x>=0&&new_x<30&&new_y>=0&&new_y<50&&mark[new_x][new_y]==false&&map[new_x][new_y]=='0'){
                        queue.add(new Node(new_x,new_y, poll.s+path[i]));//每次入队时，带上前面的路径和自己的路径
                    }
                }
            }
    
        }
    }
    class Node{
        int x;
        int y;
        String s;
    
        Node(int x,int y,String s){
            this.x=x;
            this.y=y;
            this.s=s;
        }
    }

结果：

![947559e7f09a7e9545babc3d7b876fbd.png][]

[947559e7f09a7e9545babc3d7b876fbd.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/25/2bde6921a87a4c2bab198da1e8306937.png