省赛真题-迷宫

不念不忘少年蓝@ 2022-12-15 11:12 175阅读 0赞

## 试题 E: 迷宫 ##

【问题描述】  
下图给出了一个迷宫的平面图，其中标记为 1 的为障碍，标记为 0 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 10 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（30 行 50 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。（如果你把以下文字复制到文本文件中，请务必检查复制的内容是否与文档中的一致。在试题目录下有一个文件 maze.txt，内容与下面的文本相同）

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

【答案】  
DDDDRRURRRRRRDRRRRDDDLDDRDDDDDDDDDDDDRDDRRRURRUURRDDDDRDRRRRRRDRRURRDDDRRRRUURUUUUUUULULLUUUURRRRUULLLUUUULLUUULUURRURRURURRRDDRRRRRDDRRDDLLLDDRRDDRDDLDDDLLDDLLLDLDDDLDDRRRRRRRRRDDDDDDRR

【代码】

package 省赛题;
    
    import 递归.Farm;
    
    import java.util.LinkedList;
    import java.util.Queue;
    import java.util.Scanner;
    
    
    class Node{
        
        int step;
        String path;
        int x,y;
    
    }
    
    public class 迷宫 {
        
        static int n,m;
        static char[][] maze=new char[60][60];
        static boolean[][] vis=new boolean[60][60];
        static int[] X={
        1,0,0,-1};
        static int[] Y={
        0,-1,1,0};
        static String[] d={
        "D","L","R","U"};
        static boolean check(int x,int y){
        
            if (x<1 || x>n ||y<1 ||y>m){
        
                return false;
            }
            if (vis[x][y]||maze[x][y]=='1'){
        
                return false;
            }
            return true;
        }
        public static void bfs(){
        
            Queue<Node> q=new LinkedList<Node>();
            Node node=new Node();
            node.step=0;
            node.path="";
            node.x=1;
            node.y=1;
            q.offer(node);
            while (!q.isEmpty()){
        
                Node top=q.poll();
                vis[top.x][top.y]=true;
                if (top.x==n&&top.y==m){
        
                    System.out.println(top.step+" "+top.path);
                    return;
                }
                for (int i = 0; i <4 ; i++) {
        
                    int newX=top.x+X[i];
                    int newY=top.y+Y[i];
                    if (check(newX,newY)){
        
                        Node temp=new Node();
                        temp.step=top.step+1;
                        temp.path=top.path+d[i];
                        temp.x=newX;
                        temp.y=newY;
                        q.offer(temp);
                    }
                }
            }
        }
    
    
        public static void main(String[] args) {
        
            Scanner scanner=new Scanner(System.in);
            n=scanner.nextInt();
            m=scanner.nextInt();
            for (int i = 1; i <=n ; i++) {
        
                String temp=scanner.next();
                for (int j = 1; j <=m ; j++) {
        
                    maze[i][j]=temp.charAt(j);
                }
            }
            bfs();
        }
    
    }