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、RD、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
运行限制
最大运行时间:1s
最大运行内存: 128M
解题思路:这一题的解题要用BFS去做,DFS找不出最短的路径,时间复杂度很高, BFS是一步一步去查找的,当查找到出口时,其步数一定是最少的, 上下左右的尝试我们可以按照字典序大小进行操作,这样可以确保在步数相同时 字典序也是最小的
代码如下:(BFS参考视频)
import java.util.LinkedList; import java.util.Queue; import java.util.Scanner; public class maze2 { //数据存放的数组 static String[][] arr1 = new String[30][50]; //代表上下左右四个方向 static int[][] direction1 = {{1, 0}, {0, -1}, {0, 1}, {-1, 0}}; static String[] direction2 = {"D", "L", "R", "U"}; //队列,先进先出 static Queue<Node1> q = new LinkedList<Node1>(); public static void main(String[] args) { Scanner scanner = new Scanner(System.in); //读取数据 for (int i = 0; i < 30; i++) { arr1[i] = scanner.next().split(""); } //队列q中压入起始结点 q.offer(new Node1(0, 0, "")); //表示该节点已经走过了 arr1[0][0] = "1"; BFS(); } static void BFS(){ int dx, dy; while (!q.isEmpty()) { //队首周围尚未压入队列的可抵达的结点压入队列 Node1 head = q.poll(); for (int i = 0; i < 4; i++) { dx = head.x + direction1[i][0]; dy = head.y + direction1[i][1]; if (dx == 29 && dy == 49) { System.out.println(head.s + direction2[i]); return; }; //处理边界问题,放置数组下标越界 if (dx >= 0 && dy >= 0 && dx <= 29 && dy <= 49 && "0".equals(arr1[dx][dy])){ q.offer(new Node1(dx, dy, head.s+direction2[i])); arr1[dx][dy] = "1"; } } } } } class Node1{ //坐标 int x,y; //s代表开始结点到当前结点的路径 String s; public Node1(int x, int y, String s) { this.x = x; this.y = y; this.s = s; } }