Leetcode Maze 总结

There is a ball in a maze with empty spaces and walls. The ball can go through empty spaces by rolling up, down, left or right, but it won't stop rolling until hitting a wall. When the ball stops, it could choose the next direction.

Given the ball's start position, the destination and the maze, determine whether the ball could stop at the destination.

The maze is represented by a binary 2D array. 1 means the wall and 0 means the empty space. You may assume that the borders of the maze are all walls. The start and destination coordinates are represented by row and column indexes.

Maze I  (BFS)

判断是否可以到达 目的地

    public boolean hasPath(int[][] maze, int[] start, int[] destination) {
        int m = maze.length, n = maze[0].length;
        boolean[][] visited = new boolean[m][n];
        int[] dx = new int[] { 0, 0, 1, -1};
        int[] dy = new int[] {-1, 1, 0, 0};
        
        Queue<int[]> queue = new LinkedList<>();
        queue.offer(start);
        visited[start[0]][start[1]] = true;
        
        while (!queue.isEmpty()) {
            int[] curr_pos = queue.poll();
            if (curr_pos[0] == destination[0] && curr_pos[1] == destination[1]) return true;
            
            for (int i = 0; i < 4; i++) {
                int x = curr_pos[0], y = curr_pos[1];
                while (x >= 0 && x < m && y >= 0 && y < n && maze[x][y] == 0) {
                    x += dx[i];
                    y += dy[i];
                }
                x -= dx[i];
                y -= dy[i];
                
                if (!visited[x][y]) {
                    visited[x][y] = true;
                    queue.offer(new int[] {x, y});
                }
            }
            
        }
        return false;

(DFS)

    int[][] dirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
    public boolean hasPath(int[][] maze, int[] start, int[] destination) {
        if (maze == null || maze.length == 0 || maze[0].length == 0) return false;
        return dfs(maze, start, destination, new boolean[maze.length][maze[0].length]);
    }
    
    private boolean dfs(int[][] maze, int[] current, int[] des, boolean[][] visited) {
        if (current[0] == des[0] && current[1] == des[1]) return true;
        int x = current[0], y = current[1];
        int m = maze.length, n = maze[0].length;
        if (x < 0 || x > m || y < 0 || y > n || visited[x][y]) return false;
        visited[x][y] = true;
        for (int i = 0; i < dirs.length; i++) {
            int dx = x, dy = y;
            while (dx >= 0 && dx < m && dy >= 0 && dy < n && maze[dx][dy] == 0) {
                dx += dirs[i][0];
                dy += dirs[i][1];
            }
            int[] pos = new int[] {dx -= dirs[i][0], dy -= dirs[i][1]};
            if (dfs(maze, pos, des, visited)) return true;
        }
        return false;
    }

Maze II

Given the ball's start position, the destination and the maze, find the shortest distance for the ball to stop at the destination. The distance is defined by the number of empty spaces traveled by the ball from the start position (excluded) to the destination (included). If the ball cannot stop at the destination, return -1.

找到 到达目的地的最短路线

(BFS)

public int shortestDistance(int[][] maze, int[] start, int[] destination) {
        Queue<int[]> q = new LinkedList<>();
        int m = maze.length, n = maze[0].length;
        int[][] dist = new int[m][n];
        for (int i = 0; i < m; i++) {
            Arrays.fill(dist[i], Integer.MAX_VALUE);
        }
        int[] dx = new int[] {-1, 0, 1, 0};
        int[] dy = new int[] { 0, 1, 0, -1};
        
        q.offer(start);
        dist[start[0]][start[1]] = 0;
        
        while (!q.isEmpty()) {
            int[] p = q.poll();
            for (int i = 0; i < 4; i++) {
                int x = p[0] + dx[i], y = p[1] + dy[i];
                int cnt = 1;
                
                while (x >=0 && x < m && y >= 0 && y < n && maze[x][y] != 1) {
                    x += dx[i];
                    y += dy[i];
                    cnt++;
                }
                x -= dx[i];
                y -= dy[i];
                cnt--;
                if (dist[p[0]][p[1]] + cnt < dist[x][y]) {
                    dist[x][y] = dist[p[0]][p[1]] + cnt;
                    q.offer(new int[] {x, y});
                }
            }
        }
        return dist[destination[0]][destination[1]] == Integer.MAX_VALUE ? -1 : dist[destination[0]][destination[1]];
    }

Maze III

public String findShortestWay(int[][] maze, int[] ball, int[] hole) {
        int m = maze.length;
        int n = maze[0].length;

        PriorityQueue<Point> pq = new PriorityQueue<Point>();
        Point start = new Point(ball[0], ball[1], 0, "");
        pq.offer(start);
        
        boolean[][] visited = new boolean[m][n];
        String[] directions = {"u", "r", "d", "l"};
        int[][] dirs = {{-1, 0}, {0, 1}, {1, 0}, {0, -1}};
        while(!pq.isEmpty()) {
            Point p = pq.poll();
            if(p.x == hole[0] && p.y == hole[1])
                return p.path;
                
            if(visited[p.x][p.y]) continue;
            visited[p.x][p.y] = true;

            for(int i = 0; i < dirs.length; i++) {
                int x = p.x;
                int y = p.y;
                int len = p.len;
                while(x + dirs[i][0] >= 0 && x + dirs[i][0] < m && y + dirs[i][1] >= 0 && y + dirs[i][1] < n && maze[x + dirs[i][0]][y + dirs[i][1]] != 1 && (x != hole[0] || y != hole[1])) {
                    x += dirs[i][0];
                    y += dirs[i][1];
                    len++;
                }
                
                Point next = new Point(x, y, len, p.path + directions[i]);
                pq.offer(next);
            }
            
        }
        return "impossible";
    }
    
    class Point implements Comparable<Point> {
        int x;
        int y;
        int len;
        String path;
        
        Point(int x, int y) {
            this.x = x;
            this.y = y;
            len = Integer.MAX_VALUE;
            path = "";
        }
        
        Point(int x, int y, int len, String path) {
            this.x = x;
            this.y = y;
            this.len = len;
            this.path = path;
        }
        
        public int compareTo(Point p) {
            return this.len == p.len? this.path.compareTo(p.path) : this.len - p.len;
        }
    }