LeetCode 778 Swim in Rising Water (二分 + DFS)

On an N x N grid, each square grid[i][j]represents the elevation at that point (i,j).

Now rain starts to fall. At time t, the depth of the water everywhere is t. You can swim from a square to another 4-directionally adjacent square if and only if the elevation of both squares individually are at most t. You can swim infinite distance in zero time. Of course, you must stay within the boundaries of the grid during your swim.

You start at the top left square (0, 0). What is the least time until you can reach the bottom right square (N-1, N-1)?

Example 1:

Input: [[0,2],[1,3]]
Output: 3
Explanation:
At time 0, you are in grid location(0, 0).You cannot go anywhere else because 4-directionally adjacent neighbors have a higher elevation than t = 0.You cannot reach point(1, 1) until time 3.When the depth of water is 3, we can swim anywhere inside the grid.

Example 2:

Input: [[0,1,2,3,4],[24,23,22,21,5],[12,13,14,15,16],[11,17,18,19,20],[10,9,8,7,6]]
Output: 16
Explanation:
 0  1  2  3  4
24 23 22 21  5
12 13 14 15 16
11 17 18 19 20
10  9  8  7  6

The final route is marked in bold.
We need to wait until time 16 so that (0, 0) and (4, 4) are connected.

Note:

1. 2 <= N <= 50.
2. grid[i][j] is a permutation of [0, ..., N*N - 1].

题目链接：https://leetcode.com/problems/swim-in-rising-water/

题目分析：水题，不应该是Hard，首先容易想到二分答案，判定就是一个easy的DFS

3ms，时间击败94.66%

class Solution {
    
    public int[] dx = {0, 1, 0, -1};
    public int[] dy = {1, 0, -1, 0};
    
    public void DFS(int x, int y, int val, boolean[][] vis, int n, int[][] grid) {
        vis[x][y] = true;
        for (int i = 0; i < 4; i++) {
            int xx = x + dx[i];
            int yy = y + dy[i];
            if (xx >= 0 && yy >= 0 && xx < n && yy < n && !vis[xx][yy] && grid[xx][yy] <= val) {
                DFS(xx, yy, val, vis, n, grid);
            }
        }
    }
    
    public boolean judge(int val, boolean[][] vis, int n, int[][] grid) {
        if (grid[0][0] > val || grid[n - 1][n - 1] > val) {
            return false;
        }
        for (int i = 0; i < n; i++) {
            Arrays.fill(vis[i], false);
        }
        DFS(0, 0, val, vis, n, grid);
        return vis[n - 1][n - 1];
    }
    
    public int swimInWater(int[][] grid) {
        int n = grid.length;
        if (n == 0) {
            return 0;
        }
        int ma = n * n - 1;
        if (grid[0][0] == ma || grid[n - 1][n - 1] == ma) {
            return ma;
        }
        boolean[][] vis = new boolean[n][n];
        int l = n, r = ma - 1, mid = 0, ans = 0;
        while (l <= r) {
            mid = (l + r) >> 1;
            if (judge(mid, vis, n, grid)) {
                ans = mid;
                r = mid - 1;
            } else {
                l = mid + 1;
            }
        }
        return ans;
    }
}