题目描述：

LeetCode 778. Swim in Rising Water

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].

题目大意：

给定长宽为N的二维方阵grid，记grid[x][y] = z表示当时刻t >= z时，x, y可达。

在grid上的移动可以瞬间完成，求从0, 0出发，到达N - 1, N - 1的最短时刻。

解题思路：

二分枚举答案 + 广度优先 / 深度优先搜索

Binary Search + BFS / DFS

Python代码：

class Solution(object):
    def swimInWater(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        N = len(grid)
        ans = N * N
        lo, hi = 0, N * N - 1
        while lo <= hi:
            mi = (lo + hi) / 2
            if self.bfs(grid, mi): hi = mi - 1
            else: lo = mi + 1
        return lo

    def bfs(self, grid, limit):
        if grid[0][0] > limit: return False
        N = len(grid)
        queue = [(0, 0)]
        visits = set(queue)
        while queue:
            x, y = queue.pop(0)
            for dx, dy in zip((1, 0, -1, 0), (0, 1, 0, -1)):
                nx, ny = x + dx, y + dy
                if nx < 0 or nx >= N or ny < 0 \
                    or ny >= N or (nx, ny) in visits \
                    or grid[nx][ny] > limit: continue
                visits.add((nx, ny))
                queue.append((nx, ny))
        return (N - 1, N - 1) in visits

 

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