Problem

You are given a 0-indexed 2D matrix grid of size m x n, where (r, c) represents:

  • A land cell if grid[r][c] = 0, or
  • A water cell containing grid[r][c] fish, if grid[r][c] > 0.

A fisher can start at any water cell (r, c) and can do the following operations any number of times:

  • Catch all the fish at cell (r, c), or
  • Move to any adjacent water cell.

Return the maximum number of fish the fisher can catch if he chooses his starting cell optimally, or 0 if no water cell exists.

An adjacent cell of the cell (r, c), is one of the cells (r, c + 1), (r, c - 1), (r + 1, c) or (r - 1, c) if it exists.

https://leetcode.com/problems/maximum-number-of-fish-in-a-grid/

Example 1:

case1

Input: grid = [[0,2,1,0],[4,0,0,3],[1,0,0,4],[0,3,2,0]]
Output: 7
Explanation: The fisher can start at cell (1,3) and collect 3 fish, then move to cell (2,3) and collect 4 fish.

Example 2:

case2

Input: grid = [[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,1]]
Output: 1
Explanation: The fisher can start at cells (0,0) or (3,3) and collect a single fish.

Constraints:

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 10
  • 0 <= grid[i][j] <= 10

Test Cases

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class Solution:
    def findMaxFish(self, grid: List[List[int]]) -> int:
solution_test.py
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import pytest

from solution import Solution


@pytest.mark.parametrize('grid, expected', [
    ([[0,2,1,0],[4,0,0,3],[1,0,0,4],[0,3,2,0]], 7),
    ([[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,1]], 1),
])
@pytest.mark.parametrize('sol', [Solution()])
def test_solution(sol, grid, expected):
    assert sol.findMaxFish(grid.copy()) == expected

Thoughts

跟 200. Number of Islands 类似，同样是漫填充算法。

扫描整个区域，如果是陆地则跳过；如果是水，则把鱼收走，并把此位置标记为陆地，将此位置放入栈。每次出栈的位置，都继续检查其上下左右的位置，做同样的判断和处理。

时间复杂度 O(m * n)，空间复杂度 O(m * n)（栈的大小）。

Code

solution.py
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class Solution:
    def findMaxFish(self, grid: list[list[int]]) -> int:
        max2 = lambda a, b: a if a >= b else b
        m = len(grid)
        n = len(grid[0])
        dirs = [(-1, 0), (1, 0), (0, -1), (0, 1)]
        max_fish = 0

        for i in range(m):
            for j in range(n):
                if grid[i][j] == 0:
                    continue

                fish = grid[i][j]
                grid[i][j] = 0
                stack = [(i, j)]
                while stack:
                    r, c = stack.pop()
                    for dr, dc in dirs:
                        nr, nc = r + dr, c + dc
                        if 0 <= nr < m and 0 <= nc < n and grid[nr][nc] != 0:
                            fish += grid[nr][nc]
                            grid[nr][nc] = 0
                            stack.append((nr, nc))

                max_fish = max2(max_fish, fish)

        return max_fish
medium
参考资料
许可协议

本文除了题目描述（Problem）部分之外，其他内容由 Calf 原创，采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。

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