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花花酱 LeetCode 2658. Maximum Number of Fish in a Grid

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

  • land cell if grid[r][c] = 0, or
  • 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.

Example 1:

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:

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. 


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

Solution: Connected Component

Similar to 花花酱 LeetCode 695. Max Area of Island

Find the connected component that has the max sum.

Time complexity: O(mn)
Space complexity: O(mn)


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