Max Area of Island

Find the largest connected region of 1s in a binary grid.

grid dfs connected-components matrix

You are given a 2D list `grid` of integers, where each cell is either `0` (water) or `1` (land). An island is a group of connected `1`s. Two cells are connected if they are adjacent horizontally or vertically (not diagonally). The area of an island is the number of `1`s it contains. Write a function `max_area_of_island(grid)` that returns the maximum island area. If there are no islands, return `0`. The grid may be empty or have zero rows/columns.

Constraints

0 <= len(grid) <= 100; 0 <= len(grid[0]) <= 100. The grid is a list of lists of integers, each element is 0 or 1. The function should not modify the input grid. Time complexity should be O(R*C) where R and C are grid dimensions.

Example

['>>> max_area_of_island([[0,0,1,0,0],\n...                   [1,1,1,0,0],\n...                   [0,1,0,0,0],\n...                   [1,1,0,0,0]])\n5', '>>> max_area_of_island([[0,0,0],\n...                   [0,0,0])\n0', '>>> max_area_of_island([[]])\n0']

20 points ~25 min

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Hints

Think about how to traverse all cells that belong to the same island exactly once.

A depth-first search (DFS) can be used to explore an island's area. Mark visited cells to avoid recounting.

Try using recursion or an explicit stack; either works.

Edge case: empty grid or all water should yield 0.

Test Results

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