What is the optimal time complexity of solving Max Area of Island?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Max Area of Island?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Max Area of Island?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Max Area of Island?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Max Area of Island

Learn how to solve the 'Max Area of Island' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

You are given an m x n binary matrix grid. An island is a group of 1s (representing land) connected 4-directionally (horizontal or vertical). You may assume all four edges of the grid are surrounded by water.

The area of an island is the number of cells with a value 1 in the island.

Return the maximum area of an island in grid. If there is no island, return 0.

Write a function maxAreaOfIsland(grid: List[List[int]]) -> int.

Constraints

•m == len(grid)
•n == len(grid[i])
•1 <= m, n <= 50
•grid[i][j] is 0 or 1

Examples

Example 1

Input

grid = [[0,0,1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,1,1,0,1,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,1,1,0,0,0],[0,0,0,0,0,0,0,1,1,0,0,0,0]]

Output

Explanation

The maximum area of an island is 6, located in the lower-right part of the grid.

Example 2

Input

grid = [[0,0,0,0,0,0,0,0]]

Output

Explanation

There are no islands in the grid, so the max area is 0.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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