Max Area of Island

Problem

You are given an m x n binary matrix grid. An island is a group of 1's connected 4-directionally. Return the maximum area of an island in grid. If there is no island, return 0.

Examples

The brute-force approach

For every land cell, count the size of its island by exploring all connected land cells. Track visited cells so you don't loop. Take the maximum across all starting cells.

max_area = 0
for each cell (r, c) where grid[r][c] == 1:
    area = count_island_size(r, c, visited)
    max_area = max(max_area, area)
return max_area

If you don't share visited tracking across island explorations, you re-explore the same island multiple times (once per cell in that island). That's O((m×n)²) in the worst case.

Spotting the pattern

This is a Graph Traversal problem. The key question to ask yourself:

How do I measure the size of each island, and how do I make sure I only measure each island once?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.