How do you approach Max Area of Island?

Run a flood-fill (DFS or BFS) from every unvisited land cell.

What are common mistakes on Max Area of Island?

Building the adjacency list in one direction on an undirected graph. Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest. Ignoring self-loops and parallel edges when the constraints allow them.

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Max Area of Island

MediumAlgorithms

Description

You are given an `m x n` binary matrix `grid`. An **island** is a group of `1`s (land) connected 4-directionally (horizontal or vertical). Return the **area** of the largest island. If there is no island, return `0`.

Example 1

Input: grid = [[0,0,1,0],[0,1,1,0],[0,0,0,0]]

Output: 3

Explanation: The single island has 3 connected cells.

Example 2

Input: grid = [[0,0],[0,0]]

Output: 0

Explanation: No land cells.

Constraints

- m == grid.length - n == grid[i].length - 1 <= m, n <= 50 - grid[i][j] is 0 or 1

Max Area of Island: approach, complexity and pitfalls

A medium graphs problem, graded against 5 test cases (3 of them hidden).

The pattern: Graphs

Nodes and edges - traversal, connectivity, cycles, and shortest paths.

Reach for it when you see: Explicit edges, a grid treated as a graph, or dependencies between items.

More Graphsproblems →

If you are stuck

Show the 3-step hint ladder

Run a flood-fill (DFS or BFS) from every unvisited land cell.
Sink each visited cell (set it to 0) so you never count it twice.
Track the maximum area returned across all starting cells.

The optimal approach

Show the approach: The approach

DFS flood-fill. From each land cell, recurse into its four neighbors, marking cells as visited by zeroing them, and sum the cells reached. The largest such sum is the answer.

Time: O(m·n) - each cell is visited once.

Space: O(m·n) recursion stack in the worst case.

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Duplicate values. Repeated values appear in the input, so any logic that assumes distinct elements - or that skips over equal neighbours - is exercised.
Zero. Zero appears in the input, which is the value most likely to break a truthiness check used in place of an explicit comparison.

Common Graphs mistakes

These apply to the pattern as a whole, not just this problem.

Building the adjacency list in one direction on an undirected graph.
Assuming the graph is connected. Most inputs allow several components, and one traversal from node 0 misses the rest.
Ignoring self-loops and parallel edges when the constraints allow them.