Number of Islands

Problem

Given an m x n 2D binary grid which represents a map of '1's (land) and '0's (water), return the number of islands.

Examples

The brute-force approach

For every '1' cell, determine whether it belongs to an island you've already counted. To check this, trace every path from that cell back to any previously counted starting point.

# Checking if two cells are in the same island without tracking visited state
# requires re-exploring from a known cell each time. O(m×n) per candidate.
count = 0
for each cell (r, c):
    if grid[r][c] == '1' and cell not yet claimed:
        for each previously found island:
            if can_reach(r, c, island_start):  # ← O(m×n) each
                claim cell
                break
        else:
            count += 1

Checking reachability without tracking visited cells costs O(m×n) per candidate cell, total O((m×n)²). The key insight is that once you find an island, you can claim every cell in it at the same time.

Spotting the pattern

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

How do I visit every cell in an island exactly once, mark it as seen, and then count how many separate islands I started from?

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.