How do you count the number of islands in a grid? | Interview Question

Q: How do you count the number of islands in a grid?

**Target Audience:** Beginners preparing for coding interviews — you should know 2-D arrays, and ideally what BFS and DFS are **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged `📌 Interview term:` with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output you see in the **Verified** section is copied from that run. ## 1. Why This Even Matters — A Story First You are handed a printed map of an archipelago drawn on squared paper: every square is either land or sea. Your job is to count the islands, and you have a highlighter. You read the map like a book, left to right, top to bottom. The first time your eye lands on an un-highlighted land square, you say "that's a new island!", add one to your count, and then highlight *every* land squar

The problem

Question presented to candidate: "You are given a 2-D grid of '1's (land) and '0's (water). An island is a group of land cells connected horizontally or vertically. Write a Python function that returns the number of islands."

What a strong answer should cover:

Model the grid as an implicit graph; an island is a connected component of land cells.
Scan every cell; each unvisited land cell starts a new island, then flood-fill (DFS or BFS) to mark the whole island.
Mark cells as visited before (or as) you explore them, either by sinking them in place or with a visited grid.
O(rows × cols) time; O(rows × cols) worst-case space for the recursion or the explicit stack.
Python details: the default recursion limit of 1000 makes recursive DFS fail on a mostly-land grid as small as 32 × 32, so an explicit list stack (or collections.deque BFS) is the robust version; strings are immutable, so convert rows to lists before sinking.

Clarifying questions expected:

Do diagonal cells count as connected?
May I modify the input grid?
How large can the grid be?

Code / implementation expected: Yes — a nested loop plus a flood fill (recursive sink and an iterative version), in Python.

grid
bfs
dfs

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Beginners preparing for coding interviews — you should know 2-D arrays, and ideally what BFS and DFS are
Difficulty: Medium
Language: Python 3

How to read this doc: every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged 📌 Interview term: with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output you see in the Verified section is copied from that run.

1. Why This Even Matters — A Story First

You are handed a printed map of an archipelago drawn on squared paper: every square is either land or sea. Your job is to count the islands, and you have a highlighter.

You read the map like a book, left to right, top to bottom. The first time your eye lands on an un-highlighted land

The solution is hidden so you can try first

10 min read · 12 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonRecursive flood fill: count islands on seven grids

Practice

PythonIterative DFS, visited grid, island sizes, 8 directions, large grids

Practice

Discussion

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