DSA interview question

Number of Islands (4-Directional)

Medium · Data structures · Topics: graph, dfs, bfs, matrix

The problem

A satellite map is a grid of '1' (land) and '0' (water). An island is a group of land cells connected horizontally or vertically (diagonals don't count), and the edge of the map counts as water. Count the islands. Scan every cell, and when you hit land that hasn't been visited, that's a new island: flood-fill it with BFS or DFS over the four neighbours so its other cells aren't counted again.

Example: 11000 / 11000 / 00100 / 00011 → 3.

Function signature

int numIslands(vector<string> grid);

Test cases

Input (rows)	Output	Explanation
`11110 11010 11000 00000`	`1`
`11000 11000 00100 00011`	`3`
`101 010 101`	`5`	Diagonals don't connect with 4 directions
`1`	`1`
`0`	`0`

(Confirm: connectivity is 4-directional only; the grid may be modified.)

How interviewers phrase it

"Given an m x n 2D binary grid of '1's (land) and '0's (water), return the number of islands" (LeetCode 200).

Clarifying questions to ask

4 or 8 directions? (4.)
May I modify the grid? (Yes: sink visited land to '0'.)
How large? (Up to 300 × 300, so iterative BFS avoids deep recursion.)

Follow-ups to expect

"How does this compare with the 8-directional version?"
"No modifying the grid?"
"DSU approach?"
"Largest island, or island perimeter?"
"Complexity?"

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