What is the optimal time complexity of solving Number of Islands?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Number of Islands?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Number of Islands?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Number of Islands?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Number of Islands

Learn how to solve the 'Number of Islands' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.

Write a function numIslands(grid: List[List[str]]) -> int.

Constraints

•m == len(grid)
•n == len(grid[i])
•1 <= m, n <= 300
•grid[i][j] is '0' or '1'

Examples

Example 1

Input

grid = [["1","1","1","1","0"],["1","1","0","1","0"],["1","1","0","0","0"],["0","0","0","0","0"]]

Output

Explanation

There is a single island consisting of all connected '1's starting from top-left.

Example 2

Input

grid = [["1","1","0","0","0"],["1","1","0","0","0"],["0","0","1","0","0"],["0","0","0","1","1"]]

Output

Explanation

There are three distinct islands separated by '0's.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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