DSA Tracker

Hard

Making a Large Island

A hard Graph problem included in Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.

Topic
Graph
Sheets
1
Core for
11 roles
Platform
LeetCode
Practice in the compilerWatch this solved step by step

The problem

Given an m x n binary grid where 1 represents land and 0 represents water, return the largest possible area of an island after changing exactly one water cell to land.

Example 1

Input
grid = [[1,0],[0,1]]
Output
3
Why
Changing the water cell at [0][1] connects the two islands, forming an island of area 3.

Example 2

Input
grid = [[1,1],[1,0]]
Output
4
Why
Changing [1][1] from water to land connects all cells into a single island of area 4.

Constraints

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 500

How to think about it

Updated 2026-09-09

Flipping a 0 to a 1 bridges whatever islands touch its four adjacent neighbors. Precompute and label each island with a unique ID (starting from 2 to avoid collision with 1 and 0), storing each island's total area in a lookup map. Then scan every 0: its potential merged area is 1 plus the sum of unique neighbor island areas. A set prevents double-counting if two neighbors belong to the same island.

Approaches, worst first

  1. Brute force flip and recount

    time O((m * n)^2) · space O(m * n)

    For every 0 in the grid, temporarily flip it to 1, run a full BFS or DFS to measure the island area, then flip it back. Catastrophically slow on a 500x500 grid.

  2. Component labeling with neighbor lookupWrite this one

    time O(m * n) · space O(m * n)

    Assign each connected island of 1s a unique integer label (2, 3, ...) and record its area in a map. Then for each cell holding 0, look at its 4 orthogonal neighbors, gather distinct island labels in a set, sum their areas plus 1, and track the global maximum.

Where people lose marks · 3
  • If the grid is already entirely land (all 1s, zero 0s), no flip can occur; the answer is m * n, not 0.
  • A single water cell may touch the SAME island on two or three sides; failing to deduplicate neighbor component IDs adds the same island's area multiple times.
  • Deep recursion stack overflow on 500x500 grid when using recursive DFS for component labeling.

The theory behind it

Graph — the ground this problem stands on. All Graph problems

What Graph is

A graph is a network of individual points, called vertices or nodes, connected by lines called edges. Think of a subway transit map, an electrical circuit, or a web of social friends. Unlike a tree, a graph has no designated top node and no parent-child hierarchy. Connections can run one-way or both ways, and paths can loop back on themselves to form closed cycles.

When to reach for it

Reach for graph algorithms when inputs describe relationships, networks, flights between cities, course prerequisites, or clone networks. Signals include finding the shortest route across unweighted connections, ordering tasks that depend on earlier tasks, counting isolated clusters, or checking whether a path contains an infinite loop. Whenever problems present pairs of related entities and ask for reachability, distances, or dependencies, graph representations apply.

How the pattern works

First convert edge lists into an adjacency list, mapping each node to an array of its neighbors. Choose your exploration strategy based on the goal: use a queue and breadth-first search to find the shortest path in unweighted networks, or use recursion and depth-first search to explore full paths and detect cycles. Because graphs can have loops, always track visited nodes in a set or boolean array. Add nodes to the visited set at the moment they enter the queue so they are never visited twice.

What each operation costs

OperationTime
visit all nodes and edges via searchO(v + e)
topological sort using in-degree countsO(v + e)
shortest path using dijkstra with a min-heapO((v + e) log v)
What usually goes wrong with Graph
  • Adding a node to the visited set when popping from the queue instead of when pushing, which lets neighboring nodes enqueue duplicate entries and wastes memory.
  • Failing to check for cycles in directed graphs when finding prerequisite orders, causing topological sort routines to hang or return incomplete lists.
  • Assuming an input graph is fully connected and scanning from only a single starting node, missing disconnected islands and isolated components.

Which roles need this problem

Graph is a core topic for these 11 roles — if you're targeting one of them, this problem is early in your path, not optional.

SDE / Backend EngineerData EngineerGame DeveloperSecurity EngineerSite Reliability EngineerCloud EngineerComputer Vision EngineerRobotics EngineerCompiler / PL EngineerBlockchain / Web3 EngineerNetworking Engineer

Secondary for 6 more roles, including Performance Engineer, Search Engineer, Information Retrieval Engineer.

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More Graph problems

Problem set and role mapping as of .