Making A Large Island
A hard Graph interview guide. Task statement, worked examples, intuition, and step-by-step solutions.
- Topic
- Graph
- Sheets
- 1
- Core for
- 12 roles
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 = [[1,1,0],[0,0,1],[0,1,1]]
- Output
- 6
- Why
- Two islands: top-left area 2 and bottom-right area 3. Flipping the center water connects both, giving 2+3+1 = 6.
Example 2
- Input
- grid = [[1,0,1],[1,0,1],[0,1,0]]
- Output
- 6
- Why
- The left pair, the right pair and the bottom 1 all touch the centre cell; flipping it joins them into one island of 6.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 500
How to think about it
Updated 2026-09-29Flipping 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
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.
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.
More Graph problems
Target Roles
Core requirement for 12 roles:
Track in your role's order
Pick your target role and all 370 problems resequence to what that interview actually asks.
Start freeProblem set and role mapping as of .