Swim in Rising Water
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
The problem
You are given an m x n grid where each cell is either 0 (land) or 1 (water). Each day, any water cell adjacent to a land cell becomes land. Return the minimum number of days to disconnect the island (the largest connected component of land cells).
Example 1
- Input
- grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]
- Output
- 2
- Why
- It takes 2 days for water to spread enough to split the island.
Example 2
- Input
- grid = [[1,1]]
- Output
- 2
- Why
- With a single row of two land cells, both must become water to disconnect.
Constraints
- 1 <= grid.length, grid[i].length <= 10
- grid[i][j] is 0 or 1
How to think about it
Updated 2026-09-09The grid represents a connectivity state where water spreading or cell removal breaks the island apart. Disconnecting an island requires checking the baseline: if it is already disconnected (0 islands or more than 1 island), 0 steps are needed. If removing a single critical cell breaks it, the answer is 1. Any 2D island can always be disconnected by clearing at most two cells (e.g. isolating a corner cell), so the answer never exceeds 2.
Approaches, worst first
Island counting with single-cell removal simulation
time O((m * n)^2) · space O(m * n)
Count connected components. If count != 1, return 0. Next, try temporarily removing each land cell one by one and recount components; if any removal yields count != 1, return 1. If no single removal disconnects it, return 2.
Tarjan articulation point detectionWrite this one
time O(m * n) · space O(m * n)
Count initial components. If != 1, return 0. Use Tarjan's algorithm on the grid graph to detect whether any articulation point exists among land cells. If yes, return 1; else return 2.
Where people lose marks · 3
- An initial grid with no land (all water) or multiple disjoint islands is already disconnected and requires 0 days/changes.
- An island consisting of only 1 or 2 land cells cannot be disconnected into two components by removing 1 cell; removing 1 leaves 0 or 1 cell, which count as disconnected under the problem definition.
- Forgetting to restore the grid cell back to land after testing its temporary removal.
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
| Operation | Time |
|---|---|
| visit all nodes and edges via search | O(v + e) |
| topological sort using in-degree counts | O(v + e) |
| shortest path using dijkstra with a min-heap | O((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.
Secondary for 6 more roles, including Performance Engineer, Search Engineer, Information Retrieval Engineer.
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