Pacific Atlantic Water Flow
A medium Graph problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Graph
- Sheets
- 2
- Core for
- 11 roles
- Platform
- LeetCode
The problem
Given an m x n matrix of non-negative integers representing heights, find all cells where water can flow to both the Pacific Ocean (top and left edges) and the Atlantic Ocean (bottom and right edges). Water flows to a neighboring cell only if that cell's height is less than or equal to the current cell's height.
Example 1
- Input
- matrix = [[1,2,2,3,5],[3,2,3,4,4],[2,4,5,3,1],[6,7,1,4,5],[5,1,1,2,4]]
- Output
- [[0,4],[1,3],[1,4],[2,2],[3,0],[3,1],[4,0]]
- Why
- These cells can each route water to both oceans via decreasing paths.
Example 2
- Input
- matrix = [[2,1],[1,2]]
- Output
- [[0,0],[0,1],[1,0],[1,1]]
- Why
- All four cells can reach both oceans in this small grid.
Constraints
- m == matrix.length
- n == matrix[i].length
- 1 <= m, n <= 200
- 0 <= matrix[i][j] <= 10^5
How to think about it
Updated 2026-09-09Instead of simulating water trickling down from all m x n cells independently, reverse the physical flow: imagine ocean water flooding uphill. Run one flood fill from the Pacific borders and another from the Atlantic borders, moving only to equal or taller neighbors. The cells reached by both floods are precisely the answer.
Approaches, worst first
Individual cell flood simulations
time O((m * n)^2) · space O(m * n)
From every coordinate (r, c), run a search downwards to see if water can reach both borders. Suffers from immense redundant re-traversal of shared downward paths.
Dual reverse ocean flood fillsWrite this one
time O(m * n) · space O(m * n)
Maintain two boolean matrices, pacific and atlantic. Flood inwards from the top/left edges into pacific, and from bottom/right edges into atlantic, stepping only onto cells with height >= current. Intersect the two matrices to collect all valid coordinates.
Where people lose marks · 3
- Water can flow across flat terrain; the search condition must allow neighbor height >= current height, not strictly greater.
- A 1x1 matrix reaches both oceans simultaneously because its single cell borders all four edges.
- Using a single visited matrix for both ocean searches causes the second flood fill to terminate early upon encountering cells visited by the first.
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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