Pattern this teaches:Graph BFS and DFS
Flood Fill
An easy Graph interview guide. Task statement, worked examples, intuition, and step-by-step solutions.
- Topic
- Graph
- Sheets
- 3
- Core for
- 12 roles
The problem
Given an m x n binary image and a starting pixel (sr, sc), flood fill the image starting from that pixel. Replace the color of the starting pixel and all 4-directionally connected pixels of the same color with a new color.
Example 1
- Input
- image = [[2,2,0],[2,1,1],[0,1,2]], sr = 0, sc = 0, newColor = 3
- Output
- [[3,3,0],[3,1,1],[0,1,2]]
- Why
- The three connected 2s around the top-left corner turn into 3; the 2 in the bottom-right is not connected and keeps its colour.
Example 2
- Input
- image = [[0,0,0],[0,0,0]], sr = 0, sc = 0, newColor = 2
- Output
- [[2,2,2],[2,2,2]]
- Why
- All pixels are connected and have the same initial color, so all become 2.
Constraints
- 1 <= image.length, image[i].length <= 50
- image[i][j] is 0 or 1
- 0 <= sr < image.length
- 0 <= sc < image[0].length
How to think about it
Updated 2026-09-29Flood fill is breadth-first or depth-first search on a grid constrained by color uniformity. Grab the starting pixel's original color before making any changes. If the target color is already equal to the original color, doing anything will spin into an infinite loop because mutating pixels never changes their visited status.
Approaches, worst first
Recursive DFS with in-place color mutation
time O(m * n) · space O(m * n)
Record `startColor = image[sr][sc]`. If `startColor === newColor`, return immediately. Otherwise, set `image[r][c] = newColor` and recurse into all 4 cardinal neighbors that match `startColor`.
Queue-based iterative BFSWrite this one
time O(m * n) · space O(m * n)
Push `(sr, sc)` to a queue after checking that `startColor !== newColor`. Dequeue points, set the cell to `newColor`, and push unvisited neighbors matching `startColor`, guaranteeing stack safety.
Where people lose marks · 3
- Invoking flood fill when `image[sr][sc] === newColor` causes infinite recursion or loop spinning if no visited check exists.
- Mutating coordinates outside bounds 0 <= r < m or 0 <= c < n before checking boundary predicates.
- Using diagonal steps; flood fill allows only 4-directional moves (up, down, left, right).
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
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