AlgoViz

Breadth-First Search

BFS explores a graph level by level, visiting all neighbors before moving to the next level. Uses a queue data structure.

IntermediateTime: O(V + E)Space: O(V)
Take Quiz
ABCDEFG
Step 1 / 0

Current Step

Click Play to start the visualization


## How Breadth-First Search Works

BFS explores a graph level by level. It starts at the root and explores all neighbors before moving to the next level of neighbors.

### Algorithm Steps:
1. Start at the source node and mark it visited
2. Add source to a queue
3. While queue is not empty:
- Dequeue a node
- For each unvisited neighbor, mark visited and enqueue
4. Repeat until all reachable nodes are visited

### Key Characteristics:
- **Uses Queue**: First-In-First-Out (FIFO) data structure
- **Shortest Path**: Finds shortest path in unweighted graphs
- **Level Order**: Visits nodes level by level

Time & Space Complexity

CaseTime Complexity
BestO(V + E)
AverageO(V + E)
WorstO(V + E)
SpaceO(V)

Practice Problems

10 problems81 total points
1

BFS Level Order Traversal

Beginner5 pts
2

Maximum Depth of Tree

Beginner5 pts
3

Number of Islands

Beginner5 pts
4

Shortest Path in Binary Matrix

Intermediate8 pts
5

Rotting Oranges

Intermediate8 pts
6

Word Ladder

Advanced10 pts
7

Minimum Knight Moves

Advanced10 pts
8

Open the Lock

Advanced10 pts
9

Shortest Path with Alternating Colors

Advanced10 pts
10

Bus Routes

Advanced10 pts