Exploring graphs breadth or depth first
Day 105 of 149
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The Maze Exploration Analogy
Imagine you're lost in a maze. Two strategies:
Strategy 1 (DFS - Depth First):
- Pick a path and go as far as possible
- Hit a dead end? Backtrack and try another route
- Like following one hallway to the very end
Strategy 2 (BFS - Breadth First):
- Check all nearby paths first
- Then move one step deeper on each
- Like ripples spreading from a stone in water
BFS and DFS are these two exploration strategies!
When To Use Which
Use DFS when:
- You need to explore all paths
- Looking for any solution (not necessarily shortest)
- Checking if something exists
Use BFS when:
- You need the shortest path
- Exploring level by level
- Finding the closest match
How They Work
DFS (goes deep first):
Start at A
A
/ \
B C
/
D
Visit: A → B → D → C (go deep before siblings)
BFS (goes wide first):
Start at A
A
/ \
B C
/
D
Visit: A → B → C → D (all of one level before next)
Real-World Examples
DFS used for:
- Solving puzzles (chess, sudoku)
- Finding if two people are connected on social media
- Navigating file systems
BFS used for:
- Finding shortest route on a map
- Social network "degrees of separation"
- Web crawlers exploring links
The Key Difference
- DFS → Goes deep, uses less memory, might not find shortest path
- BFS → Finds shortest path, but uses more memory
In One Sentence
BFS explores neighbors first (shortest paths), while DFS explores deeply first (good for exhaustive search).
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