Graphs Pattern: LeetCode Guide & Problems
DFS and BFS on adjacency lists for connectivity, cycles, and path problems.
Problems (10)
| Problem | Solution | Link | |
|---|---|---|---|
| Clone Graph
#Graph
#DFS
#BFS | Solution | ||
| Pacific Atlantic Water Flow
#Graph
#DFS
#BFS | Solution | ||
| Number of Connected Components in Undirected Graph ★
#Graph
#DFS
#Union Find | Solution | ||
| Surrounded Regions
#Array
#DFS
#BFS | Solution | ||
| Minimum Height Trees
#DFS
#BFS
#Graph | Solution | ||
| Network Delay Time
#DFS
#BFS
#Graph | Solution | ||
| Find Eventual Safe States
#DFS
#BFS
#Graph | Solution | ||
| All Paths From Source to Target
#Backtracking
#DFS
#BFS | Solution | ||
| Cheapest Flights Within K Stops
#Dynamic Programming
#DFS
#BFS | Solution | ||
| Graph Valid Tree ★
#Depth-First Search
#Breadth-First Search
#Union Find | Solution |
Mastering the Graphs Pattern for Coding Interviews
1. Mental Model & Visual Intuition
The Graphs pattern is designed to eliminate redundant work and reduce search spaces. Rather than evaluating every possible state using a naive brute-force approach, this pattern relies on an invariant that allows you to safely discard subproblems that cannot lead to an optimal answer. When encountering an interview question, look for core triggers such as monotonicity, contiguous constraints, optimal substructure, or overlapping subproblems.
2. Algorithmic Invariants & Step-by-Step Execution
To implement this pattern flawlessly under interview conditions, structure your thought process into three discrete steps:
- State Initialization: Define your boundaries, pointers, or memoization tables clearly before entering loops.
- State Transition: Update tracking variables incrementally as new elements enter or leave your active evaluation window.
- Feasibility Check: When constraints are violated, systematically shrink or adjust your state until the valid invariant is restored.
3. Time and Space Complexity Trade-Offs
In top-tier technical interviews at Google, Meta, and Amazon, arriving at a working solution is only half the battle. You must explicitly justify why your approach achieves optimal Big-O bounds. For Graphs, the target time complexity is typically O(V + E) while maintaining an auxiliary space complexity of O(V) for visited set. Always discuss whether an in-place modification or two-pass traversal can save memory.
4. Common Interview Edge Cases to Test
Before informing your interviewer that you have completed coding, trace your logic against these standard high-failure test cases:
- Empty inputs, single-element collections, or all-identical values.
- Inputs with negative numbers, duplicates, or extreme values that could cause integer overflow.
- Odd versus even length inputs when dealing with pointer convergence or tree midpoints.
Related Guide
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