What is the Graphs pattern?

The Graphs pattern is a systematic approach to solving a class of coding interview problems. By recognizing the Graphs structure, you can solve problems in optimal time complexity using proven techniques.

When should I use the Graphs pattern?

Use the Graphs pattern when the problem structure matches its recognition signals — typically when brute force would be O(n²) or worse, and the pattern reduces complexity to O(V + E).

What is the time complexity of Graphs?

The Graphs pattern typically runs in O(V + E) time and uses O(V) space. The exact complexity depends on the specific sub-variant being applied.

Is Graphs important for coding interviews?

Yes — the Graphs pattern is frequently tested at FAANG companies and competitive engineering interviews. Mastering this pattern gives you a reliable framework to solve many problem variations quickly.

How do I practice the Graphs pattern?

Start by studying the pattern's mental model and recognition signals on DSAPatterns, then practice the curated LeetCode problems below in order from Easy to Hard. Aim for pattern recognition before memorizing solutions.

← back to patterns

pattern / HARD

Graphs.

Traverse and analyze graph structures

complexity

time

O(V + E)

space

O(V)

practice questions

browse and solve all 0 pattern questions →

02' — visual

interactive

Sliding window — k = 3

Maximum sum subarray

Window

[0, 2]

Sum

Step

0 / 3

03'

mental
model.

Represent graph as adjacency list. Use BFS with queue or DFS with stack/recursion. Track visited set.

Graph algorithms form a major category. Includes BFS, DFS, shortest path, MST, topological sort, and union find patterns.

when to use ✓

01BFS for shortest path (unweighted)
02Dijkstra for weighted shortest path
03Union find for connectivity
04Topological sort for dependencies

when not ✗

01Tree-specific problems (use tree patterns)

04'

recognition signals

Network of nodes and edges

Shortest path problems

Connected components

Dependency resolution

BFSDFSDijkstraBellman FordFloyd WarshallUnion FindTopological SortKruskal/Prim MST

05'

templates

python

1# Beginner: Fixed-size sliding window
2def max_sum_k(nums, k):
3   n = len(nums)
4   if n < k:
5      return 0
6   window_sum = sum(nums[:k])
7   max_sum = window_sum
8   for i in range(k, n):
9      window_sum += nums[i] - nums[i - k]
10      max_sum = max(max_sum, window_sum)
11   return max_sum

common mistakes

01Not marking nodes as visited
02Confusing directed vs undirected
03Forgetting to handle disconnected components

interview tips

01Always clarify graph representation
02Build adjacency list first
03Practice all major algorithms

06'

practice this pattern

0 curated problems from LeetCode

See all

No questions found for this pattern yet.

07'

faq

1# Beginner: Fixed-size sliding window

2def max_sum_k(nums, k):

3 n = len(nums)

4 if n < k:

5 return 0

6 window_sum = sum(nums[:k])

7 max_sum = window_sum

8 for i in range(k, n):

9 window_sum += nums[i] - nums[i - k]

10 max_sum = max(max_sum, window_sum)

11 return max_sum