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Graph Theory
Heavy-Light Decomposition
Problemset
Discussion
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Graph Fundamentals
0/41
Depth First Search (DFS)
0/41
Breadth First Search (BFS)
0/40
Flood Fill & Grid Graphs
0/32
Bipartite Graphs
0/48
Tree Fundamentals
0/44
Tree Diameter & Center
0/45
Subtree DP
0/44
Floyd-Warshall Algorithm
0/41
Dijkstra's Algorithm
0/40
Bellman-Ford Algorithm
0/48
Mixed Practice - Shortest Paths
0/36
Disjoint Set Union (DSU)
0/49
Minimum Spanning Trees
0/48
Topological Sort
0/41
DP on DAGs
0/50
Mixed Practice: Graph Traversals
0/35
Strongly Connected Components
0/45
2-SAT
0/51
Mixed Practice: Connectivity & MST
0/35
Rerooting Technique
0/39
Euler Tour Technique
0/51
Mixed Practice: Tree Fundamentals
0/29
Binary Lifting
0/50
Lowest Common Ancestor (LCA)
0/51
Games on Graphs
0/62
Heavy-Light Decomposition
0/49
1
Intro
2
The Path Query Problem
3
Why Subtree Tricks Fail
4
The Chain Idea
5
Subtree Size
6
Heavy and Light Edges
7
Heavy Paths as Chains
8
The $O(\log n)$ Chain Property
9
Path to LCA Structure
10
Chain Decomposition DFS
11
Chain Positions
12
Chain Heads
13
Segment Tree per Chain
14
Single Segment Tree Improvement
15
Path Query Algorithm
16
Depth Array
17
Parent Array
18
Update Operation
19
Edge Queries vs Vertex Queries
20
LCA in HLD
21
Complexity Analysis
22
Implementation - Preprocessing
23
Implementation - Decomposition
24
Implementation - Segment Tree
25
Implementation - Path Query
26
Path Updates
27
Path Sum Queries
28
Problems - Path Queries II - Read Statement
29
Path Queries II - Heavy Edges
30
Path Queries II - Segment Tree
31
Path Queries II - Query Algorithm
32
Path Queries II - Update Algorithm
33
Path Queries II - Complexity
34
Path Queries II - Implementation
35
Path Queries II - Lessons
36
Problems - QTREE - Read Statement
37
QTREE - Edge to Vertex Mapping
38
QTREE - Query Path Edges
39
QTREE - Edge Update
40
QTREE - Complexity
41
QTREE - Implementation Notes
42
QTREE - Lessons
43
When to Use HLD
44
HLD vs LCA Binary Lifting
45
Common Mistakes
46
Quiz: Heavy Edge Definition
47
Quiz: Chain Crossing Bound
48
Quiz: Query Complexity
49
Section Recap
Centroid Decomposition
0/55
Small-to-Large Merging
0/40
Functional Graphs
0/47
Mixed Practice: Advanced Tree Techniques
0/36
Bridges and Articulation Points
0/58
Network Flow
0/54
Maximum Bipartite Matching
0/50
Minimum Cut
0/47
Euler Paths and Circuits
0/37
Mixed Practice: Advanced Graphs
0/24
27.1
Intro
3 minutes
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Tasks
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