Segment Trees
Segment trees answer range queries and handle point updates in O(log n). Learn build, query, update.
Lessons
1. Intro
Why segment trees matter
2. Segment Tree Structure
Divide and conquer on arrays
3. Array Representation
Storing the tree in an array
4. Building the Tree
Bottom-up construction
5. Range Query
Answering queries in O(log n)
6. Point Update
Modifying single elements
7. Problem - Range Sum Query Mutable
Classic application
8. Segment Tree Implementation
Complete solution structure
9. Range Sum Query Solution
Implement your solution
10. Range Minimum Query
Different operations
11. Segment Tree Generalization
Associative operations
12. The Range Update Problem
Why lazy propagation exists
13. Lazy Propagation Structure
The lazy array
14. Push Down Operation
Propagating lazy values
15. Range Update with Lazy
O(log n) range updates
16. Query with Lazy
Handling pending updates
17. Problem - Range Addition
Apply lazy propagation
18. Range Addition Solution
Implement your solution
19. Range Set Operation
Overwriting instead of adding
20. Problem - Count of Range Sum
Coordinate compression
21. Count Range Sum Approach
Prefix sums + segment tree
22. Count Range Sum Solution
Implement your solution
23. Iterative Segment Tree
Non-recursive implementation
24. Iterative Query and Update
Bottom-up operations
25. Problem - Count Smaller After Self
Segment tree for inversions
26. Count Smaller Solution
Process right to left
27. 2D Segment Trees
Extending to matrices
28. Problem - Range Sum Query 2D Mutable
2D segment tree application
29. 2D Segment Tree Solution
Implement your solution
30. Persistent Segment Trees
Version control for trees
31. Dynamic Segment Trees
Handling sparse ranges
32. Segment Tree vs BIT
When to use which
33. Common Segment Tree Bugs
Debugging tips
34. Quiz: Segment Trees
Test your understanding
35. Section Recap
What you learned
Practice Problems
Perfect introduction to segment trees with alternating OR/XOR operations. Teaches the fundamental concept of building a tree structure with point updates and querying.
Combines segment tree concepts with greedy coloring strategy. Great for understanding how segment trees can be applied to non-traditional problems.
Classic problem demonstrating non-commutative merge operations in segment trees. Essential for understanding complex segment tree node merging.
Excellent problem combining segment trees with counting inversions and frequency queries. Teaches coordinate compression with segment trees.
Combines tree flattening (DFS ordering) with segment trees for subtree queries. Essential for learning Euler tour technique with segment trees.
Uses segment tree with GCD queries to solve a counting problem. Great for understanding how segment trees handle mathematical operations over ranges.
Requires coordinate compression and range update/query on large intervals. Perfect for learning sparse segment trees and memory optimization.
Teaches checking if segments form a tree structure using segment tree for interval overlap queries. Combines graph theory with segment trees.
Classic lazy propagation problem with circular array handling. Essential for mastering range updates with lazy propagation and wraparound ranges.
Advanced lazy propagation with range sorting queries on strings. Demonstrates segment tree with multiple counters and batch updates.
Mind-bending problem requiring adding Fibonacci sequences to ranges. Showcases advanced lazy propagation techniques with linear recurrences.
Introduces 'Segment Tree Beats' concept with modulo operations. Teaches amortized analysis for operations that don't fit standard lazy propagation.
The foundational segment tree problem. Perfect for learning basic segment tree implementation with point updates and range sum queries.
Applies segment trees to geometric problems with coordinate compression. Teaches handling large coordinate spaces with lazy propagation.
Requires implementing a dynamic set of intervals with segment tree. Great for understanding range assignment operations and interval tracking.
Classic problem demonstrating segment tree for counting inversions. Essential for interview preparation with coordinate compression.
Advanced application combining prefix sums with segment tree for range counting. Tests coordinate compression and complex counting strategies.
Modified inversion counting with condition nums[i] > 2*nums[j]. Reinforces coordinate compression and segment tree counting techniques.
Sweep line technique with segment tree for interval overlap counting. Perfect for learning dynamic interval insertions and maximum overlap queries.
Modern problem combining DP with segment tree for range maximum queries. Demonstrates how segment trees optimize DP transitions.