usaco-guide/content/5_Gold/PURQ.md

id	title	author	prerequisites	description
PURQ	1D Point Update Range Query	Benjamin Qi	Gold - Point Update Range Sum	General range queries for associative operations with segment tree.

A segment tree allows you to do point update and range query in O(\log N) time each for any associative operation. Historically, no gold problem has required the use of a segment tree in place of a binary indexed tree, but it's still good to know (and you might find it simpler).

Tutorials

• CPH 9.3, 28.1 (Segment Trees Revisited)
• Codeforces Tutorial
• CSAcademy Tutorial
• cp-algorithms
• Slides from CPC.3

Problems

Can try solving some of the BIT questions w/ segtree.

• CSES
  • Range Minimum Queries II
    • just min segtree
  • Subarray Sum Queries
  • Hotel Queries
• Normal SegTree
  • USACO Gold Springboards
    • can use segment tree with min query in place of the map mentioned in analysis
  • USACO Old Gold Seating (check ...)
  • USACO Old Gold Optimal Milking (check ...)
  • USACO Old Gold Marathon (check ...)
  • USACO Plat Balancing (check ...)
  • USACO Plat Nocross
  • POI Cards
  • CSES Area of Rectangles
    • use segment tree that keeps track of minimum and # of minimums