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---
slug: /plat/2DRQ
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title: "2D Range Queries"
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author: Benjamin Qi
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order: 3
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prerequisites:
-
- Platinum - 1D Range Queries
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---
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Extending Range Queries to 2D (and beyond).
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See [my implementations ](https://github.com/bqi343/USACO/tree/master/Implementations/content/data-structures/2D%20Range%20Queries%20(15.2 )).
## Static Array Queries
- [Multi-Dimensional RMQ (retrograd) ](https://codeforces.com/blog/entry/53810 )
- GP of Serbia 2020 B
## 2D BIT
### Tutorials
- [GFG 2D BIT ](https://www.geeksforgeeks.org/two-dimensional-binary-indexed-tree-or-fenwick-tree/ )
- [TopCoder BIT ](https://www.topcoder.com/community/competitive-programming/tutorials/binary-indexed-trees/ )
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You can extend the 1D BIT solution for range update + range query to higher dimensions as well (USACO Camp - "Cows Play Global Thermonuclear War").
- [Paper ](https://arxiv.org/pdf/1311.6093.pdf )
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### Problems
- [CSES Forest Queries II ](https://cses.fi/problemset/task/1739 )
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- [thecodingwizard's implementation ](https://github.com/thecodingwizard/competitive-programming/blob/master/cses/Forest%20Queries%20II.cpp )
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- [DMOJ Soriya's Programming Project ](https://dmoj.ca/problem/dmopc19c7p5 )
- compressed 2D BIT
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- it is rather difficult to pass within time and memory limits
- lazy BIT is not enough, must use compressed BIT
- Use `\n` instead of `endl`
- See [Benq's 2D offline BIT ](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/2D%20Range%20Queries%20(15.2 )/BIT2DOff%20(15.2).h)
- See [Benq's 1D offline BIT ](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/1D%20Range%20Queries%20(9.2 )/BIToff.h)
- BIT wrapped around 1D offline BIT is also too slow; use 2D offline BIT.
- [thecodingwizard's implementation with benq's 2d offline bit ](https://github.com/thecodingwizard/competitive-programming/blob/master/DMOJ/Soriyas%20Programming%20Project.cpp )
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- or do divide & conquer with a 1D BIT
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- same as first problem here: https://robert1003.github.io/2020/01/31/cdq-divide-and-conquer.html
- [thecodingwizard's (messy) implementation ](https://github.com/thecodingwizard/competitive-programming/blob/master/DMOJ/Soriya%20Programming%20Project%201d%20BIT%20cdq%20dnc.cpp ) based off of article above
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- [IOI 2007 Pairs ](https://wcipeg.com/problem/ioi0722 )
- [DMOJ Crowded Cities ](https://dmoj.ca/problem/bfs17p6 )
## 2D Segment Tree
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Note: no lazy propagation in 2D.
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- Short Description
- CSES 28.2, 28.4
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- Segment Tree (or BIT) nested inside segment tree
- use 2D offline BIT whenever possible rather than an online 2D segment tree (faster, lower memory)
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- Problems
- [USACO Plat Friendcross ](http://www.usaco.org/index.php?page=viewproblem2&cpid=722 )
- [USACO Plat Mowing ](http://www.usaco.org/index.php?page=viewproblem2&cpid=601 )
- [POI Tetris 3D ](https://szkopul.edu.pl/problemset/problem/OQjANSOOD_-c38gh8p6g3Gxp/site/?key=statement )
- [IOI 2013 Game ](http://wcipeg.com/problem/ioi1323 )
