usaco-guide/content/4_Silver/Binary_Search.md

---
id: binary-search
title: "Binary Search on the Answer"
author: Darren Yao
---

## Binary Searching on the Answer

Oftentimes used when you need to find the minimum or maximum of some quantity such that it satisfies some property.
 
### Tutorial

  - Intro to USACO 12.1

### Problems

 - USACO
   - [USACO Silver - Cow Dance](http://www.usaco.org/index.php?page=viewproblem2&cpid=690)
     - binary search on $K$ and simulate
   - [USACO Silver - Convention](http://www.usaco.org/index.php?page=viewproblem2&cpid=858)
     - determine whether $M$ buses suffice if every cow waits at most $T$ minutes
     - use a greedy strategy (applies to next two problems as well)
   - [USACO Silver - Angry Cows](http://usaco.org/index.php?page=viewproblem2&cpid=594)
     - check in $O(N)$ how many haybales you can destroy with fixed radius $R$
   - [USACO Silver - Social Distancing](http://www.usaco.org/index.php?page=viewproblem2&cpid=1038)
     - check in $O(N+M)$ how many cows you can place with distance $D$
   - [USACO Silver - Loan Repayment](http://www.usaco.org/index.php?page=viewproblem2&cpid=991)
     - requires some rather tricky analysis to speed up naive $O(N\log N)$ solution
 - CF
   - [The Meeting Place Cannot Be Changed](http://codeforces.com/contest/782/problem/B) [](48)
   - [Preparing for Merge Sort](http://codeforces.com/contest/847/problem/B) [](53)
   - [Level Generation](http://codeforces.com/problemset/problem/818/F) [](54)
   - [Packmen](http://codeforces.com/contest/847/problem/E) [](57)
   - [Office Keys](http://codeforces.com/problemset/problem/830/A) [](60)
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`
refactor order into ordering.js 2020-06-15 23:19:07 +00:00			`id: binary-search`
move around sorting 2020-06-16 01:58:45 +00:00			`title: "Binary Search on the Answer"`
			`author: Darren Yao`
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`

fix some formatting 2020-06-08 18:07:48 +00:00			`## Binary Searching on the Answer`

			`Oftentimes used when you need to find the minimum or maximum of some quantity such that it satisfies some property.`
Update 4_Silver_BinSearch.md 2020-06-07 07:38:45 +00:00
fix some formatting 2020-06-08 18:07:48 +00:00			`### Tutorial`
+ General 2020-06-08 19:51:58 +00:00
fix some formatting 2020-06-08 18:07:48 +00:00			`- Intro to USACO 12.1`

Update 4_Silver_BinSearch.md 2020-06-05 23:02:56 +00:00			`### Problems`
fix some formatting 2020-06-08 18:07:48 +00:00
rearrange bronze 2020-06-09 04:01:24 +00:00			`- USACO`
			`- [USACO Silver - Cow Dance](http://www.usaco.org/index.php?page=viewproblem2&cpid=690)`
			`- binary search on $K$ and simulate`
			`- [USACO Silver - Convention](http://www.usaco.org/index.php?page=viewproblem2&cpid=858)`
			`- determine whether $M$ buses suffice if every cow waits at most $T$ minutes`
			`- use a greedy strategy (applies to next two problems as well)`
			`- [USACO Silver - Angry Cows](http://usaco.org/index.php?page=viewproblem2&cpid=594)`
			`- check in $O(N)$ how many haybales you can destroy with fixed radius $R$`
			`- [USACO Silver - Social Distancing](http://www.usaco.org/index.php?page=viewproblem2&cpid=1038)`
			`- check in $O(N+M)$ how many cows you can place with distance $D$`
			`- [USACO Silver - Loan Repayment](http://www.usaco.org/index.php?page=viewproblem2&cpid=991)`
			`- requires some rather tricky analysis to speed up naive $O(N\log N)$ solution`
			`- CF`
			`- [The Meeting Place Cannot Be Changed](http://codeforces.com/contest/782/problem/B) [](48)`
			`- [Preparing for Merge Sort](http://codeforces.com/contest/847/problem/B) [](53)`
			`- [Level Generation](http://codeforces.com/problemset/problem/818/F) [](54)`
			`- [Packmen](http://codeforces.com/contest/847/problem/E) [](57)`
			`- [Office Keys](http://codeforces.com/problemset/problem/830/A) [](60)`