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---
slug: /silver/binary-search
title: "Binary Search"
author: Nathan Chen (incomplete)
author: Unknown
order: 4
prerequisites:
-
@ -12,3 +12,24 @@ Binary search can be used on monotonic functions for a logarithmic runtime.
<!-- END DESCRIPTION -->
## The Basic Application
Find an element in a sorted array in O(log N) time.
### Tutorial
- [GeeksForGeeks]([https://www.geeksforgeeks.org/binary-search/](https://www.geeksforgeeks.org/binary-search/))
- [Wikipedia]([https://en.wikipedia.org/wiki/Binary_search_algorithm](https://en.wikipedia.org/wiki/Binary_search_algorithm))
### Problems
- [USACO Silver Counting Haybales]([http://www.usaco.org/index.php?page=viewproblem2&cpid=666](http://www.usaco.org/index.php?page=viewproblem2&cpid=666))
## Binary Searching on the Answer
Oftentimes used when you need to find the "minimum" or "maximum" of some quantity that satisfies a property.
### Tutorial
- [CPH Section 12.1]([https://www.overleaf.com/project/5e73f65cde1d010001224d8a](https://www.overleaf.com/project/5e73f65cde1d010001224d8a))
### Problems
- [USACO Silver Cownvention]([http://www.usaco.org/index.php?page=viewproblem2&cpid=858](http://www.usaco.org/index.php?page=viewproblem2&cpid=858))
- [USACO Silver Cow Dance]([http://www.usaco.org/index.php?page=viewproblem2&cpid=690](http://www.usaco.org/index.php?page=viewproblem2&cpid=690))
- [USACO Silver Social Distancing]([http://www.usaco.org/index.php?page=viewproblem2&cpid=1038](http://www.usaco.org/index.php?page=viewproblem2&cpid=1038))
- [USACO Silver Loan Repayment]([http://www.usaco.org/index.php?page=viewproblem2&cpid=991](http://www.usaco.org/index.php?page=viewproblem2&cpid=991))
- Also needs some math and "sqrt" analysis
- [USACO Silver Angry Cows]([http://usaco.org/index.php?page=viewproblem2&cpid=594](http://usaco.org/index.php?page=viewproblem2&cpid=594))