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---
slug: /silver/binary-search
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title: "Binary Search"
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author: Nathan Chen
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order: 4
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prerequisites:
-
- Silver - Sorting
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---
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Binary search can be used on monotonic functions for a logarithmic runtime.
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## The Basic Application
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"Find an element in a sorted array in O(log N) time." This is a very basic form of binary search. Other variations are similar, like "Given K, find the largest element less than K in a sorted array."
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### Tutorial
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- [GeeksForGeeks ](https://www.geeksforgeeks.org/binary-search/ )
- [Wikipedia ](https://en.wikipedia.org/wiki/Binary_search_algorithm )
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### Library Functions to do Binary Search:
#### Java
- [Arrays.binarySearch ](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html )
- [Collections.binarySearch ](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html )
#### C++
- [lower_bound ](http://www.cplusplus.com/reference/algorithm/lower_bound/ )
- [upper_bound ](http://www.cplusplus.com/reference/algorithm/upper_bound/ )
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### Problems
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- [USACO Silver Counting Haybales ](http://www.usaco.org/index.php?page=viewproblem2&cpid=666 )
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## Binary Searching on the Answer
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Oftentimes used when you need to find the minimum or maximum of some quantity such that it satisfies some property.
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### Tutorial
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- [Introduction to USACO Section 12.1 ](https://darrenyao.com/usacobook/java.pdf )
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### Problems
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- [USACO Silver Cownvention ](http://www.usaco.org/index.php?page=viewproblem2&cpid=858 )
- [USACO Silver Cow Dance ](http://www.usaco.org/index.php?page=viewproblem2&cpid=690 )
- [USACO Silver Social Distancing ](http://www.usaco.org/index.php?page=viewproblem2&cpid=1038 )
- [USACO Silver Loan Repayment ](http://www.usaco.org/index.php?page=viewproblem2&cpid=991 )
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- Also needs some math and "sqrt" analysis
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- [USACO Silver Angry Cows ](http://usaco.org/index.php?page=viewproblem2&cpid=594 )
