Merge branch 'master' of https://github.com/thecodingwizard/usaco-training-2.0

content/2_Silver/4_Silver_BinSearch.md

@@ -1,11 +1,41 @@
 ---
 slug: /silver/binary-search
 title: "Binary Search"
-author: Unknown
+author: Nathan Chen
 order: 4
 prerequisites: 
  - 
      - Silver - Sorting
 ---
 
+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/)
+- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_algorithm)
+### 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/)
+### Problems
+ - [USACO Silver Counting Haybales](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 such that it satisfies some property.
+  ### Tutorial
+  - [CPH Section 12.1](https://www.overleaf.com/project/5e73f65cde1d010001224d8a)
+### Problems
+- [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)
+	- Also needs some math and "sqrt" analysis
+- [USACO Silver Angry Cows](http://usaco.org/index.php?page=viewproblem2&cpid=594)