This is originally posted at https://shawnlyu.com/algorithms/binary-search-find-upper-and-lower-bound/

This post will introduce one specific application of Binary Search, i.e., when you are asked to find the upper or lower bound, or more precisely, when you need to find the maximum of the smallest value or the minimum of the largest value.

Binary Search is an algorithm to search for a target from a sorted array. It selects the middle element in the array and compares it against the target; if they are not equal, it eliminates one half of the array and keeps searching the other half in the same manner(Wikipedia).

The most basic application of it is to find a number or a position from an array. Some practices could be found on Leetcode:

• 278. First Bad Version
• 33. Search in Rotated Sorted Array
• 34. Find First and Last Position of Element in Sorted Array
• 4. Median of Two Sorted Arrays

Another popular case to apply is when you are asked to find the maximum of the smallest value or the minimum of the largest value. Let’ take 410. Split Array Largest Sum from Leetcode as an example to illustrate how to deal with this kind of problem.

#data-structures #computer-science #binary-search #leetcode #data-science