Yufei Tao Binary Search and Worst-Case Analysis So, the average and the worst case cost of binary search, in big-O notation, is O(logN) . Analysis of Binary Search In the base case, the algorithm will end up either finding the element or just failing and returning false. As we are now done with the code of the binary search, let's move to its analysis. Let me explain the procedure step by step- 1. One of the key reasons to use a binary search tree is that when the tree is balanced, you can guarantee the searches take [math]O(\log{n})[/math] time. Binary search algorithm is being used to search an element ‘item’ in this linear array. Unfortunately when the tree is not balanced the time it takes to perform a Running time of binary search Our mission is to provide a free, world-class education to anyone, anywhere. When n is large, this running time is much lower than the time 4n + 3 of our rst algorithm. Suppose you have an array a[n] of n … The average cost of a successful search is about the same as the worst case where an item is not found in the array, both being roughly equal to logN. Example: For an array with 16 elements, the best case scenario is that a binary search will find the element on the first go and, in the worst case, on the fourth go (2 4 = 16). Donate or volunteer today! Binary Search is one of the most widely used searching techniques. The worst-case time of binary search isat most f 2 (n) = 10(1 + log n). Khan Academy is a 501(c)(3) nonprofit organization. If search ends in success, it sets loc to the index of the element otherwise it sets loc to -1. Variables beg and end keeps track of the index of the first and last element of the array or sub array in which the element is being searched at that instant.