Refer My Notes

An optimal binary search tree is a binary search tree for which the nodes are arranged on levels such that the tree cost is minimum. If the probabilities of searching for elements of a set are known from accumulated data from past searches, then Binary Search Tree (BST) should be such that the average number of comparisons in a search should be minimum. eg. Lets the elements to be searched are A, B, C, D and probabilities of searching these items are 0.1, 0.2, 0.4 and 0.3 respectively. Lets consider 2 out of 14 possible BST containing these keys. Figure 1 Figure 2 Average number of comparison is calculated as sum of level*probability(key element) for each element of the tree. Lets the level of tree start from 1. Therefore, for figure 1 -     Average number of comparison = 1*0.1 +2*0.2 +3*0.4 +4*0.3  = 2.9                                  ...