Data Structures | Binary Trees | Question 12
A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is stored at X. For a node stored at X[i], the left child, if any, is stored in X[2i] and the right child, if any, in X[2i+1]. To be able to store any binary tree on n vertices the minimum size of X should be. (GATE CS 2006)
(C) 2n + 1
(D) 2^n — 1
Explanation: For a right skewed binary tree, number of nodes will be 2^n – 1. For example, in below binary tree, node ‘A’ will be stored at index 1, ‘B’ at index 3, ‘C’ at index 7 and ‘D’ at index 15.
A \ \ B \ \ C \ \ D