A complete binary tree with N nodes may be stored in an array A of length N by storing the root at A[0],and then storing in successive array locations the nodes of the tree in increasing order of the level of nodes.If nodes in the same level are stored in left to right order,then the node stored at A[k] will be a leaf if and only if
A) 2k+1 ≥ N
B) 2k+1 N
C) k/2 N
D) None of the above

Question

A complete binary tree with N nodes may be stored in an array A of length N by storing the root at A[0],and then storing in successive array locations the nodes of the tree in increasing order of the level of nodes.If nodes in the same level are stored in left to right order,then the node stored at A[k] will be a leaf if and only if
A) 2k+1 ≥ N
B) 2k+1 > N
C) k/2 > N
D) None of the above

Quizplus · Accepted Answer

A complete binary tree with N nodes has N-1 internal nodes and N leaves. The internal nodes are stored in the array A from index 0 to N-2, and the leaves are stored in the array A from index N-1 to N-1. Therefore, the node stored at A[k] will be a leaf if and only if k ≥ N-1, which is equivalent to 2k+1 ≥ N.

A Complete Binary Tree with N Nodes May Be Stored