Trees Quiz Question 6

#1

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[1]. 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.

Please explain the solution to this problem.

#2

consider worst case senerio
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