Data Structures and Algorithms in C++
Data Structures and Algorithms in C++
2nd Edition
ISBN: 9780470383278
Author: Michael T. Goodrich
Publisher: Wiley, John & Sons, Incorporated
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Chapter 4, Problem 12C

Explanation of Solution

Finding minimum and maximum of “n” numbers:

  • Assume that a binary tree is created with “n” number of nodes.
  • A binary tree can consists of fewer left children nodes and fewer right children nodes.
  • Sometimes, it may not contain any children node.
  • To find the minimum and maximum value, “n2” number of comparisons is required if the total number of children nodes is even.
  • (n1)2+1” number of comparisons is required to find the minimum and maximum value, if the total number of children nodes is odd.
  • Hence, there is “m” number of comparisons in worst case.
  • Therefore, it can have,

m+m2+m4+m8+....+2=2m2

  • When the total number of children node is even, total number of comparisons to find the minimum and maximum value is,

n2+n2<3n2

  • When

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