Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 12, Problem 3P

(a)

Program Plan Intro

To argue the average depth of a node in tree T is 12xTd(x,T)=12P(T) .

(b)

Program Plan Intro

To argue that if a tree has n nodes then P(T)=P(TL)+P(TR)+n1 where TL is left sub-tree and TR is right sub-tree of the tree T .

(c)

Program Plan Intro

To show the average total path length of BST is P(n)=1ni=0n1(P(i)+P(ni1)+n1) .

(d)

Program Plan Intro

To rewrite the equation P(n) as P(n)=2nk=1n1P(k)+Θ(n) .

(e)

Program Plan Intro

To explain the randomized version of quicksort takes the cost of P(n)=O(nlgn) .

(f)

Program Plan Intro

To describe the comparison of quicksort is equals to the comparisons need to insert the elements in BST.

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