EBK DATA STRUCTURES AND ALGORITHMS IN C
EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Chapter 2, Problem 8E

Explanation of Solution

Finding kth smallest integer:

Given an array of elements and a number “k” where “k” is smaller than array size. The problem is to find kth smallest element in given array.

For Example: Input array = {7,5,4,3,2}, k = 3

The result for the above example would be 4, as 4 is the third smallest element of array.

Complexity Analysis:

Refer exercise question 8 from chapter 2 for given algorithm

  • In the given algorithm, the outer for loop iterates “k” times .
  • In the first iteration of outer for loop the inner for loop iterates n-1 times .
  • In the second iteration of outer for loop the inner for loop iterates n-2 times.
  • In the third iteration of outer for loop the inner for loop iterates n-3 times.
  • Similarly, in the kth iteration of outer for loop the inner for loop iterates n-k times.

The complexity of given algorithm is been calculated as shown below:

Complexity  = (n-1) + (n-2)+…(n-k)            = (n+…+n) – (1+2+…k)            = n

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