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 ${\text{k}}^{\text{th}}$ 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 ${\text{k}}^{\text{th}}$ iteration of outer for loop the inner for loop iterates n-k times.

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

$\begin{array}{l}\text{Complexity = }\left(\text{n-1}\right)\text{ + }\left(\text{n-2}\right)\text{+…}\left(\text{n-k}\right)\\ \text{ = }\left(\text{n+…+n}\right)\text{ – }\left(\text{1+2+…k}\right)\\ \text{ = n}\end{array}$