GATE CS 2025 Set 1 Q.33: Searching and Sorting Algorithms

The pseudocode of a function fun() is given below:

fun(int A[0,...,n-1]){
    for i=0 to n-2
        for j=0 to n-i-2
            if (A[j]>A[j+1])
                then swap A[j] and A[j+1]
}

Let $A[0, \dots, 29]$ be an array storing 30 distinct integers in descending order. The number of swap operations that will be performed, if the function fun() is called with $A[0, \dots, 29]$ as argument, is __________. (Answer in integer)

Your answer

Official answer and solution

Official answer: 435
From: Official GATE 2025 answer key

Solution

Recognize fun() as standard Bubble Sort, where each swap removes exactly one inversion from the array.

The function fun() implements standard Bubble Sort. For an array of $n = 30$ distinct elements sorted in strictly descending order, every pair of elements $(A[p], A[q])$ with $p < q$ is an inversion ( $A[p] > A[q]$ ), and each swap of adjacent elements reduces the number of inversions by $1$ until the array is sorted:

\text{Total swaps} = \sum_{i=0}^{28} (29 - i) = \binom{30}{2} = \frac{30 \times 29}{2} = 435

Final answer

435

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 33 of 65
Section: Computer Science and Information Technology

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