ISRO CS 2017 - Question 9

Introduction

The ISRO CS 2017 - Question 9 is a programming question from the ISRO Computer Science 2017 exam. In this question, we are given a sorted array of integers and we need to find the number of pairs of integers in the array whose sum is equal to a given number.

Problem Statement

Given a sorted array of integers arr and a number num, find the number of pairs of integers in the array whose sum is equal to num.

Input

• arr - An array of n integers (1 <= n <= 10^5) where each integer a_i (-10^9 <= a_i <= 10^9) is sorted in non-descending order.
• num - An integer (−10^9 <= num <= 10^9).

Output

• An integer representing the number of pairs of integers whose sum is equal to num.

Example

Input:

arr = [1, 2, 3, 4, 5, 6, 8, 9]
num = 7

Output:

2

Explanation: The two pairs are (1,6) and (2,5).

Solution

We can solve this problem using a two-pointer approach. We start by initializing two pointers, one at the beginning of the array and the other at the end. We then check the sum of the values pointed to by the two pointers. If the sum is equal to num, we increment our count of pairs and move both pointers. If the sum is less than num, we move our left pointer to the right. If the sum is greater than num, we move our right pointer to the left. We continue doing this until both pointers meet.

Code

def count_pairs(arr, num):
    n = len(arr)
    count = 0
    i, j = 0, n - 1
    while i < j:
        if arr[i] + arr[j] == num:
            count += 1
            i += 1
            j -= 1
        elif arr[i] + arr[j] < num:
            i += 1
        else:
            j -= 1
    return count

The above code is written in Python and uses the two-pointer approach to find the number of pairs whose sum is equal to `num`. The time complexity of this solution is O(n) and the space complexity is O(1).