Profitable Project Pairs

In a tech company, there are n projects available for the team to work on. Due to resource constraints, they can only work on any two of the projects. The expected profits for each project are provided in the array profit, while the implementation costs are given in the array implementationCost.

Task

The task is to determine the number of pairs of projects that can be chosen from the available options such that the company earns a profit after implementing both projects. That is, projects indexed i and j are chosen if:

(profit[i] - implementationCost[i]) + (profit[j] - implementationCost[j]) > 0

Example

n = 5
profit = [2, 3, 4, 5, 1]
implementationCost = [3, 4, 5, 1, 2]

Profitable Pairs

Pair of Projects (0-based)    Net Profit from the first Project    Net Profit from the second project
[0, 2]                         2 - 3 = -1                           7 - 5 = 2
[1, 2]                         3 - 4 = -1                           7 - 5 = 2
[2, 3]                         7 - 5 = 2                            1 - 1 = 0
[3, 4]                         1 - 1 = 0                            2 - 2 = 0

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Divisible Range

A quiz on Mathematics and Number Theory contains the following problem.

Task

Given an integer array arr that consists of n elements, and 2 integers k and x, find the number of pairs of indices i, j (0 ≤ i, j < n, j < n) such that:

• arr[i] ≤ arr[j]
• There are exactly k elements in the range [arr[i], arr[j]] that are divisible by x

Example

n = 4
arr = [1, 3, 5, 7]
k = 2
x = 2

Valid pairs of indices:

(0, 2): arr[0] = 1, arr[2] = 5
        Number of elements in [1, 5] divisible by 2 are 2: i.e. 2 and 4

(1, 3): arr[1] = 3, arr[3] = 7
        Number of elements in [3, 7] divisible by 2 are 2: i.e. 4 and 6

There is no other pair of indices for which the given condition is true so the answer is 2.

Function Description

Complete the function countDivisiblePairs in the editor below.

countDivisiblePairs has the following parameters:
    int arr[n]: the given elements
    int k: the count of elements to be divisible by x
    int x: the divisor

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