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# Minimum and Maximum number of pairs in m teams of n people in C++

## Problem statement

**N** participants of the competition were split into **M** teams in some manner so that each team has at least one participant. After the competition each pair of participants from the same team became friends.

Your task is to write a program that will find the minimum and the maximum number of pairs of friends that could have formed by the end of the competition.

## Algorithm

1. We can obtain max pairs using below formula: maxPairs = ((n – m) * (n – m + 1)) / 2 2. We can obtain min pairs using below formula: minPairs = m * (((n - m) / m + 1) * ((n - m) / m)) / 2 + ceil((n - m) / double(m)) * ((n - m) % m);

## Example

#include <iostream> #include <cmath> using namespace std; void getPairs(int n, int m){ int maxPairs = ((n - m + 1) * (n - m)) / 2; int minPairs = m * (((n - m) / m + 1) * ((n - m) / m)) / 2 + ceil((n - m) / double(m)) * ((n - m) % m); cout << "Minimum pairs = " << minPairs << "\n"; cout << "Maximum pairs = " << maxPairs << "\n"; } int main(){ getPairs(3, 2); return 0; }

## Output

When you compile and execute the above program. It generates the following output−

Minimum pairs = 1 Maximum pairs = 1

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