Count Number of Teams

There are n soldiers standing in a line. Each soldier is assigned a unique rating value.

You have to form a team of 3 soldiers amongst them under the following rules:

• Choose 3 soldiers with index (i, j, k) with rating (rating[i], rating[j], rating[k]).
• A team is valid if: (rating[i] < rating[j] < rating[k]) or (rating[i] > rating[j] > rating[k]) where (0 <= i < j < k < n).

Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).

Example :

Input: rating = [2,5,3,4,1]
Output: 3
Explanation: We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). 

Approach:

C++

#include <bits/stdc++.h>
using namespace std;

int numTeams(vector<int> &rating)
{
    int N = rating.size();
    vector<int> large(N, 0);
    vector<int> small(N, 0);

    for (int i = 0; i < N - 1; i++)
    {
        for (int j = i + 1; j < N; j++)
        {
            if (rating[i] > rating[j])
                large[i]++;
            else
                small[i]++;
        }
    }

    int team = 0;

    for (int i = 0; i < N - 2; i++)
    {
        for (int j = i + 1; j < N - 1; j++)
        {
            if (rating[i] > rating[j])
                team += large[j];
            else
                team += small[j];
        }
    }

    return team;
}
int main()
{
    vector<int> rating = {2, 5, 3, 4, 1};

    cout << numTeams(rating);

    return 0;
}