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 1:

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).

Example 2:

Input: rating = [2,1,3]
Output: 0
Explanation: We can't form any team given the conditions.

Example 3:

Input: rating = [1,2,3,4]
Output: 4

Constraints:

• n == rating.length
• 3 <= n <= 1000
• 1 <= rating[i] <= 105
• All the integers in rating are unique.

SOLUTION:

class Solution:
    def numTeams(self, rating: List[int]) -> int:
        n = len(rating)
        bigger = {}
        smaller = {}
        for i in range(n):
            for j in range(i + 1, n):
                if rating[i] > rating[j]:
                    smaller[i] = smaller.get(i, []) + [j]
                if rating[i] < rating[j]:
                    bigger[i] = bigger.get(i, []) + [j]
        total = 0
        for a in bigger:
            for b in bigger.get(a, []):
                total += len(bigger.get(b, []))
        for a in smaller:
            for b in smaller.get(a, []):
                total += len(smaller.get(b, []))
        return total