count_number_of_teams.py

'''
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).
'''

class Solution:
    def numTeams(self, rating: List[int]) -> int:
        res = 0
        for i in range(1, len(rating) - 1):
            less, greater = [0, 0], [0, 0]
            for j in range(i):
                if rating[j] < rating[i]:
                    less[0] += 1
                else:
                    greater[0] += 1
            
            for k in range(i+1, len(rating)):
                if rating[i] < rating[k]:
                    less[1] += 1
                else:
                    greater[1] += 1
            res += less[0] * less[1] + greater[0] * greater[1]
        return res
      
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