Count number of teams

Time: O(N^2); Space: O(1); medium

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 == len(rating)

  • 1 <= n <= 200

  • 1 <= rating[i] <= 10^5

Hints:

  1. BruteForce, check all possibilities.

1. Dynamic programming [O(N^2), O(1)]

[1]:

class Solution1(object):
    """
    Time: O(N^2)
    Space: O(1)
    """
    def numTeams(self, rating):
        """
        :type rating: List[int]
        :rtype: int
        """
        result = 0

        for i in range(1, len(rating)-1):
            less, greater = [0]*2, [0]*2

            for j in range(len(rating)):
                if rating[i] > rating[j]:
                    less[i < j] += 1
                if rating[i] < rating[j]:
                    greater[i < j] += 1

            result += less[0]*greater[1] + greater[0]*less[1]

        return result

[2]:

s = Solution1()

rating = [2,5,3,4,1]
assert s.numTeams(rating) == 3

rating = [2,1,3]
assert s.numTeams(rating) == 0

rating = [1,2,3,4]
assert s.numTeams(rating) == 4