Count Number of Teams

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- Tag: #dynamicprogramming, #lis

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
- 1 <= n <= 200
- 1 <= rating[i] <= 10^5

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

- Solution:

## https://code.dennyzhang.com/count-number-of-teams ## Basic Ideas: dynamic programming ## Complexity: Time O(n^2), Space O(n) class Solution: def numTeams(self, rating: List[int]) -> int: n = len(rating) dp = [[0, 0] for i in range(n)] res = 0 for k in range(1, n): for j in range(0, k): # . j. k if rating[j]<rating[k]: res += dp[j][0] dp[k][0] += 1 if rating[j]>rating[k]: res += dp[j][1] dp[k][1] += 1 return res