1395_count-number-of-teams.md

title
1395. Count Number of Teams

Problem

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

Solution

Brute Force

/**
 * @param {number[]} rating
 * @return {number}
 */
var numTeams = function(rating) {
    let ans = 0;
    let n = rating.length;
    for(let i=0;i<n;i++){
        for(let j=i+1;j<n;j++){
            for(let k=j+1;k<n;k++){
                if(rating[i] < rating[j] && rating[j] < rating[k]){
                    ans++
                } else if(rating[i] > rating[j] && rating[j] > rating[k]){
                    ans++
                }
            }
        }
    }
    return ans
};

• Time Complexity: O(n^3)
• Space Complexity: O(1)