Count Number of Teams

Problem statement

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: 3Explanation: 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: 0Explanation: 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.

My solution

/**
 * @param {number[]} rating
 * @return {number}
 */
var numTeams = function(rating) {
    const lesserDp = Array.from({
        length: rating.length
    }, () => 0)
    const greaterDp = Array.from({
        length: rating.length
    }, () => 0)
    
    let count = 0;
    
    for (let i = 0; i < rating.length; i++) {
        for (let j = 0; j < i; j++) {
            if (rating[j] < rating[i]) {
                lesserDp[i]++;
                
                count += lesserDp[j]
            }
            
            if (rating[j] > rating[i]) {
                greaterDp[i]++;
                count += greaterDp[j]
            }
        }
    }
    
    return count;
};