Count Number of Teams

Description

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(javascript)

/**
 * @param {number[]} rating
 * @return {number}
 */
const numTeams = function (rating) {
  const memo = {}
  const aux = (index, count, gt = true) => {
    const key = `${index},${count},${gt}`
    if (memo[key] !== undefined) {
      return memo[key]
    }
    if (count === 3) {
      return 1
    }
    let result = 0
    for (let i = index + 1; i < rating.length; i++) {
      if (rating[i] > rating[index] && gt) {
        result += aux(i, count + 1, gt)
      }
      if (rating[i] < rating[index] && !gt) {
        result += aux(i, count + 1, gt)
      }
    }
    memo[key] = result
    return memo[key]
  }
  let result = 0
  for (let i = 0; i < rating.length; i++) {
    result += aux(i, 1, true) + aux(i, 1, false)
  }
  return result
}