Beautiful Triplets

Given a sequence of integers a, a triplet (a[i], a[j], a[k]) is beautiful if:

• i < j < k
• a[j] - a[i] = a[k] - a[j] = d

Given an increasing sequenc of integers and the value of d, count the number of beautiful triplets in the sequence.

For example, the sequence arr = [2, 2, 3, 4, 5] and d = 1. There are three beautiful triplets, by index: [i, j, k] = [0, 2, 3], [1, 2, 3], [2, 3, 4]. To test the first triplet, arr[j] - arr[i] = 3 - 2 = 1 and arr[k] = arr[j] = 4 - 3 = 1.

Function Description

Complete the beautifulTriplets function in the editor below. It must return an integer that represents the number of beautiful triplets in the sequence.

beautifulTriplets has the following parameters:

• d: an integer
• arr: an array of integers, sorted ascending

Input Format

The first line contains 2 space-separated integers n and d, the length of the sequence and the beautiful difference.
The second line contains n space-separated integers arr[i].

Constraints

Output Format

Print a single line denoting the number of beautiful triplets in the sequence.

Sample Input

1
2

7 3
1 2 4 5 7 8 10

Sample Output

1

3

Explanation

The input sequence is 1, 2, 4, 5, 6, 8, 10, and our beautiful difference d = 3. There are many possible triplets (arr[i], arr[j], arr[k]), but our only beautiful triplets are (1, 4, 7), (4, 7, 10) and (2, 5, 8) by value not index. Please see the equations below:

• 7 - 4 = 4 - 1 = 3 = d
• 10 - 7 = 7 - 4 = 3 = d
• 8 - 5 = 5 - 2 = 3 = d

Recall that a beautiful triplet satisfies the following equivalence relation:
arr[j] - arr[i] = arr[k] - arr[j] = d where i < j < k.

Solution Accepted

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function beautifulTriplets(d, arr) {
  const arraySet = new Set(arr);
  const array = [...arr];

  return array.reduce((target, number) => {
    new Array(3).fill(0).reduce((innerTarget, item, index) => {
      let value = number + index * d;
      arraySet.has(value) && innerTarget++;
      return innerTarget;
    }, 0) === 3 && target++;

    return target;
  }, 0);
}