Count Good Triplets in an Array

Difficulty: Hard

Topics:
Array , Binary Search , Binary Indexed Tree , Divide and Conquer , Merge Sort , Ordered Set , Segment Tree

Hint:
You are given two 0-indexed arrays nums1 and nums2 of length n, both of which are permutations of [0, 1, ..., n - 1].

A good triplet is a set of 3 distinct values which are present in increasing order by position both in nums1 and nums2. In other words, if we consider pos1v as the index of the value v in nums1 and pos2v as the index of the value v in nums2, then a good triplet will be a set (x, y, z) where 0 <= x, y, z <= n - 1, such that pos1x < pos1y < pos1z and pos2x < pos2y < pos2z.

Return the total number of good triplets.

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Example 1

Input: nums1 = [2,0,1,3], nums2 = [0,1,2,3] Output: 1 Explanation: There are 4 triplets (x, y, z) such that pos1x < pos1y < pos1z. They are (2,0,1), (2,0,3), (2,1,3), and (0,1,3). Out of those triplets, only the triplet (0,1,3) satisfies pos2x < pos2y < pos2z. Hence, there is only 1 good triplet.

Example 2

Input: nums1 = [4,0,1,3,2], nums2 = [4,1,0,2,3] Output: 4 Explanation: The 4 good triplets are (4,0,3), (4,0,2), (4,1,3), and (4,1,2).

Constraints

• $n = \text{nums1.length} = \text{nums2.length}$
• $3 \le n \le 10^5$
• $0 \le \text{nums1}[i], \ \text{nums2}[i] \le n - 1$
• $\text{nums1 and nums2 are permutations of } \{ 0, 1, \dots, n - 1 \}$