Count Good Triplets in an Array

arraybinary searchdivide and conquer

Problem Statement

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 pos1 _v as the index of the value v in nums1 and pos2 _v 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 pos1 _x < pos1 _y < pos1 _z and pos2 _x < pos2 _y < pos2 _z .

Return the total number of good triplets .

Examples

Example 1

Input: nums1 = [2,0,1,3], nums2 = [0,1,2,3]
Output: 1
There are 4 triplets (x,y,z) such that pos1 _x < pos1 _y < pos1 _z . 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 pos2 _x < pos2 _y < pos2 _z . Hence, there is only 1 good triplet.

Example 2

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

Constraints

n == nums1.length == nums2.length

3 <= n <= 10 ^5

0 <= nums1[i], nums2[i] <= n - 1

nums1 and nums2 are permutations of [0, 1, ..., n - 1] .

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicBinary Search