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.
Examples
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 == nums1.length == nums2.length
3 <= n <= 105
0 <= nums1[i], nums2[i] <= n - 1
nums1 and nums2 are permutations of [0, 1, ..., n - 1].
2179. Count Good Triplets in an Array
Hard
50 Points
Array
Binary Search
Divide and Conquer
Binary Indexed Tree
Segment Tree
Merge Sort
Ordered Set
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.
Examples
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 == nums1.length == nums2.length
3 <= n <= 105
0 <= nums1[i], nums2[i] <= n - 1
nums1 and nums2 are permutations of [0, 1, ..., n - 1].
Count Good Triplets in an Array - Practice Coding | SlaveCode