Count the number of index triplets whose pairwise absolute differences stay within given bounds.
Problem
Given an array of integers nums and three integers a, b, and c, count how many triplets of indices (i, j, k) satisfy:
0 <= i < j < k < nums.length|nums[i] - nums[j]| <= a|nums[j] - nums[k]| <= b|nums[i] - nums[k]| <= c
Return the total number of such good triplets.
This is a straightforward counting problem: you need to examine ordered index triplets and test whether they meet all three value-difference constraints.
Input Format
- An integer array
nums - Three integers
a,b, andc
Output Format
- Return one integer: the number of good triplets
Constraints
3 <= nums.length- The array contains integers
a,b, andcare non-negative integers
Example 1
Input
nums = [3,0,1,1,9,7], a = 7, b = 2, c = 3
Output
4
Explanation
The good triplets are indexed by (0,1,2), (0,1,3), (0,2,3), and (1,2,3).
Example 2
Input
nums = [1,1,2,2,3], a = 0, b = 0, c = 1
Output
0
Explanation
No ordered triplet of indices satisfies all three difference constraints.
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