K Inverse Pairs Array
HardDynamic Programming2d dp
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An inverse pair in an array is a pair of indices (i, j) with i < j and a[i] > a[j].
Given n and k, count how many permutations of 1, 2, ..., n contain exactly k inverse pairs. Return the count modulo 10^9 + 7. If no permutation qualifies, return 0.
Aim for O(n * k) time.
Examples
Input: n = 3, k = 0
Output: 1
Only [1,2,3] has no inverse pairs.
Input: n = 3, k = 1
Output: 2
[1,3,2] and [2,1,3] each have exactly one inverse pair.
Constraints
- 1 <= n <= 1000
- 0 <= k <= 1000
What the interviewer grades
A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.