How to Solve Count the Number of Inversions Problem
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Count the Number of Inversions
You are given an integer n and a 2D array requirements, where requirements[i] = [endi, cnti] represents the end index and the inversion count of each requirement. A pair of indices (i, j) from an inte...
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Understanding the Count the Number of Inversions Problem
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Problem Statement
You are given an integer n and a 2D array requirements, where requirements[i] = [endi, cnti] represents the end index and the inversion count of each requirement. A pair of indices (i, j) from an integer array nums is called an inversion if: i < j and nums[i] > nums[j] Return the number of permutations perm of [0, 1, 2, ..., n - 1] such that for all requirements[i], perm[0..endi] has exactly cnti inversions. Since the answer may be very large, return it modulo 109 + 7.
Count the Number of Inversions
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Examples
n = 3, requirements = [[2,2],[0,0]]2The two permutations are: [2, 0, 1] Prefix [2, 0, 1] has inversions (0, 1) and (0, 2). Prefix [2] has 0 inversions. [1, 2, 0] Prefix [1, 2, 0] has inversions (0, 2) and (1, 2). Prefix [1] has 0 inversions.
n = 3, requirements = [[2,2],[1,1],[0,0]]1The only satisfying permutation is [2, 0, 1]: Prefix [2, 0, 1] has inversions (0, 1) and (0, 2). Prefix [2, 0] has an inversion (0, 1). Prefix [2] has 0 inversions.
n = 2, requirements = [[0,0],[1,0]]1The only satisfying permutation is [0, 1]: Prefix [0] has 0 inversions. Prefix [0, 1] has an inversion (0, 1).
Constraints
2 <= n <= 3001 <= requirements.length <= nrequirements[i] = [endi, cnti]0 <= endi <= n - 10 <= cnti <= 400The input is generated such that there is at least one i such that endi == n - 1.The input is generated such that all endi are unique.How Interview Coder Helps with Leetcode Problems
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