{ "data": { "question": { "questionId": "3460", "questionFrontendId": "3193", "boundTopicId": null, "title": "Count the Number of Inversions", "titleSlug": "count-the-number-of-inversions", "content": "

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.

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A pair of indices (i, j) from an integer array nums is called an inversion if:

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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.

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Since the answer may be very large, return it modulo 109 + 7.

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Example 1:

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Input: n = 3, requirements = [[2,2],[0,0]]

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Output: 2

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Explanation:

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The two permutations are:

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Example 2:

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Input: n = 3, requirements = [[2,2],[1,1],[0,0]]

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Output: 1

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Explanation:

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The only satisfying permutation is [2, 0, 1]:

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Example 3:

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Input: n = 2, requirements = [[0,0],[1,0]]

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Output: 1

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Explanation:

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The only satisfying permutation is [0, 1]:

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Constraints:

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Compiled with clang 17 using the latest C++ 20 standard, and libstdc++ provided by GCC 11.

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Python 2.7.12.

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Ruby 3.2

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Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

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Go 1.21

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Python 3.11.

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Kotlin 1.9.0.

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PHP 8.2.

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TypeScript 5.1.6, Node.js 20.10.0.

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Racket CS v8.11

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