Package g3101_3200.s3193_count_the_number_of_inversions

Class Solution

java.lang.Object
g3101_3200.s3193_count_the_number_of_inversions.Solution
public class Solution extends Object
3193 - Count the Number of Inversions.

Hard

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.

Example 1:

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

Output: 2

Explanation:

The 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.

Example 2:

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

Output: 1

Explanation:

The 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.

Example 3:

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

Output: 1

Explanation:

The only satisfying permutation is [0, 1]:

  • Prefix [0] has 0 inversions.
  • Prefix [0, 1] has an inversion (0, 1).

Constraints:

  • 2 <= n <= 300
  • 1 <= requirements.length <= n
  • requirements[i] = [endi, cnti]
  • 0 <= endi <= n - 1
  • 0 <= cnti <= 400
  • The 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.

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • numberOfPermutations

      public int numberOfPermutations(int n, int[][] r)