629. K Inverse Pairs Array

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題目敘述

For an integer array nums, an inverse pair is a pair of integers [i, j] where 0 <= i < j < nums.length and nums[i] > nums[j].

Given two integers n and k, return the number of different arrays consist of numbers from 1 to n such that there are exactly k inverse pairs. Since the answer can be huge, return it modulo 10^9 + 7.

Example 1

Input: n = 3, k = 0 Output: 1 Explanation: Only the array [1,2,3] which consists of numbers from 1 to 3 has exactly 0 inverse pairs.

Example 2

Input: n = 3, k = 1 Output: 2 Explanation: The array [1,3,2] and [2,1,3] have exactly 1 inverse pair.

解題思路

Solution

class Solution {
    private static final int MOD = 1000000007;
    
    public static int kInversePairs(int n, int k) {
        int[][] dp = new int[n + 1][k + 1];

        for (int i = 0; i <= n; i++) {
            dp[i][0] = 1;
        }

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= k; j++) {
                dp[i][j] = (dp[i][j - 1] + dp[i - 1][j]) % MOD;
                if (j >= i) {
                    dp[i][j] = (dp[i][j] - dp[i - 1][j - i] + MOD) % MOD;
                }
            }
        }

        return dp[n][k];
    }
}