Today I have done leetcode's January LeetCoding Challenge with cpp.

January LeetCoding Challenge 27

Description

K Inverse Pairs Array

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 109 + 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.

Constraints:

• 1 <= n <= 1000
• 0 <= k <= 1000

Solution

const int MOD = 1e9 + 7;
int values[1001][1001] = {};
const int SZ = 1000;
void init(int N) {
  values[0][0] = 1;
  for(int i = 1; i <= N; ++i) {
    int nextJ = i * (i + 1) / 2;
    int J = i * (i - 1) / 2;
    J = J > SZ ? SZ : J;
    nextJ = nextJ > SZ ? SZ : nextJ;
    for(int j = 0; j <= J; ++j) {
      values[i][j] = (j ? values[i][j - 1] : 0) + values[i - 1][j] - (i > j ? 0 : values[i - 1][j - i]);
      values[i][j] = (values[i][j] % MOD + MOD) % MOD;
    }
    for(int j = J + 1; j <= nextJ; ++j) {
      values[i][j] = values[i][j - 1];
    }
  }
}

class Solution {
public:
  int kInversePairs(int n, int k) {
    if(!k) return 1;
    init(n);
    int answer = values[n][k] - values[n][k - 1];
    answer = (answer % MOD + MOD) % MOD;
    return answer;
  }
};

// Accepted
// 80/80 cases passed (66 ms)
// Your runtime beats 27.47 % of cpp submissions
// Your memory usage beats 44.5 % of cpp submissions (11 MB)