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

October LeetCoding Challenge 7

Description

Build Array Where You Can Find The Maximum Exactly K Comparisons

You are given three integers n, m and k. Consider the following algorithm to find the maximum element of an array of positive integers:

You should build the array arr which has the following properties:

• arr has exactly n integers.
• 1 <= arr[i] <= m where (0 <= i < n).
• After applying the mentioned algorithm to arr, the value search_cost is equal to k.

Return the number of ways to build the array arr under the mentioned conditions. As the answer may grow large, the answer must be computed modulo 109 + 7.

Example 1:

Input: n = 2, m = 3, k = 1
Output: 6
Explanation: The possible arrays are [1, 1], [2, 1], [2, 2], [3, 1], [3, 2] [3, 3]

Example 2:

Input: n = 5, m = 2, k = 3
Output: 0
Explanation: There are no possible arrays that satisify the mentioned conditions.

Example 3:

Input: n = 9, m = 1, k = 1
Output: 1
Explanation: The only possible array is [1, 1, 1, 1, 1, 1, 1, 1, 1]

Constraints:

• 1 <= n <= 50
• 1 <= m <= 100
• 0 <= k <= n

Solution

class Solution {
public:
  int numOfArrays(int n, int m, int k) {
    const int MOD = 1e9 + 7;
    int dp[51][101][51] = {};
    int pre[51][101][51] = {};
    for(int i = 0; i <= m; ++i) {
      dp[1][i][1] = 1;
      pre[1][i][1] = i;
    }

    for(int len = 2; len <= n; ++len) {
      for(int mmax = 1; mmax <= m; ++mmax) {
        for(int cost = 1; cost <= k; ++cost) {
          dp[len][mmax][cost] = (1LL * mmax * dp[len - 1][mmax][cost]) % MOD;
          
          dp[len][mmax][cost] += pre[len - 1][mmax - 1][cost - 1];
          dp[len][mmax][cost] %= MOD;

          pre[len][mmax][cost] = pre[len][mmax - 1][cost] + dp[len][mmax][cost];
          pre[len][mmax][cost] %= MOD;
        }
      }
    }

    return pre[n][m][k];
  }
};

// Accepted
// 28/28 cases passed (3 ms)
// Your runtime beats 98.62 % of cpp submissions
// Your memory usage beats 43.32 % of cpp submissions (8.5 MB)