2023-12-26 Daily Challenge

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

December LeetCoding Challenge 26

Description

Number of Dice Rolls With Target Sum

You have n dice, and each die has k faces numbered from 1 to k.

Given three integers n, k, and target, return the number of possible ways (out of the kn total ways) to roll the dice, so the sum of the face-up numbers equals target. Since the answer may be too large, return it modulo 109 + 7.

 

Example 1:

Input: n = 1, k = 6, target = 3
Output: 1
Explanation: You throw one die with 6 faces.
There is only one way to get a sum of 3.

Example 2:

Input: n = 2, k = 6, target = 7
Output: 6
Explanation: You throw two dice, each with 6 faces.
There are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.

Example 3:

Input: n = 30, k = 30, target = 500
Output: 222616187
Explanation: The answer must be returned modulo 109 + 7.

 

Constraints:

  • 1 <= n, k <= 30
  • 1 <= target <= 1000

Solution

int dp[2][1001];
const int MOD = 1e9 + 7;
class Solution {
public:
  int numRollsToTarget(int d, int f, int target) {
    if(d * f < target || d > target) return 0;
    if(d == target) return 1;
    memset(dp, 0, sizeof(dp));
    dp[0][0] = 1;
    for(int i = 1; i <= d; ++i) {
      int parity = i & 1;
      for(int j = 0; j < i; ++j) {
        dp[parity][j] = 0;
      }
      for(int j = i; j <= i * f; ++j) {
        dp[parity][j] = 0;
        for(int k = 1; k <= f; ++k) {
          if(j - k < 0) continue;
          dp[parity][j] += dp[!parity][j - k];
          dp[parity][j] %= MOD;
        }
      }
      // for(int j = 0; j <= i * f; ++j) {
      //   cout << dp[parity][j] << ' ';
      // }
      // cout << endl;
    }
    return dp[d & 1][target];
  }
};

// Accepted
// 65/65 cases passed (0 ms)
// Your runtime beats 100.00 % of cpp submissions
// Your memory usage beats 99.60 % of cpp submissions (5.9 MB)
Algorithm