Dice Roll Simulation

Problem Statement

A die simulator generates a random number from 1 to 6 for each roll. You introduced a constraint to the generator such that it cannot roll the number i more than rollMax[i] (1-indexed) consecutive times.

Given an array of integers rollMax and an integer n, return the number of distinct sequences that can be obtained with exact n rolls. Since the answer may be too large, return it modulo 10``<sup>9</sup> + 7.

Two sequences are considered different if at least one element differs from each other.

Example 1:

Input: n = 2, rollMax = [1,1,2,2,2,3]
Output: 34

Explanation:

There will be 2 rolls of die, if there are no constraints on the die, there are 6 * 6 = 36 possible combinations. In this case, looking at rollMax array, the numbers 1 and 2 appear at most once consecutively, therefore sequences (1,1) and (2,2) cannot occur, so the final answer is 36-2 = 34.

Example 2:

Input: n = 2, rollMax = [1,1,1,1,1,1]
Output: 30

Example 3:

Input: n = 3, rollMax = [1,1,1,2,2,3]
Output: 181

Constraints:

• 1 <= n <= 5000
• rollMax.length == 6
• 1 <= rollMax[i] <= 15

Code

Python Code

class Solution:
    def dieSimulator(self, n: int, rollMax: List[int]) -> int:
        MOD=10**9+7
        dp=[[[0]*(max(rollMax)+1) for i in range(6)] for j in range(n)]
        for i in range(6):
            dp[0][i][1]=1
        for i in range(1,n):
            for j in range(6):
                for k in range(1,rollMax[j]+1):
                    if(k==1):
                        for p in range(6):
                            if(p!=j):
                                dp[i][j][k]+=sum(dp[i-1][p])%MOD
                    else:
                        dp[i][j][k]=dp[i-1][j][k-1]
        res=0
        for j in range(6):
            for k in range(1,rollMax[j]+1):
                res=(res+dp[n-1][j][k])%MOD
        return res