1223. Dice Roll Simulation

https://leetcode.com/problems/dice-roll-simulation

Description

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 109 + 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

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