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g1201_1300.s1223_dice_roll_simulation.readme.md Maven / Gradle / Ivy

1223\. Dice Roll Simulation

Hard

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`