How to Solve Dice Roll Simulation Problem
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Dice Roll Simulation
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 tim...
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Understanding the Dice Roll Simulation Problem
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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 109 + 7. Two sequences are considered different if at least one element differs from each other.
Dice Roll Simulation
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Examples
n = 2, rollMax = [1,1,2,2,2,3]
34
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.
n = 2, rollMax = [1,1,1,1,1,1]
30
n = 3, rollMax = [1,1,1,2,2,3]
181
Constraints
1 <= n <= 5000
rollMax.length == 6
1 <= rollMax[i] <= 15
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