Is Dice Roll Simulation easy or hard?

Dice Roll Simulation is classified as a Hard problem because it requires careful state design in dynamic programming. The main challenge is handling consecutive roll constraints efficiently without exploding the state space.

Dice Roll Simulation Python/Java solution

Python and Java implementations typically use dynamic programming with either a 3D state dp[i][j][k] or an optimized 2D state dp[i][j]. Both compute transitions for the six dice faces and apply modulo 1e9+7 to avoid integer overflow.

How to solve Dice Roll Simulation in O(n)?

Use a dynamic programming table where dp[i][j] stores the number of sequences of length i ending with face j. Compute transitions using the total sequences from the previous step and subtract sequences that would exceed rollMax[j]. This avoids tracking streak length explicitly and keeps each iteration limited to the six faces.

What is the best approach for Dice Roll Simulation?

The most efficient approach uses dynamic programming. A 2D DP formulation tracks the number of sequences ending with each dice face and subtracts sequences that would violate the rollMax consecutive constraint. This reduces the state space compared to a full 3D DP while keeping the time complexity around O(n * 6).

Is Dice Roll Simulation asked at Google/Amazon/Meta?

Dice Roll Simulation represents the type of constraint-based dynamic programming problem commonly asked in interviews at companies like Google, Amazon, and Meta. The focus is on modeling state transitions and optimizing DP dimensions rather than brute-force enumeration.

What data structure is used in Dice Roll Simulation?

The solution primarily uses arrays for dynamic programming states. A 3D array tracks roll index, face value, and consecutive count, while the optimized approach uses a 2D DP array plus prefix totals to manage transitions efficiently.

What is the time complexity of Dice Roll Simulation?

The straightforward dynamic programming solution with a 3D state runs in O(n * 6 * maxRoll) time because it tracks the roll index, dice face, and streak length. An optimized 2D DP version reduces the complexity to roughly O(n * 6) by removing the explicit streak dimension and adjusting counts using previous states.

Description Hints 2 Solution Video 28:08

1223. Dice Roll Simulation

Hard51.4% acceptance2 companies

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

Asked at 2 companies

Akuna Capital

Google

Topics

Array Dynamic Programming

Hints open one at a time

Hint 1

Think on Dynamic Programming.

Hint 2

DP(pos, last) which means we are at the position pos having as last the last character seen.

28:08

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