How do you solve Dice Roll Simulation on LeetCode?

Dice Roll Simulation (LeetCode #1223) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * 6 * 6) time complexity and O(n * 6) space complexity. Key insight: Dynamic programming is essential for optimizing problems with overlapping subproblems.

What is the brute force solution for Dice Roll Simulation?

The brute force approach for Dice Roll Simulation is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach generates all possible sequences of rolls and then filters out the invalid ones based on the rollMax constraints. This method is straightforward but inefficient due to the exponential growth of combinations. The optimal Optimal Solution approach improves this to O(n * 6 * 6).

What algorithm or data structure is used to solve Dice Roll Simulation?

Dice Roll Simulation uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, State Transition.

What are the interview tips for Dice Roll Simulation?

Always clarify the problem constraints before jumping into coding. Discuss your thought process and approach with the interviewer. Consider edge cases and how they might affect your solution.

What are common mistakes when solving Dice Roll Simulation?

Not considering the constraints properly when counting sequences. Overlooking the need to use modulo operations to avoid overflow.

#1223

Dice Roll Simulation

Hard

ArrayDynamic ProgrammingDynamic ProgrammingState Transition

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * 6 * 6)
Space	O(1)	O(n * 6)

💡

Intuition

Time O(n * 6 * 6)Space O(n * 6)

Using dynamic programming, we can efficiently count valid sequences by maintaining a state that tracks the last rolled number and how many times it has been rolled consecutively. This avoids generating all sequences explicitly.

⚙️

Algorithm

3 steps

1Step 1: Initialize a DP array where dp[i][j] represents the number of valid sequences of length i ending with the number j.
2Step 2: Iterate through each length from 1 to n, and for each possible last roll, calculate valid sequences based on previous rolls.
3Step 3: Use the rollMax constraints to limit how many times a number can be repeated consecutively.

solution.py17 lines

1# Full working Python code
2MOD = 10**9 + 7
3
4def dieSimulator(n, rollMax):
5    dp = [[0] * 6 for _ in range(n + 1)]
6    for j in range(6):
7        dp[1][j] = 1
8    for i in range(2, n + 1):
9        for j in range(6):
10            for k in range(6):
11                if j != k:
12                    dp[i][j] = (dp[i][j] + sum(dp[i - 1])) % MOD
13                else:
14                    for m in range(1, rollMax[j] + 1):
15                        if i - m >= 0:
16                            dp[i][j] = (dp[i][j] + dp[i - m][j]) % MOD
17    return sum(dp[n]) % MOD

ℹ

Complexity note: The time complexity is O(n * 6 * 6) because we iterate through each roll length (n), and for each last roll (6 options), we check against all other rolls (6 options).

1Dynamic programming is essential for optimizing problems with overlapping subproblems.
2Understanding constraints helps in designing the state transitions effectively.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.