How hard is LeetCode 2318. Number of Distinct Roll Sequences?

LeetCode 2318. Number of Distinct Roll Sequences is rated Hard on LeetCode.

What topics does LeetCode 2318. Number of Distinct Roll Sequences cover?

LeetCode 2318. Number of Distinct Roll Sequences is tagged Memoization and Dynamic Programming on LeetCode.

Number of Distinct Roll Sequences — LeetCode 2318 Python Solution

HardMemoizationDynamic Programming

Problem: #2318
Pattern: Dynamic Programming
Reading time: 4 min
Source: leetcode.com

The problem

You are given an integer n. You roll a fair 6-sided dice n times.

Example

Input: n = 4
Output: 184
Explanation: Some of the possible sequences are (1, 2, 3, 4), (6, 1, 2, 3), (1, 2, 3, 1), etc.

Python solution

Python

class Solution:
    def distinctSequences(self, n: int) -> int:
        if n == 1:
            return 6
        mod = 10**9 + 7
        dp = [[[0] * 6 for _ in range(6)] for _ in range(n + 1)]
        for i in range(6):
            for j in range(6):
                if gcd(i + 1, j + 1) == 1 and i != j:
                    dp[2][i][j] = 1
        for k in range(3, n + 1):
            for i in range(6):
                for j in range(6):
                    if gcd(i + 1, j + 1) == 1 and i != j:
                        for h in range(6):
                            if gcd(h + 1, i + 1) == 1 and h != i and h != j:
                                dp[k][i][j] += dp[k - 1][h][i]
        ans = 0
        for i in range(6):
            for j in range(6):
                ans += dp[-1][i][j]
        return ans % mod

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2318. Number of Distinct Roll Sequences is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming and Memoization.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2318. Number of Distinct Roll Sequences?: LeetCode 2318. Number of Distinct Roll Sequences is rated Hard on LeetCode.
What topics does LeetCode 2318. Number of Distinct Roll Sequences cover?: LeetCode 2318. Number of Distinct Roll Sequences is tagged Memoization and Dynamic Programming on LeetCode.