LeetCode 2318: Number of Distinct Roll Sequences Solution

Master LeetCode problem 2318 (Number of Distinct Roll Sequences), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2318. Number of Distinct Roll Sequences

Hard

Dynamic Programming Memoization

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming to keep track of the number of valid sequences at each step. We can define a state dp[i][j] as the number of valid sequences of length i ending with j. We can then transition to the next state based on the constraints given in the problem.

At each step, we need to consider the valid transitions from the previous state. We can iterate over the previous state dp[i-1][k] and check if we can transition to the current state dp[i][j] based on the conditions mentioned in the problem.

After calculating the number of valid sequences for each step, we can sum up the total number of valid sequences of length n to get the final result.

Time complexity: O(n66) = O(n), where n is the input integer n. Space complexity: O(n*6)

Solution Code

class Solution {
    public int numRollsToTarget(int n, int faces, int target) {
        int MOD = 1000000007;
        int[][] dp = new int[n + 1][target + 1];
        dp[0][0] = 1;
        
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= faces; j++) {
                for (int k = j; k <= target; k++) {
                    dp[i][k] = (dp[i][k] + dp[i - 1][k - j]) % MOD;
                }
            }
        }
        
        return dp[n][target];
    }
}

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