LeetCode 1155: Number of Dice Rolls With Target Sum Solution

Master LeetCode problem 1155 (Number of Dice Rolls With Target Sum), a medium 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.

1155. Number of Dice Rolls With Target Sum

Medium

Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We create a 2D dp array where dp[i][j] represents the number of ways to get a sum of j using i dice. We then iterate through each dice and each possible sum to calculate the number of ways to reach that sum.

Initialize a 2D dp array of size (n+1) x (target+1), where dp[i][j] represents the number of ways to get a sum of j using i dice.
Base case: dp[0][0] = 1 (There is 1 way to get a sum of 0 using 0 dice).
Iterate through each dice (i) from 1 to n and each possible sum (j) from 1 to target.
For each dice and sum, calculate the number of ways to reach that sum by summing up the number of ways for all possible outcomes of the current dice roll.
Return dp[n][target] % (10^9 + 7) as the final result.

Time Complexity: O(n * target * k) Space Complexity: O(n * target)

Solution Code

class Solution {
    public int numRollsToTarget(int n, int k, 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 <= target; j++) {
                for (int l = 1; l <= k; l++) {
                    if (j - l >= 0) {
                        dp[i][j] = (dp[i][j] + dp[i - 1][j - l]) % mod;
                    }
                }
            }
        }
        return dp[n][target];
    }
}

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