LeetCode 1692: Count Ways to Distribute Candies Solution

Master LeetCode problem 1692 (Count Ways to Distribute Candies), 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.

1692. Count Ways to Distribute Candies

Hard

Dynamic Programming

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. We can create a 2D DP array where dp[i][j] represents the number of ways to distribute i candies to j people such that each person gets at least one candy. We can initialize the base cases where dp[0][0] = 1 and dp[0][j] = 0 for j > 0.

Then, we can iterate over the number of candies and the number of people, filling in the DP array based on the recurrence relation: dp[i][j] = dp[i][j-1] + dp[i-j][j].

Finally, the answer will be the value in dp[n][k] where n is the number of candies and k is the number of people.

Time Complexity:

The time complexity of this solution is O(n*k) where n is the number of candies and k is the number of people.

Space Complexity:

The space complexity of this solution is O(n*k) for the DP array.

Solution Code

class Solution {
    public int waysToDistribute(int n, int k) {
        int mod = (int)1e9 + 7;
        long[][] dp = new long[n+1][k+1];
        dp[0][0] = 1;
        
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= k; j++) {
                dp[i][j] = (dp[i][j-1] + dp[i-1][j] * j) % mod;
            }
        }
        
        return (int)dp[n][k];
    }
}

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