LeetCode 2928: Distribute Candies Among Children I Solution

Master LeetCode problem 2928 (Distribute Candies Among Children I), a easy 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.

2928. Distribute Candies Among Children I

Easy

Math Combinatorics Enumeration

Problem Explanation

Explanation

To solve this problem, we can use a recursive approach along with memoization to avoid recalculating the same subproblems. We can define a recursive function that takes the remaining candies to distribute, the current child we are distributing candies to, and the limit on the number of candies a child can have. We can iterate through all possible distributions by assigning candies to the current child and recursively calling the function for the next child.

Algorithm:

Define a recursive function distributeCandies that takes the remaining candies, the current child index, and the limit.
Initialize a memoization array to store the number of ways to distribute the remaining candies for a given child and limit.
In the recursive function:
- Base case: If all children have been assigned candies, return 1 if there are no candies left to distribute, else return 0.
- If the number of ways to distribute the remaining candies at the current child index and limit is already calculated, return it from the memoization array.
- Iterate through all possible ways to distribute candies to the current child within the limit, recursively call the function for the next child with updated parameters, and sum up the results.
- Store the result in the memoization array and return it.
Call the recursive function with initial parameters (n, 0, limit) to get the total number of ways.

Time Complexity:

The time complexity of this solution is O(n * limit^3) due to memoization.

Space Complexity:

The space complexity is O(n * limit) to store the memoization array.

Solution Code

class Solution {
    public int distributeCandies(int n, int limit) {
        int[][][] memo = new int[n + 1][3][limit + 1];
        return distributeCandies(n, 0, limit, memo);
    }
    
    private int distributeCandies(int candies, int childIndex, int limit, int[][][] memo) {
        if (childIndex == 3) {
            return candies == 0 ? 1 : 0;
        }
        
        if (memo[candies][childIndex][limit] != 0) {
            return memo[candies][childIndex][limit];
        }
        
        int ways = 0;
        for (int i = 0; i <= limit && i <= candies; i++) {
            ways += distributeCandies(candies - i, childIndex + 1, limit, memo);
        }
        
        memo[candies][childIndex][limit] = ways;
        return ways;
    }
}

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