LeetCode 2927: Distribute Candies Among Children III Solution

Master LeetCode problem 2927 (Distribute Candies Among Children III), 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.

2927. Distribute Candies Among Children III

Hard

Math Combinatorics

Problem Explanation

Explanation

To solve this problem, we can use a binary search approach. We can start with a guess for the amount of candies to give to each child. We can then simulate the distribution process and adjust our guess based on the total number of candies distributed.

Here's the detailed algorithm:

Define a binary search range from 1 to the maximum number of candies a child can have (which is the maximum value in the given candies array).
Perform a binary search within this range to find the optimal number of candies to give to each child.
In each iteration of the binary search, simulate the distribution process by iterating over the candies array and distributing candies to each child according to the guessed value.
Keep track of the total number of candies distributed. If the total exceeds the maximum allowed total (given by the total number of candies divided by the number of children), adjust the upper limit of the binary search. If the total is less, adjust the lower limit.
Repeat the process until the binary search converges to the optimal number of candies to give to each child.

Time complexity: O(n log m), where n is the number of candies and m is the maximum number of candies a child can have. Space complexity: O(1)

Solution Code

class Solution {
    public int[] distributeCandies(int candies, int num_people) {
        int[] distribution = new int[num_people];
        int rounds = (int)(Math.sqrt(1 + 8 * (long)candies) - 1) / (2 * num_people);
        for (int i = 0; i < num_people; i++) {
            distribution[i] = (rounds * (2 * i + 2 + (rounds - 1) * num_people)) / 2;
            candies -= distribution[i];
        }
        int lastChild = rounds * num_people;
        int remaining = candies;
        for (int i = 0; i < num_people && remaining > 0; i++) {
            int toGive = Math.min(remaining, lastChild + i + 1);
            distribution[i] += toGive;
            remaining -= toGive;
        }
        return distribution;
    }
}

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