Is Distribute Candies Among Children I easy or hard?

The problem is classified as Easy on LeetCode with an acceptance rate above 70%. The main challenge is recognizing that the task is counting bounded integer solutions rather than generating every combination.

Distribute Candies Among Children I Python/Java solution

In Python or Java, implement a loop for the first child's candies and compute the valid range for the second child using min and max bounds. Add the size of the valid interval to the answer. The logic uses only integer arithmetic and runs in O(n) time with constant extra space.

How to solve Distribute Candies Among Children I in O(n)?

Iterate the number of candies given to the first child from 0 to limit. For each value x, compute the remaining candies r = n - x. The second child can take values from max(0, r - limit) to min(limit, r). The number of integers in this range gives the valid distributions for that iteration. Summing these counts yields the final answer in O(n) time.

What is the best approach for Distribute Candies Among Children I?

The best approach is an iterative combinatorial counting method. Iterate the candies given to the first child, then compute the valid range for the second child using the remaining candies and the per-child limit. The third child's value is determined automatically. This reduces the problem to O(n) time and O(1) space.

Is Distribute Candies Among Children I asked at Google/Amazon/Meta?

Problems involving constrained distributions and integer equations frequently appear in interviews at companies like Google, Amazon, and Meta. While this exact question may not always appear, the underlying pattern—counting bounded integer solutions using combinatorics—is a common interview concept.

What data structure is used in Distribute Candies Among Children I?

No complex data structures are required. The solution relies on simple arithmetic and iteration. The core idea comes from combinatorics and enumeration rather than arrays, stacks, or hash maps.

What is the time complexity of Distribute Candies Among Children I?

The optimized combinatorial solution runs in O(n) time because it iterates possible values for the first child's candies once and counts valid assignments mathematically. Space complexity is O(1). A naive enumeration approach may take O(n^2) time depending on how many combinations are checked.

Description Hints 1 Solution Video 1:00

2928. Distribute Candies Among Children I

Easy75.7% acceptance2 companies

You are given two positive integers n and limit.

Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.

Example 1:

Input: n = 5, limit = 2
Output: 3
Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).

Example 2:

Input: n = 3, limit = 3
Output: 10
Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).

Constraints:

1 <= n <= 50
1 <= limit <= 50

Asked at 2 companies

Rubrik Amazon

Topics

Hints open one at a time

Hint 1

Use three nested for loops to check all the triplets.

1:00

Still stuck?Read 3 approaches, or watch a walkthrough.

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