How do you solve Distribute Candies Among Children I on LeetCode?

Distribute Candies Among Children I (LeetCode #2928) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the constraints of the problem helps in optimizing the solution.

What is the brute force solution for Distribute Candies Among Children I?

The brute force approach for Distribute Candies Among Children I is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks all possible distributions of candies among the three children. By using three nested loops, we can iterate through all possible combinations of candies each child can receive, ensuring that the total does not exceed 'n' and each child does not receive more than 'limit'. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Distribute Candies Among Children I?

Distribute Candies Among Children I uses the following concepts: Math, Combinatorics, Enumeration. The recommended patterns to study are: Combinatorial Counting, Dynamic Programming.

What are the interview tips for Distribute Candies Among Children I?

Always start with a brute force solution to understand the problem better. Think about how you can reduce the number of iterations by using mathematical insights. Be mindful of the constraints and edge cases when implementing your solution.

What are common mistakes when solving Distribute Candies Among Children I?

Not considering edge cases where 'n' is less than the total possible candies. Failing to check the bounds for each child's candy count.

#2928

Distribute Candies Among Children I

Easy

MathCombinatoricsEnumerationCombinatorial CountingDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

Instead of checking all combinations, we can use a mathematical approach to count valid distributions directly. By calculating the maximum candies each child can receive and using combinatorial counting, we can derive the total number of distributions efficiently.

⚙️

Algorithm

3 steps

1Step 1: Determine the maximum candies each child can receive, which is the minimum of 'limit' and 'n'.
2Step 2: Use a combinatorial formula to calculate the number of ways to distribute the remaining candies after ensuring each child gets at least 0 and at most 'limit'.
3Step 3: Return the total count of valid distributions.

solution.py9 lines

1def distributeCandies(n, limit):
2    max_candies = min(limit, n)
3    count = 0
4    for a in range(max_candies + 1):
5        for b in range(max_candies + 1):
6            c = n - a - b
7            if 0 <= c <= max_candies:
8                count += 1
9    return count

ℹ

Complexity note: The time complexity is O(n) because we only iterate through possible values of 'a' and 'b', while calculating 'c' directly. The space complexity is O(1) since we only use a few variables for counting.

1Understanding the constraints of the problem helps in optimizing the solution.
2Using combinatorial counting can significantly reduce the number of iterations needed.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.