How do you solve Distribute Money to Maximum Children on LeetCode?

Distribute Money to Maximum Children (LeetCode #2591) 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: Distributing money must consider both the total amount and the constraints on individual amounts.

What is the time complexity of Distribute Money to Maximum Children?

The optimal solution for Distribute Money to Maximum Children runs in O(n) time and uses O(1) space. The time complexity is O(n) because we check each possible k only once, leading to a linear scan.

What is the brute force solution for Distribute Money to Maximum Children?

The brute force approach for Distribute Money to Maximum Children is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible number of children that can receive exactly 8 dollars, starting from the maximum possible down to zero. This way, we can check if the remaining money can be distributed to the other children while adhering to the rules. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Distribute Money to Maximum Children?

Distribute Money to Maximum Children uses the following concepts: Math, Greedy. The recommended patterns to study are: Greedy, Mathematical Constraints.

What are the interview tips for Distribute Money to Maximum Children?

Always clarify the constraints and edge cases before diving into coding. Think about how you can reduce the number of iterations or checks to improve efficiency. Practice explaining your thought process clearly as you code, as this helps interviewers understand your approach.

What are common mistakes when solving Distribute Money to Maximum Children?

Failing to check if remaining money equals 4 times the remaining children, which leads to invalid distributions. Not considering edge cases where money is just enough to give each child 1 dollar.

#2591

Distribute Money to Maximum Children

Easy

MathGreedyGreedyMathematical Constraints

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)

The optimal approach calculates the maximum number of children that can receive 8 dollars directly by checking the constraints of the remaining money and children. This avoids unnecessary iterations and checks.

⚙️

Algorithm

4 steps

1Step 1: Calculate the maximum possible k as min(children, money // 8).
2Step 2: Calculate the remaining money after giving k children 8 dollars.
3Step 3: Check if the remaining money can be distributed among the remaining children without violating the rules.
4Step 4: If valid, return k. If not, decrement k and repeat until a valid distribution is found or return -1.

solution.py8 lines

1def maxChildren(money, children):
2    max_k = min(children, money // 8)
3    for k in range(max_k, -1, -1):
4        remaining_money = money - k * 8
5        remaining_children = children - k
6        if remaining_money >= remaining_children and remaining_money != 4 * remaining_children:
7            return k
8    return -1

ℹ

Complexity note: The time complexity is O(n) because we check each possible k only once, leading to a linear scan.

1Distributing money must consider both the total amount and the constraints on individual amounts.
2The problem can be approached by iterating downwards from the maximum possible distribution to find the first valid configuration.

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