Leetcode #2591: Distribute Money to Maximum Children
In this guide, we solve Leetcode #2591 Distribute Money to Maximum Children in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an integer money denoting the amount of money (in dollars) that you have and another integer children denoting the number of children that you must distribute the money to. You have to distribute the money according to the following rules: All money must be distributed.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Greedy, Math
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: money = 20, children = 3
Output: 1
Explanation:
The maximum number of children with 8 dollars will be 1. One of the ways to distribute the money is:
- 8 dollars to the first child.
- 9 dollars to the second child.
- 3 dollars to the third child.
It can be proven that no distribution exists such that number of children getting 8 dollars is greater than 1.
Python Solution
class Solution:
def distMoney(self, money: int, children: int) -> int:
if money < children:
return -1
if money > 8 * children:
return children - 1
if money == 8 * children - 4:
return children - 2
# money-8x >= children-x, x <= (money-children)/7
return (money - children) // 7
Complexity
The time complexity is O(n log n). The space complexity is O(1) to O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.