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Distribute Money to Maximum Children

Difficulty: Easy

Problem Description

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 must distribute the money according to the following rules: All money must be distributed, everyone must receive at least 1 dollar, and nobody receives 4 dollars. Return the maximum number of children who may receive exactly 8 dollars if you distribute the money according to the aforementioned rules. If there is no way to distribute the money, return -1.

Key Insights

  • Each child must receive at least 1 dollar, so the minimum amount of money needed is equal to the number of children.
  • The distribution must ensure that no child receives exactly 4 dollars.
  • The goal is to maximize the number of children receiving exactly 8 dollars while adhering to the constraints.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve the problem, we can use a greedy approach. First, we need to check if it is possible to distribute the money according to the rules. We can calculate the maximum number of children that can receive 8 dollars by checking how much money will be left after giving 8 dollars to a certain number of children. We must ensure that the remaining money can be distributed among the other children without violating the constraints (e.g., ensuring no child receives 4 dollars).

  1. Calculate the maximum possible children that can receive 8 dollars.
  2. For each possible number of children that could receive 8 dollars (from maximum to minimum), check if the remaining money can be distributed to the other children such that none receive 4 dollars and each receives at least 1 dollar.
  3. If a valid distribution is found, return the number of children receiving 8 dollars.

Code Solutions

def maxChildrenWithEightDollars(money: int, children: int) -> int:
    # Calculate the maximum number of children that can receive 8 dollars
    max_eight_children = money // 8

    # Iterate from max_eight_children down to 0
    for eight_children in range(max_eight_children, -1, -1):
        # Remaining money after giving 8 dollars to 'eight_children'
        remaining_money = money - (eight_children * 8)
        # Remaining children
        remaining_children = children - eight_children
        
        # Check if remaining money can be distributed
        if remaining_children > 0:
            # Each remaining child must get at least 1 dollar and cannot get 4 dollars
            if remaining_money >= remaining_children and remaining_money != 4 * remaining_children:
                return eight_children
        
        # If there are no remaining children, check if the remaining money is non-negative
        elif remaining_money >= 0:
            return eight_children
    
    return -1
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