Minimum Amount of Time to Fill Cups

Problem Description

You have a water dispenser that can dispense cold, warm, and hot water. Every second, you can either fill up 2 cups with different types of water, or 1 cup of any type of water. You are given a 0-indexed integer array amount of length 3 where amount[0], amount[1], and amount[2] denote the number of cold, warm, and hot water cups you need to fill respectively. Return the minimum number of seconds needed to fill up all the cups.

Key Insights

• Each second, you can fill 2 cups of different types or 1 cup of any type.
• The goal is to minimize the total time taken to fill all cups.
• The maximum cups needed of any type influences the total time taken.
• The maximum of the three amounts can determine if pairs can be formed or if single fills are necessary.

Space and Time Complexity

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

Solution

To solve this problem, we can use a greedy approach. The key is to always fill cups in pairs when possible, which minimizes time. We can take the maximum value from the amounts to determine the number of seconds needed. If the maximum amount is greater than the sum of the other two, the time needed will be equal to the maximum amount. Otherwise, the time will be the ceiling of half the total cups needed.

1. Calculate the total cups needed by summing the amounts.
2. Identify the maximum amount of cups needed for any single type.
3. If the maximum amount is greater than the sum of the other two amounts, return that maximum.
4. Otherwise, return the ceiling of half the total cups.

Code Solutions