title
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.
Example 1:
Input: amount = [1,4,2]
Output: 4
Explanation: One way to fill up the cups is:
Second 1: Fill up a cold cup and a warm cup.
Second 2: Fill up a warm cup and a hot cup.
Second 3: Fill up a warm cup and a hot cup.
Second 4: Fill up a warm cup.
It can be proven that 4 is the minimum number of seconds needed.
Example 2:
Input: amount = [5,4,4]
Output: 7
Explanation: One way to fill up the cups is:
Second 1: Fill up a cold cup, and a hot cup.
Second 2: Fill up a cold cup, and a warm cup.
Second 3: Fill up a cold cup, and a warm cup.
Second 4: Fill up a warm cup, and a hot cup.
Second 5: Fill up a cold cup, and a hot cup.
Second 6: Fill up a cold cup, and a warm cup.
Second 7: Fill up a hot cup.
Example 3:
Input: amount = [5,0,0]
Output: 5
Explanation: Every second, we fill up a cold cup.
Constraints:
amount.length == 30 <= amount[i] <= 100
solution
We can use the technique of greedy and category discussion.
At every step only choose the max-2 cups to be filled.
class Solution:
def fillCups(self, amount: List[int]) -> int:
a, b, c = sorted(amount, reverse=True)
if b + c < a:
return a
t = b + c - a
if t % 2 == 0:
return (t // 2) + a
# t is odd
return ((t - 1) // 2) + a + 1