1561. Maximum Number of Coins You Can Get

#Problem

There are 3n piles of coins of varying size, you and your friends will take piles of coins as follows:

• In each step, you will choose any 3 piles of coins (not necessarily consecutive).
• Of your choice, Alice will pick the pile with the maximum number of coins.
• You will pick the next pile with the maximum number of coins.
• Your friend Bob will pick the last pile.
• Repeat until there are no more piles of coins.

Given an array of integers piles where piles[i] is the number of coins in the iᵗʰ pile.

Return the maximum number of coins that you can have.

https://leetcode.cn/problems/maximum-number-of-coins-you-can-get/

Example 1:

Input: piles = [2,4,1,2,7,8]
Output: 9
Explanation: Choose the triplet (2, 7, 8), Alice Pick the pile with 8 coins, you the pile with 7 coins and Bob the last one.
Choose the triplet (1, 2, 4), Alice Pick the pile with 4 coins, you the pile with 2 coins and Bob the last one.
The maximum number of coins which you can have are: 7 + 2 = 9.
On the other hand if we choose this arrangement (1, 2, 8), (2, 4, 7) you only get 2 + 4 = 6 coins which is not optimal.

Example 2:

Input: piles = [2,4,5]
Output: 4

Example 3:

Input: piles = [9,8,7,6,5,1,2,3,4]
Output: 18

Constraints:

• 3 <= piles.length <= 10⁵
• piles.length % 3 == 0
• 1 <= piles[i] <= 10⁴

#Test Cases

class Solution:
    def maxCoins(self, piles: List[int]) -> int:

import pytest

from solution import Solution


@pytest.mark.parametrize('piles, expected', [
    ([2,4,1,2,7,8], 9),
    ([2,4,5], 4),
    ([9,8,7,6,5,1,2,3,4], 18),
])
@pytest.mark.parametrize('sol', [Solution()])
def test_solution(sol, piles, expected):
    assert sol.maxCoins(piles.copy()) == expected

#Thoughts

每次都取最大的两堆和最小的一堆，可以得到的硬币总数最多。

先对 piles 逆序排序，从第二大开始隔一个取一个，取 piles / 3 次即为可以得到的硬币总数。

时间复杂度 O(n log n)，做 in-place 排序额外的空间复杂度 O(1)。

#Code

class Solution:
    def maxCoins(self, piles: list[int]) -> int:
        piles.sort(reverse=True)
        return sum(piles[i] for i in range(1, len(piles) // 3 * 2, 2))