maximum-number-of-coins-you-can-get

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Algorithms

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

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

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

Return the maximum number of coins that you can have.

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

<pre>
Input: piles = [2,4,5]
Output: 4
</pre>

Example 3:

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

&nbsp;
Constraints:

<ul>
	<li><code>3 &lt;= piles.length &lt;= 105</code></li>
	<li><code>piles.length % 3 == 0</code></li>
	<li><code>1 &lt;= piles[i] &lt;= 104</code></li>
</ul>

maxCoins

Maximum Number of Coins You Can Get

Greedy

Array

Math

Game Theory

Sorting

有 3n 堆数目不一的硬币，你和你的朋友们打算按以下方式分硬币：

<ul>
	<li>每一轮中，你将会选出 任意 3 堆硬币（不一定连续）。</li>
	<li>Alice 将会取走硬币数量最多的那一堆。</li>
	<li>你将会取走硬币数量第二多的那一堆。</li>
	<li>Bob 将会取走最后一堆。</li>
	<li>重复这个过程，直到没有更多硬币。</li>
</ul>

给你一个整数数组 <code>piles</code> ，其中 <code>piles[i]</code> 是第 <code>i</code> 堆中硬币的数目。

返回你可以获得的最大硬币数目。

&nbsp;

示例 1：

<pre>输入：piles = [2,4,1,2,7,8]
输出：9
解释：选出 (2, 7, 8) ，Alice 取走 8 枚硬币的那堆，你取走 7 枚硬币的那堆，Bob 取走最后一堆。
选出 (1, 2, 4) , Alice 取走 4 枚硬币的那堆，你取走 2 枚硬币的那堆，Bob 取走最后一堆。
你可以获得的最大硬币数目：7 + 2 = 9.
考虑另外一种情况，如果选出的是 (1, 2, 8) 和 (2, 4, 7) ，你就只能得到 2 + 4 = 6 枚硬币，这不是最优解。
</pre>

示例 2：

<pre>输入：piles = [2,4,5]
输出：4
</pre>

示例 3：

<pre>输入：piles = [9,8,7,6,5,1,2,3,4]
输出：18
</pre>

&nbsp;

提示：

<ul>
	<li><code>3 &lt;= piles.length &lt;= 10^5</code></li>
	<li><code>piles.length % 3 == 0</code></li>
	<li><code>1 &lt;= piles[i] &lt;= 10^4</code></li>
</ul>