maximum-alternating-subsequence-sum

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Algorithms

The alternating sum of a 0-indexed array is defined as the sum of the elements at even indices minus the sum of the elements at odd indices.

<ul>
	<li>For example, the alternating sum of <code>[4,2,5,3]</code> is <code>(4 + 5) - (2 + 3) = 4</code>.</li>
</ul>

Given an array <code>nums</code>, return the maximum alternating sum of any subsequence of <code>nums</code> (after reindexing the elements of the subsequence).

<ul>
</ul>

A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements&#39; relative order. For example, <code>[2,7,4]</code> is a subsequence of <code>[4,2,3,7,2,1,4]</code> (the underlined elements), while <code>[2,4,2]</code> is not.

&nbsp;
Example 1:

<pre>
Input: nums = [4,2,5,3]
Output: 7
Explanation: It is optimal to choose the subsequence [4,2,5] with alternating sum (4 + 5) - 2 = 7.
</pre>

Example 2:

<pre>
Input: nums = [5,6,7,8]
Output: 8
Explanation: It is optimal to choose the subsequence [8] with alternating sum 8.
</pre>

Example 3:

<pre>
Input: nums = [6,2,1,2,4,5]
Output: 10
Explanation: It is optimal to choose the subsequence [6,1,5] with alternating sum (6 + 5) - 1 = 10.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 105</code></li>
</ul>

maxAlternatingSum

Maximum Alternating Subsequence Sum

Maximum Alternating Subarray Sum

maximum-alternating-subarray-sum

最大交替子数组和

Maximum Element-Sum of a Complete Subset of Indices

maximum-element-sum-of-a-complete-subset-of-indices

完全子集的最大元素和

Array

Dynamic Programming

一个下标从 0 开始的数组的 交替和 定义为 偶数 下标处元素之 和 减去 奇数 下标处元素之 和 。

<ul>
	<li>比方说，数组 <code>[4,2,5,3]</code> 的交替和为 <code>(4 + 5) - (2 + 3) = 4</code> 。</li>
</ul>

给你一个数组 <code>nums</code> ，请你返回 <code>nums</code> 中任意子序列的 最大交替和 （子序列的下标 重新 从 0 开始编号）。

<ul>
</ul>

一个数组的 子序列 是从原数组中删除一些元素后（也可能一个也不删除）剩余元素不改变顺序组成的数组。比方说，<code>[2,7,4]</code> 是 <code>[4,2,3,7,2,1,4]</code> 的一个子序列（加粗元素），但是 <code>[2,4,2]</code> 不是。

 

示例 1：

<pre>输入：nums = [4,2,5,3]
输出：7
解释：最优子序列为 [4,2,5] ，交替和为 (4 + 5) - 2 = 7 。
</pre>

示例 2：

<pre>输入：nums = [5,6,7,8]
输出：8
解释：最优子序列为 [8] ，交替和为 8 。
</pre>

示例 3：

<pre>输入：nums = [6,2,1,2,4,5]
输出：10
解释：最优子序列为 [6,1,5] ，交替和为 (6 + 5) - 1 = 10 。
</pre>

 

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 105</code></li>
</ul>