count-partitions-with-even-sum-difference

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Algorithms

You are given an integer array <code>nums</code> of length <code>n</code>.

A partition is defined as an index <code>i</code> where <code>0 &lt;= i &lt; n - 1</code>, splitting the array into two non-empty subarrays such that:

<ul>
	<li>Left subarray contains indices <code>[0, i]</code>.</li>
	<li>Right subarray contains indices <code>[i + 1, n - 1]</code>.</li>
</ul>

Return the number of partitions where the difference between the sum of the left and right subarrays is even.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [10,10,3,7,6]

Output: 4

Explanation:

The 4 partitions are:

<ul>
	<li><code>[10]</code>, <code>[10, 3, 7, 6]</code> with a sum difference of <code>10 - 26 = -16</code>, which is even.</li>
	<li><code>[10, 10]</code>, <code>[3, 7, 6]</code> with a sum difference of <code>20 - 16 = 4</code>, which is even.</li>
	<li><code>[10, 10, 3]</code>, <code>[7, 6]</code> with a sum difference of <code>23 - 13 = 10</code>, which is even.</li>
	<li><code>[10, 10, 3, 7]</code>, <code>[6]</code> with a sum difference of <code>30 - 6 = 24</code>, which is even.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: nums = [1,2,2]

Output: 0

Explanation:

No partition results in an even sum difference.
</div>

Example 3:

<div class="example-block">
Input: nums = [2,4,6,8]

Output: 3

Explanation:

All partitions result in an even sum difference.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= n == nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
</ul>

countPartitions

Count Partitions with Even Sum Difference

Array

Math

Prefix Sum

给你一个长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;。

分区&nbsp;是指将数组按照下标&nbsp;<code>i</code>&nbsp;（<code>0 &lt;= i &lt; n - 1</code>）划分成两个 非空 子数组，其中：

<ul>
	<li>左子数组包含区间&nbsp;<code>[0, i]</code>&nbsp;内的所有下标。</li>
	<li>右子数组包含区间&nbsp;<code>[i + 1, n - 1]</code>&nbsp;内的所有下标。</li>
</ul>

对左子数组和右子数组先求元素 和 再做 差 ，统计并返回差值为 偶数 的 分区 方案数。

&nbsp;

示例 1：

<div class="example-block">
输入：nums = [10,10,3,7,6]

输出：4

解释：

共有 4 个满足题意的分区方案：

<ul>
	<li><code>[10]</code>、<code>[10, 3, 7, 6]</code>&nbsp;元素和的差值为&nbsp;<code>10 - 26 = -16</code>&nbsp;，是偶数。</li>
	<li><code>[10, 10]</code>、<code>[3, 7, 6]</code> 元素和的差值为&nbsp;<code>20 - 16 = 4</code>，是偶数。</li>
	<li><code>[10, 10, 3]</code>、<code>[7, 6]</code> 元素和的差值为&nbsp;<code>23 - 13 = 10</code>，是偶数。</li>
	<li><code>[10, 10, 3, 7]</code>、<code>[6]</code> 元素和的差值为&nbsp;<code>30 - 6 = 24</code>，是偶数。</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入：nums = [1,2,2]

输出：0

解释：

不存在元素和的差值为偶数的分区方案。
</div>

示例 3：

<div class="example-block">
输入：nums = [2,4,6,8]

输出：3

解释：

所有分区方案都满足元素和的差值为偶数。
</div>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= n == nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
</ul>