split-array-with-minimum-difference

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Algorithms

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

Split the array into exactly two subarrays, <code>left</code> and <code>right</code>, such that <code>left</code> is strictly increasing and <code>right</code> is strictly decreasing.

Return the minimum possible absolute difference between the sums of <code>left</code> and <code>right</code>. If no valid split exists, return <code>-1</code>.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,3,2]

Output: 2

Explanation:

<table style="border: 1px solid black;">
	<thead>
		<tr>
			<th style="border: 1px solid black;"><code>i</code></th>
			<th style="border: 1px solid black;"><code>left</code></th>
			<th style="border: 1px solid black;"><code>right</code></th>
			<th style="border: 1px solid black;">Validity</th>
			<th style="border: 1px solid black;"><code>left</code> sum</th>
			<th style="border: 1px solid black;"><code>right</code> sum</th>
			<th style="border: 1px solid black;">Absolute difference</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 1px solid black;">0</td>
			<td style="border: 1px solid black;">[1]</td>
			<td style="border: 1px solid black;">[3, 2]</td>
			<td style="border: 1px solid black;">Yes</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">5</td>
			<td style="border: 1px solid black;"><code>|1 - 5| = 4</code></td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">[1, 3]</td>
			<td style="border: 1px solid black;">[2]</td>
			<td style="border: 1px solid black;">Yes</td>
			<td style="border: 1px solid black;">4</td>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;"><code>|4 - 2| = 2</code></td>
		</tr>
	</tbody>
</table>

Thus, the minimum absolute difference is 2.
</div>

Example 2:

<div class="example-block">
Input: nums = [1,2,4,3]

Output: 4

Explanation:

<table style="border: 1px solid black;">
	<thead>
		<tr>
			<th style="border: 1px solid black;"><code>i</code></th>
			<th style="border: 1px solid black;"><code>left</code></th>
			<th style="border: 1px solid black;"><code>right</code></th>
			<th style="border: 1px solid black;">Validity</th>
			<th style="border: 1px solid black;"><code>left</code> sum</th>
			<th style="border: 1px solid black;"><code>right</code> sum</th>
			<th style="border: 1px solid black;">Absolute difference</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 1px solid black;">0</td>
			<td style="border: 1px solid black;">[1]</td>
			<td style="border: 1px solid black;">[2, 4, 3]</td>
			<td style="border: 1px solid black;">No</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">9</td>
			<td style="border: 1px solid black;">-</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">[1, 2]</td>
			<td style="border: 1px solid black;">[4, 3]</td>
			<td style="border: 1px solid black;">Yes</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">7</td>
			<td style="border: 1px solid black;"><code>|3 - 7| = 4</code></td>
		</tr>
		<tr>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">[1, 2, 4]</td>
			<td style="border: 1px solid black;">[3]</td>
			<td style="border: 1px solid black;">Yes</td>
			<td style="border: 1px solid black;">7</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;"><code>|7 - 3| = 4</code></td>
		</tr>
	</tbody>
</table>

Thus, the minimum absolute difference is 4.
</div>

Example 3:

<div class="example-block">
Input: nums = [3,1,2]

Output: -1

Explanation:

No valid split exists, so the answer is -1.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= nums.length &lt;= 105</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 105</code></li>
</ul>

`i`	`left`	`right`	Validity	`left` sum	`right` sum	Absolute difference
0	[1]	[3, 2]	Yes	1	5	`\|1 - 5\| = 4`
1	[1, 3]	[2]	Yes	4	2	`\|4 - 2\| = 2`

`i`	`left`	`right`	Validity	`left` sum	`right` sum	Absolute difference
0	[1]	[2, 4, 3]	No	1	9	-
1	[1, 2]	[4, 3]	Yes	3	7	`\|3 - 7\| = 4`
2	[1, 2, 4]	[3]	Yes	7	3	`\|7 - 3\| = 4`