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| 1 | +<h2><a href="https://leetcode.com/problems/minimum-difference-in-sums-after-removal-of-elements">Minimum Difference in Sums After Removal of Elements</a></h2> <img src='https://img.shields.io/badge/Difficulty-Hard-red' alt='Difficulty: Hard' /><hr><p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> consisting of <code>3 * n</code> elements.</p> |
| 2 | + |
| 3 | +<p>You are allowed to remove any <strong>subsequence</strong> of elements of size <strong>exactly</strong> <code>n</code> from <code>nums</code>. The remaining <code>2 * n</code> elements will be divided into two <strong>equal</strong> parts:</p> |
| 4 | + |
| 5 | +<ul> |
| 6 | + <li>The first <code>n</code> elements belonging to the first part and their sum is <code>sum<sub>first</sub></code>.</li> |
| 7 | + <li>The next <code>n</code> elements belonging to the second part and their sum is <code>sum<sub>second</sub></code>.</li> |
| 8 | +</ul> |
| 9 | + |
| 10 | +<p>The <strong>difference in sums</strong> of the two parts is denoted as <code>sum<sub>first</sub> - sum<sub>second</sub></code>.</p> |
| 11 | + |
| 12 | +<ul> |
| 13 | + <li>For example, if <code>sum<sub>first</sub> = 3</code> and <code>sum<sub>second</sub> = 2</code>, their difference is <code>1</code>.</li> |
| 14 | + <li>Similarly, if <code>sum<sub>first</sub> = 2</code> and <code>sum<sub>second</sub> = 3</code>, their difference is <code>-1</code>.</li> |
| 15 | +</ul> |
| 16 | + |
| 17 | +<p>Return <em>the <strong>minimum difference</strong> possible between the sums of the two parts after the removal of </em><code>n</code><em> elements</em>.</p> |
| 18 | + |
| 19 | +<p> </p> |
| 20 | +<p><strong class="example">Example 1:</strong></p> |
| 21 | + |
| 22 | +<pre> |
| 23 | +<strong>Input:</strong> nums = [3,1,2] |
| 24 | +<strong>Output:</strong> -1 |
| 25 | +<strong>Explanation:</strong> Here, nums has 3 elements, so n = 1. |
| 26 | +Thus we have to remove 1 element from nums and divide the array into two equal parts. |
| 27 | +- If we remove nums[0] = 3, the array will be [1,2]. The difference in sums of the two parts will be 1 - 2 = -1. |
| 28 | +- If we remove nums[1] = 1, the array will be [3,2]. The difference in sums of the two parts will be 3 - 2 = 1. |
| 29 | +- If we remove nums[2] = 2, the array will be [3,1]. The difference in sums of the two parts will be 3 - 1 = 2. |
| 30 | +The minimum difference between sums of the two parts is min(-1,1,2) = -1. |
| 31 | +</pre> |
| 32 | + |
| 33 | +<p><strong class="example">Example 2:</strong></p> |
| 34 | + |
| 35 | +<pre> |
| 36 | +<strong>Input:</strong> nums = [7,9,5,8,1,3] |
| 37 | +<strong>Output:</strong> 1 |
| 38 | +<strong>Explanation:</strong> Here n = 2. So we must remove 2 elements and divide the remaining array into two parts containing two elements each. |
| 39 | +If we remove nums[2] = 5 and nums[3] = 8, the resultant array will be [7,9,1,3]. The difference in sums will be (7+9) - (1+3) = 12. |
| 40 | +To obtain the minimum difference, we should remove nums[1] = 9 and nums[4] = 1. The resultant array becomes [7,5,8,3]. The difference in sums of the two parts is (7+5) - (8+3) = 1. |
| 41 | +It can be shown that it is not possible to obtain a difference smaller than 1. |
| 42 | +</pre> |
| 43 | + |
| 44 | +<p> </p> |
| 45 | +<p><strong>Constraints:</strong></p> |
| 46 | + |
| 47 | +<ul> |
| 48 | + <li><code>nums.length == 3 * n</code></li> |
| 49 | + <li><code>1 <= n <= 10<sup>5</sup></code></li> |
| 50 | + <li><code>1 <= nums[i] <= 10<sup>5</sup></code></li> |
| 51 | +</ul> |
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