leetcode-problemset/leetcode-cn/originData/partition-array-into-two-arrays-to-minimize-sum-difference.json

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            "title": "Partition Array Into Two Arrays to Minimize Sum Difference",
            "titleSlug": "partition-array-into-two-arrays-to-minimize-sum-difference",
            "content": "<p>You are given an integer array <code>nums</code> of <code>2 * n</code> integers. You need to partition <code>nums</code> into <strong>two</strong> arrays of length <code>n</code> to <strong>minimize the absolute difference</strong> of the <strong>sums</strong> of the arrays. To partition <code>nums</code>, put each element of <code>nums</code> into <strong>one</strong> of the two arrays.</p>\n\n<p>Return <em>the <strong>minimum</strong> possible absolute difference</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"example-1\" src=\"https://assets.leetcode.com/uploads/2021/10/02/ex1.png\" style=\"width: 240px; height: 106px;\" />\n<pre>\n<strong>Input:</strong> nums = [3,9,7,3]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> One optimal partition is: [3,9] and [7,3].\nThe absolute difference between the sums of the arrays is abs((3 + 9) - (7 + 3)) = 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [-36,36]\n<strong>Output:</strong> 72\n<strong>Explanation:</strong> One optimal partition is: [-36] and [36].\nThe absolute difference between the sums of the arrays is abs((-36) - (36)) = 72.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"example-3\" src=\"https://assets.leetcode.com/uploads/2021/10/02/ex3.png\" style=\"width: 316px; height: 106px;\" />\n<pre>\n<strong>Input:</strong> nums = [2,-1,0,4,-2,-9]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> One optimal partition is: [2,4,-9] and [-1,0,-2].\nThe absolute difference between the sums of the arrays is abs((2 + 4 + -9) - (-1 + 0 + -2)) = 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 15</code></li>\n\t<li><code>nums.length == 2 * n</code></li>\n\t<li><code>-10<sup>7</sup> &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>\n</ul>\n",
            "translatedTitle": "将数组分成两个数组并最小化数组和的差",
            "translatedContent": "<p>给你一个长度为 <code>2 * n</code>&nbsp;的整数数组。你需要将&nbsp;<code>nums</code>&nbsp;分成&nbsp;<strong>两个</strong>&nbsp;长度为&nbsp;<code>n</code>&nbsp;的数组，分别求出两个数组的和，并 <strong>最小化</strong>&nbsp;两个数组和之&nbsp;<b>差的绝对值</b>&nbsp;。<code>nums</code>&nbsp;中每个元素都需要放入两个数组之一。</p>\n\n<p>请你返回&nbsp;<strong>最小</strong>&nbsp;的数组和之差。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"example-1\" src=\"https://assets.leetcode.com/uploads/2021/10/02/ex1.png\" style=\"width: 240px; height: 106px;\"></p>\n\n<pre><b>输入：</b>nums = [3,9,7,3]\n<b>输出：</b>2\n<strong>解释：</strong>最优分组方案是分成 [3,9] 和 [7,3] 。\n数组和之差的绝对值为 abs((3 + 9) - (7 + 3)) = 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [-36,36]\n<b>输出：</b>72\n<strong>解释：</strong>最优分组方案是分成 [-36] 和 [36] 。\n数组和之差的绝对值为 abs((-36) - (36)) = 72 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"example-3\" src=\"https://assets.leetcode.com/uploads/2021/10/02/ex3.png\" style=\"width: 316px; height: 106px;\"></p>\n\n<pre><b>输入：</b>nums = [2,-1,0,4,-2,-9]\n<b>输出：</b>0\n<strong>解释：</strong>最优分组方案是分成 [2,4,-9] 和 [-1,0,-2] 。\n数组和之差的绝对值为 abs((2 + 4 + -9) - (-1 + 0 + -2)) = 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 15</code></li>\n\t<li><code>nums.length == 2 * n</code></li>\n\t<li><code>-10<sup>7</sup> &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>\n</ul>\n",
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                "The target sum for the two partitions is sum(nums) / 2.",
                "Could you reduce the time complexity if you arbitrarily divide nums into two halves (two arrays)? Meet-in-the-Middle?",
                "For both halves, pre-calculate a 2D array where the kth index will store all possible sum values if only k elements from this half are added.",
                "For each sum of k elements in the first half, find the best sum of n-k elements in the second half such that the two sums add up to a value closest to the target sum from hint 1. These two subsets will form one array of the partition."
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