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"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> </p>\n<p><strong>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>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>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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 15</code></li>\n\t<li><code>nums.length == 2 * n</code></li>\n\t<li><code>-10<sup>7</sup> <= nums[i] <= 10<sup>7</sup></code></li>\n</ul>\n",
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"hints": [
"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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