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"content": "<p>You are given an integer array <code>nums</code> and an integer <code>goal</code>.</p>\n\n<p>You want to choose a subsequence of <code>nums</code> such that the sum of its elements is the closest possible to <code>goal</code>. That is, if the sum of the subsequence's elements is <code>sum</code>, then you want to <strong>minimize the absolute difference</strong> <code>abs(sum - goal)</code>.</p>\n\n<p>Return <em>the <strong>minimum</strong> possible value of</em> <code>abs(sum - goal)</code>.</p>\n\n<p>Note that a subsequence of an array is an array formed by removing some elements <strong>(possibly all or none)</strong> of the original array.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,-7,3,5], goal = 6\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Choose the whole array as a subsequence, with a sum of 6.\nThis is equal to the goal, so the absolute difference is 0.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [7,-9,15,-2], goal = -5\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> Choose the subsequence [7,-9,-2], with a sum of -4.\nThe absolute difference is abs(-4 - (-5)) = abs(1) = 1, which is the minimum.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3], goal = -7\n<strong>Output:</strong> 7\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 40</code></li>\n\t<li><code>-10<sup>7</sup> <= nums[i] <= 10<sup>7</sup></code></li>\n\t<li><code>-10<sup>9</sup> <= goal <= 10<sup>9</sup></code></li>\n</ul>\n",
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"hints": [
"The naive solution is to check all possible subsequences. This works in O(2^n).",
"Divide the array into two parts of nearly is equal size.",
"Consider all subsets of one part and make a list of all possible subset sums and sort this list.",
"Consider all subsets of the other part, and for each one, let its sum = x, do binary search to get the nearest possible value to goal - x in the first part."
],
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