mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
197 lines
23 KiB
JSON
197 lines
23 KiB
JSON
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"categoryTitle": "Algorithms",
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"title": "Closest Subsequence Sum",
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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 class=\"example\">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 class=\"example\">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 class=\"example\">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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"translatedTitle": "最接近目标值的子序列和",
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"translatedContent": "<p>给你一个整数数组 <code>nums</code> 和一个目标值 <code>goal</code> 。</p>\n\n<p>你需要从 <code>nums</code> 中选出一个子序列，使子序列元素总和最接近 <code>goal</code> 。也就是说，如果子序列元素和为 <code>sum</code> ，你需要 <strong>最小化绝对差</strong> <code>abs(sum - goal)</code> 。</p>\n\n<p>返回 <code>abs(sum - goal)</code> 可能的 <strong>最小值</strong> 。</p>\n\n<p>注意，数组的子序列是通过移除原始数组中的某些元素（可能全部或无）而形成的数组。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = [5,-7,3,5], goal = 6\n<strong>输出：</strong>0\n<strong>解释：</strong>选择整个数组作为选出的子序列，元素和为 6 。\n子序列和与目标值相等，所以绝对差为 0 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [7,-9,15,-2], goal = -5\n<strong>输出：</strong>1\n<strong>解释：</strong>选出子序列 [7,-9,-2] ，元素和为 -4 。\n绝对差为 abs(-4 - (-5)) = abs(1) = 1 ，是可能的最小值。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>nums = [1,2,3], goal = -7\n<strong>输出：</strong>7\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</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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"The naive solution is to check all possible subsequences. This works in O(2^n).",
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"Divide the array into two parts of nearly is equal size.",
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"Consider all subsets of one part and make a list of all possible subset sums and sort this list.",
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"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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