mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
173 lines
20 KiB
JSON
173 lines
20 KiB
JSON
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"questionId": "1911",
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"questionFrontendId": "1785",
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"categoryTitle": "Algorithms",
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"boundTopicId": 635605,
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"title": "Minimum Elements to Add to Form a Given Sum",
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"content": "<p>You are given an integer array <code>nums</code> and two integers <code>limit</code> and <code>goal</code>. The array <code>nums</code> has an interesting property that <code>abs(nums[i]) <= limit</code>.</p>\n\n<p>Return <em>the minimum number of elements you need to add to make the sum of the array equal to </em><code>goal</code>. The array must maintain its property that <code>abs(nums[i]) <= limit</code>.</p>\n\n<p>Note that <code>abs(x)</code> equals <code>x</code> if <code>x >= 0</code>, and <code>-x</code> otherwise.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,-1,1], limit = 3, goal = -4\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> You can add -2 and -3, then the sum of the array will be 1 - 1 + 1 - 2 - 3 = -4.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,-10,9,1], limit = 100, goal = 0\n<strong>Output:</strong> 1\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= limit <= 10<sup>6</sup></code></li>\n\t<li><code>-limit <= nums[i] <= limit</code></li>\n\t<li><code>-10<sup>9</sup> <= goal <= 10<sup>9</sup></code></li>\n</ul>\n",
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"translatedContent": "<p>给你一个整数数组 <code>nums</code> ，和两个整数 <code>limit</code> 与 <code>goal</code> 。数组 <code>nums</code> 有一条重要属性：<code>abs(nums[i]) <= limit</code> 。</p>\n\n<p>返回使数组元素总和等于 <code>goal</code> 所需要向数组中添加的 <strong>最少元素数量</strong> ，添加元素 <strong>不应改变</strong> 数组中 <code>abs(nums[i]) <= limit</code> 这一属性。</p>\n\n<p>注意，如果 <code>x >= 0</code> ，那么 <code>abs(x)</code> 等于 <code>x</code> ；否则，等于 <code>-x</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,-1,1], limit = 3, goal = -4\n<strong>输出：</strong>2\n<strong>解释：</strong>可以将 -2 和 -3 添加到数组中，数组的元素总和变为 1 - 1 + 1 - 2 - 3 = -4 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,-10,9,1], limit = 100, goal = 0\n<strong>输出：</strong>1\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= limit <= 10<sup>6</sup></code></li>\n\t<li><code>-limit <= nums[i] <= limit</code></li>\n\t<li><code>-10<sup>9</sup> <= goal <= 10<sup>9</sup></code></li>\n</ul>\n",
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"Try thinking about the problem as if the array is empty. Then you only need to form goal using elements whose absolute value is <= limit.",
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"You can greedily set all of the elements except one to limit or -limit, so the number of elements you need is ceil(abs(goal)/ limit).",
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"You can \"normalize\" goal by offsetting it by the sum of the array. For example, if the goal is 5 and the sum is -3, then it's exactly the same as if the goal is 8 and the array is empty.",
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"The answer is ceil(abs(goal-sum)/limit) = (abs(goal-sum)+limit-1) / limit."
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