leetcode-problemset/leetcode-cn/originData/maximum-value-at-a-given-index-in-a-bounded-array.json

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        "question": {
            "questionId": "1929",
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            "categoryTitle": "Algorithms",
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            "title": "Maximum Value at a Given Index in a Bounded Array",
            "titleSlug": "maximum-value-at-a-given-index-in-a-bounded-array",
            "content": "<p>You are given three positive integers:&nbsp;<code>n</code>, <code>index</code>, and <code>maxSum</code>. You want to construct an array <code>nums</code> (<strong>0-indexed</strong>)<strong> </strong>that satisfies the following conditions:</p>\n\n<ul>\n\t<li><code>nums.length == n</code></li>\n\t<li><code>nums[i]</code> is a <strong>positive</strong> integer where <code>0 &lt;= i &lt; n</code>.</li>\n\t<li><code>abs(nums[i] - nums[i+1]) &lt;= 1</code> where <code>0 &lt;= i &lt; n-1</code>.</li>\n\t<li>The sum of all the elements of <code>nums</code> does not exceed <code>maxSum</code>.</li>\n\t<li><code>nums[index]</code> is <strong>maximized</strong>.</li>\n</ul>\n\n<p>Return <code>nums[index]</code><em> of the constructed array</em>.</p>\n\n<p>Note that <code>abs(x)</code> equals <code>x</code> if <code>x &gt;= 0</code>, and <code>-x</code> otherwise.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, index = 2,  maxSum = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> nums = [1,2,<u><strong>2</strong></u>,1] is one array that satisfies all the conditions.\nThere are no arrays that satisfy all the conditions and have nums[2] == 3, so 2 is the maximum nums[2].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 6, index = 1,  maxSum = 10\n<strong>Output:</strong> 3\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= maxSum &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= index &lt; n</code></li>\n</ul>\n",
            "translatedTitle": "有界数组中指定下标处的最大值",
            "translatedContent": "<p>给你三个正整数 <code>n</code>、<code>index</code> 和 <code>maxSum</code> 。你需要构造一个同时满足下述所有条件的数组 <code>nums</code>（下标 <strong>从 0 开始</strong> 计数）：</p>\n\n<ul>\n\t<li><code>nums.length == n</code></li>\n\t<li><code>nums[i]</code> 是 <strong>正整数</strong> ，其中 <code>0 &lt;= i &lt; n</code></li>\n\t<li><code>abs(nums[i] - nums[i+1]) &lt;= 1</code> ，其中 <code>0 &lt;= i &lt; n-1</code></li>\n\t<li><code>nums</code> 中所有元素之和不超过 <code>maxSum</code></li>\n\t<li><code>nums[index]</code> 的值被 <strong>最大化</strong></li>\n</ul>\n\n<p>返回你所构造的数组中的 <code>nums[index]</code> 。</p>\n\n<p>注意：<code>abs(x)</code> 等于 <code>x</code> 的前提是 <code>x &gt;= 0</code> ；否则，<code>abs(x)</code> 等于 <code>-x</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>n = 4, index = 2,  maxSum = 6\n<strong>输出：</strong>2\n<strong>解释：</strong>数组 [1,1,<strong>2</strong>,1] 和 [1,2,<strong>2</strong>,1] 满足所有条件。不存在其他在指定下标处具有更大值的有效数组。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>n = 6, index = 1,  maxSum = 10\n<strong>输出：</strong>3\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= maxSum &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= index &lt; n</code></li>\n</ul>\n",
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            "hints": [
                "What if the problem was instead determining if you could generate a valid array with nums[index] == target?",
                "To generate the array, set nums[index] to target, nums[index-i] to target-i, and nums[index+i] to target-i. Then, this will give the minimum possible sum, so check if the sum is less than or equal to maxSum.",
                "n is too large to actually generate the array, so you can use the formula 1 + 2 + ... + n = n * (n+1) / 2 to quickly find the sum of nums[0...index] and nums[index...n-1].",
                "Binary search for the target. If it is possible, then move the lower bound up. Otherwise, move the upper bound down."
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