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            "questionId": "2211",
            "questionFrontendId": "2090",
            "categoryTitle": "Algorithms",
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            "title": "K Radius Subarray Averages",
            "titleSlug": "k-radius-subarray-averages",
            "content": "<p>You are given a <strong>0-indexed</strong> array <code>nums</code> of <code>n</code> integers, and an integer <code>k</code>.</p>\n\n<p>The <strong>k-radius average</strong> for a subarray of <code>nums</code> <strong>centered</strong> at some index <code>i</code> with the <strong>radius</strong> <code>k</code> is the average of <strong>all</strong> elements in <code>nums</code> between the indices <code>i - k</code> and <code>i + k</code> (<strong>inclusive</strong>). If there are less than <code>k</code> elements before <strong>or</strong> after the index <code>i</code>, then the <strong>k-radius average</strong> is <code>-1</code>.</p>\n\n<p>Build and return <em>an array </em><code>avgs</code><em> of length </em><code>n</code><em> where </em><code>avgs[i]</code><em> is the <strong>k-radius average</strong> for the subarray centered at index </em><code>i</code>.</p>\n\n<p>The <strong>average</strong> of <code>x</code> elements is the sum of the <code>x</code> elements divided by <code>x</code>, using <strong>integer division</strong>. The integer division truncates toward zero, which means losing its fractional part.</p>\n\n<ul>\n\t<li>For example, the average of four elements <code>2</code>, <code>3</code>, <code>1</code>, and <code>5</code> is <code>(2 + 3 + 1 + 5) / 4 = 11 / 4 = 2.75</code>, which truncates to <code>2</code>.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/07/eg1.png\" style=\"width: 343px; height: 119px;\" />\n<pre>\n<strong>Input:</strong> nums = [7,4,3,9,1,8,5,2,6], k = 3\n<strong>Output:</strong> [-1,-1,-1,5,4,4,-1,-1,-1]\n<strong>Explanation:</strong>\n- avg[0], avg[1], and avg[2] are -1 because there are less than k elements <strong>before</strong> each index.\n- The sum of the subarray centered at index 3 with radius 3 is: 7 + 4 + 3 + 9 + 1 + 8 + 5 = 37.\n  Using <strong>integer division</strong>, avg[3] = 37 / 7 = 5.\n- For the subarray centered at index 4, avg[4] = (4 + 3 + 9 + 1 + 8 + 5 + 2) / 7 = 4.\n- For the subarray centered at index 5, avg[5] = (3 + 9 + 1 + 8 + 5 + 2 + 6) / 7 = 4.\n- avg[6], avg[7], and avg[8] are -1 because there are less than k elements <strong>after</strong> each index.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [100000], k = 0\n<strong>Output:</strong> [100000]\n<strong>Explanation:</strong>\n- The sum of the subarray centered at index 0 with radius 0 is: 100000.\n  avg[0] = 100000 / 1 = 100000.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [8], k = 100000\n<strong>Output:</strong> [-1]\n<strong>Explanation:</strong> \n- avg[0] is -1 because there are less than k elements before and after index 0.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i], k &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "半径为 k 的子数组平均值",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的数组 <code>nums</code> ，数组中有 <code>n</code> 个整数，另给你一个整数 <code>k</code> 。</p>\n\n<p><strong>半径为 k 的子数组平均值</strong> 是指：<code>nums</code> 中一个以下标 <code>i</code> 为 <strong>中心</strong> 且 <strong>半径</strong> 为 <code>k</code> 的子数组中所有元素的平均值，即下标在&nbsp;<code>i - k</code> 和 <code>i + k</code> 范围（<strong>含</strong> <code>i - k</code> 和 <code>i + k</code>）内所有元素的平均值。如果在下标 <code>i</code> 前或后不足 <code>k</code> 个元素，那么<strong> 半径为 k 的子数组平均值 </strong>是 <code>-1</code> 。</p>\n\n<p>构建并返回一个长度为 <code>n</code> 的数组<em> </em><code>avgs</code><em> </em>，其中<em> </em><code>avgs[i]</code><em> </em>是以下标 <code>i</code> 为中心的子数组的<strong> 半径为 k 的子数组平均值 </strong>。</p>\n\n<p><code>x</code> 个元素的 <strong>平均值</strong> 是 <code>x</code> 个元素相加之和除以 <code>x</code> ，此时使用截断式 <strong>整数除法</strong> ，即需要去掉结果的小数部分。</p>\n\n<ul>\n\t<li>例如，四个元素 <code>2</code>、<code>3</code>、<code>1</code> 和 <code>5</code> 的平均值是 <code>(2 + 3 + 1 + 5) / 4 = 11 / 4 = 2.75</code>，截断后得到 <code>2</code> 。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/07/eg1.png\" style=\"width: 343px; height: 119px;\" /></p>\n\n<pre>\n<strong>输入：</strong>nums = [7,4,3,9,1,8,5,2,6], k = 3\n<strong>输出：</strong>[-1,-1,-1,5,4,4,-1,-1,-1]\n<strong>解释：</strong>\n- avg[0]、avg[1] 和 avg[2] 是 -1 ，因为在这几个下标前的元素数量都不足 k 个。\n- 中心为下标 3 且半径为 3 的子数组的元素总和是：7 + 4 + 3 + 9 + 1 + 8 + 5 = 37 。\n  使用截断式 <strong>整数除法</strong>，avg[3] = 37 / 7 = 5 。\n- 中心为下标 4 的子数组，avg[4] = (4 + 3 + 9 + 1 + 8 + 5 + 2) / 7 = 4 。\n- 中心为下标 5 的子数组，avg[5] = (3 + 9 + 1 + 8 + 5 + 2 + 6) / 7 = 4 。\n- avg[6]、avg[7] 和 avg[8] 是 -1 ，因为在这几个下标后的元素数量都不足 k 个。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [100000], k = 0\n<strong>输出：</strong>[100000]\n<strong>解释：</strong>\n- 中心为下标 0 且半径 0 的子数组的元素总和是：100000 。\n  avg[0] = 100000 / 1 = 100000 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [8], k = 100000\n<strong>输出：</strong>[-1]\n<strong>解释：</strong>\n- avg[0] 是 -1 ，因为在下标 0 前后的元素数量均不足 k 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i], k &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "To calculate the average of a subarray, you need the sum and the K. K is already given. How could you quickly calculate the sum of a subarray?",
                "Use the Prefix Sums method to calculate the subarray sums.",
                "It is possible that the sum of all the elements does not fit in a 32-bit integer type. Be sure to use a 64-bit integer type for the prefix sum array."
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