leetcode-problemset/leetcode-cn/originData/find-the-score-of-all-prefixes-of-an-array.json

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            "questionId": "2676",
            "questionFrontendId": "2640",
            "categoryTitle": "Algorithms",
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            "title": "Find the Score of All Prefixes of an Array",
            "titleSlug": "find-the-score-of-all-prefixes-of-an-array",
            "content": "<p>We define the <strong>conversion array</strong> <code>conver</code> of an array <code>arr</code> as follows:</p>\n\n<ul>\n\t<li><code>conver[i] = arr[i] + max(arr[0..i])</code> where <code>max(arr[0..i])</code> is the maximum value of <code>arr[j]</code> over <code>0 &lt;= j &lt;= i</code>.</li>\n</ul>\n\n<p>We also define the <strong>score</strong> of an array <code>arr</code> as the sum of the values of the conversion array of <code>arr</code>.</p>\n\n<p>Given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>, return <em>an array </em><code>ans</code><em> of length </em><code>n</code><em> where </em><code>ans[i]</code><em> is the score of the prefix</em> <code>nums[0..i]</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,7,5,10]\n<strong>Output:</strong> [4,10,24,36,56]\n<strong>Explanation:</strong> \nFor the prefix [2], the conversion array is [4] hence the score is 4\nFor the prefix [2, 3], the conversion array is [4, 6] hence the score is 10\nFor the prefix [2, 3, 7], the conversion array is [4, 6, 14] hence the score is 24\nFor the prefix [2, 3, 7, 5], the conversion array is [4, 6, 14, 12] hence the score is 36\nFor the prefix [2, 3, 7, 5, 10], the conversion array is [4, 6, 14, 12, 20] hence the score is 56\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,2,4,8,16]\n<strong>Output:</strong> [2,4,8,16,32,64]\n<strong>Explanation:</strong> \nFor the prefix [1], the conversion array is [2] hence the score is 2\nFor the prefix [1, 1], the conversion array is [2, 2] hence the score is 4\nFor the prefix [1, 1, 2], the conversion array is [2, 2, 4] hence the score is 8\nFor the prefix [1, 1, 2, 4], the conversion array is [2, 2, 4, 8] hence the score is 16\nFor the prefix [1, 1, 2, 4, 8], the conversion array is [2, 2, 4, 8, 16] hence the score is 32\nFor the prefix [1, 1, 2, 4, 8, 16], the conversion array is [2, 2, 4, 8, 16, 32] hence the score is 64\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "一个数组所有前缀的分数",
            "translatedContent": "<p>定义一个数组 <code>arr</code>&nbsp;的 <strong>转换数组</strong>&nbsp;<code>conver</code>&nbsp;为：</p>\n\n<ul>\n\t<li><code>conver[i] = arr[i] + max(arr[0..i])</code>，其中&nbsp;<code>max(arr[0..i])</code>&nbsp;是满足 <code>0 &lt;= j &lt;= i</code>&nbsp;的所有&nbsp;<code>arr[j]</code>&nbsp;中的最大值。</li>\n</ul>\n\n<p>定义一个数组 <code>arr</code>&nbsp;的 <strong>分数</strong>&nbsp;为 <code>arr</code>&nbsp;转换数组中所有元素的和。</p>\n\n<p>给你一个下标从 <strong>0</strong>&nbsp;开始长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;，请你返回一个长度为 <code>n</code>&nbsp;的数组<em>&nbsp;</em><code>ans</code>&nbsp;，其中&nbsp;<code>ans[i]</code>是前缀&nbsp;<code>nums[0..i]</code>&nbsp;的分数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>nums = [2,3,7,5,10]\n<b>输出：</b>[4,10,24,36,56]\n<b>解释：</b>\n对于前缀 [2] ，转换数组为 [4] ，所以分数为 4 。\n对于前缀 [2, 3] ，转换数组为 [4, 6] ，所以分数为 10 。\n对于前缀 [2, 3, 7] ，转换数组为 [4, 6, 14] ，所以分数为 24 。\n对于前缀 [2, 3, 7, 5] ，转换数组为 [4, 6, 14, 12] ，所以分数为 36 。\n对于前缀 [2, 3, 7, 5, 10] ，转换数组为 [4, 6, 14, 12, 20] ，所以分数为 56 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [1,1,2,4,8,16]\n<b>输出：</b>[2,4,8,16,32,64]\n<b>解释：</b>\n对于前缀 [1] ，转换数组为 [2] ，所以分数为 2 。\n对于前缀 [1, 1]，转换数组为 [2, 2] ，所以分数为 4 。\n对于前缀 [1, 1, 2]，转换数组为 [2, 2, 4] ，所以分数为 8 。\n对于前缀 [1, 1, 2, 4]，转换数组为 [2, 2, 4, 8] ，所以分数为 16 。\n对于前缀 [1, 1, 2, 4, 8]，转换数组为 [2, 2, 4, 8, 16] ，所以分数为 32 。\n对于前缀 [1, 1, 2, 4, 8, 16]，转换数组为 [2, 2, 4, 8, 16, 32] ，所以分数为 64 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Keep track of the prefix maximum of the array",
                "Establish a relationship between ans[i] and ans[i-1]",
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