mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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184 lines
24 KiB
JSON
184 lines
24 KiB
JSON
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"title": "Beautiful Towers I",
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"content": "<p>You are given a <strong>0-indexed</strong> array <code>maxHeights</code> of <code>n</code> integers.</p>\n\n<p>You are tasked with building <code>n</code> towers in the coordinate line. The <code>i<sup>th</sup></code> tower is built at coordinate <code>i</code> and has a height of <code>heights[i]</code>.</p>\n\n<p>A configuration of towers is <strong>beautiful</strong> if the following conditions hold:</p>\n\n<ol>\n\t<li><code>1 <= heights[i] <= maxHeights[i]</code></li>\n\t<li><code>heights</code> is a <strong>mountain</strong> array.</li>\n</ol>\n\n<p>Array <code>heights</code> is a <strong>mountain</strong> if there exists an index <code>i</code> such that:</p>\n\n<ul>\n\t<li>For all <code>0 < j <= i</code>, <code>heights[j - 1] <= heights[j]</code></li>\n\t<li>For all <code>i <= k < n - 1</code>, <code>heights[k + 1] <= heights[k]</code></li>\n</ul>\n\n<p>Return <em>the <strong>maximum possible sum of heights</strong> of a beautiful configuration of towers</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> maxHeights = [5,3,4,1,1]\n<strong>Output:</strong> 13\n<strong>Explanation:</strong> One beautiful configuration with a maximum sum is heights = [5,3,3,1,1]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i] \n- heights is a mountain of peak i = 0.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 13.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> maxHeights = [6,5,3,9,2,7]\n<strong>Output:</strong> 22\n<strong>Explanation:</strong> One beautiful configuration with a maximum sum is heights = [3,3,3,9,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 3.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 22.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> maxHeights = [3,2,5,5,2,3]\n<strong>Output:</strong> 18\n<strong>Explanation:</strong> One beautiful configuration with a maximum sum is heights = [2,2,5,5,2,2]. This configuration is beautiful since:\n- 1 <= heights[i] <= maxHeights[i]\n- heights is a mountain of peak i = 2. \nNote that, for this configuration, i = 3 can also be considered a peak.\nIt can be shown that there exists no other beautiful configuration with a sum of heights greater than 18.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n == maxHeights <= 10<sup>3</sup></code></li>\n\t<li><code>1 <= maxHeights[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"translatedTitle": "美丽塔 I",
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"translatedContent": "<p>给你一个长度为 <code>n</code> 下标从 <strong>0</strong> 开始的整数数组 <code>maxHeights</code> 。</p>\n\n<p>你的任务是在坐标轴上建 <code>n</code> 座塔。第 <code>i</code> 座塔的下标为 <code>i</code> ，高度为 <code>heights[i]</code> 。</p>\n\n<p>如果以下条件满足，我们称这些塔是 <strong>美丽</strong> 的：</p>\n\n<ol>\n\t<li><code>1 <= heights[i] <= maxHeights[i]</code></li>\n\t<li><code>heights</code> 是一个 <strong>山状</strong> 数组。</li>\n</ol>\n\n<p>如果存在下标 <code>i</code> 满足以下条件，那么我们称数组 <code>heights</code> 是一个 <strong>山状</strong> 数组：</p>\n\n<ul>\n\t<li>对于所有 <code>0 < j <= i</code> ，都有 <code>heights[j - 1] <= heights[j]</code></li>\n\t<li>对于所有 <code>i <= k < n - 1</code> ，都有 <code>heights[k + 1] <= heights[k]</code></li>\n</ul>\n\n<p>请你返回满足 <b>美丽塔</b> 要求的方案中，<strong>高度和的最大值</strong> 。</p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>maxHeights = [5,3,4,1,1]\n<b>输出：</b>13\n<b>解释：</b>和最大的美丽塔方案为 heights = [5,3,3,1,1] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i] \n- heights 是个山状数组，峰值在 i = 0 处。\n13 是所有美丽塔方案中的最大高度和。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>maxHeights = [6,5,3,9,2,7]\n<b>输出：</b>22\n<strong>解释：</strong> 和最大的美丽塔方案为 heights = [3,3,3,9,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，峰值在 i = 3 处。\n22 是所有美丽塔方案中的最大高度和。</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>maxHeights = [3,2,5,5,2,3]\n<b>输出：</b>18\n<strong>解释：</strong>和最大的美丽塔方案为 heights = [2,2,5,5,2,2] ，这是一个美丽塔方案，因为：\n- 1 <= heights[i] <= maxHeights[i]\n- heights 是个山状数组，最大值在 i = 2 处。\n注意，在这个方案中，i = 3 也是一个峰值。\n18 是所有美丽塔方案中的最大高度和。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n == maxHeights <= 10<sup>3</sup></code></li>\n\t<li><code>1 <= maxHeights[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"Try all the possible indices <code>i</code> as the peak.",
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"If <code>i</code> is the peak, start from <code>heights[i] = maxHeights[i]</code>, and <code>heights[j] = max(maxHeights[j], heights[j + 1])</code> for <code>0 <= j < i </code>",
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"If <code>i</code> is the peak, start from <code>heights[i] = maxHeights[i]</code>, and heights[j] = max(maxHeights[j], heights[j - 1]) for <code>i < j < heights.size()</code>"
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