leetcode-problemset/leetcode-cn/originData/maximize-the-total-height-of-unique-towers.json

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            "questionId": "3510",
            "questionFrontendId": "3301",
            "categoryTitle": "Algorithms",
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            "title": "Maximize the Total Height of Unique Towers",
            "titleSlug": "maximize-the-total-height-of-unique-towers",
            "content": "<p>You are given an array <code>maximumHeight</code>, where <code>maximumHeight[i]</code> denotes the <strong>maximum</strong> height the <code>i<sup>th</sup></code> tower can be assigned.</p>\n\n<p>Your task is to assign a height to each tower so that:</p>\n\n<ol>\n\t<li>The height of the <code>i<sup>th</sup></code> tower is a positive integer and does not exceed <code>maximumHeight[i]</code>.</li>\n\t<li>No two towers have the same height.</li>\n</ol>\n\n<p>Return the <strong>maximum</strong> possible total sum of the tower heights. If it&#39;s not possible to assign heights, return <code>-1</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> maximumHeight<span class=\"example-io\"> = [2,3,4,3]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">10</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can assign heights in the following way: <code>[1, 2, 4, 3]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> maximumHeight<span class=\"example-io\"> = [15,10]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">25</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can assign heights in the following way: <code>[15, 10]</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> maximumHeight<span class=\"example-io\"> = [2,2,1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">-1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>It&#39;s impossible to assign positive heights to each index so that no two towers have the same height.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= maximumHeight.length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= maximumHeight[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "高度互不相同的最大塔高和",
            "translatedContent": "<p>给你一个数组&nbsp;<code>maximumHeight</code>&nbsp;，其中&nbsp;<code>maximumHeight[i]</code>&nbsp;表示第 <code>i</code>&nbsp;座塔可以达到的 <strong>最大</strong>&nbsp;高度。</p>\n\n<p>你的任务是给每一座塔分别设置一个高度，使得：</p>\n\n<ol>\n\t<li>第 <code>i</code>&nbsp;座塔的高度是一个正整数，且不超过&nbsp;<code>maximumHeight[i]</code>&nbsp;。</li>\n\t<li>所有塔的高度互不相同。</li>\n</ol>\n\n<p>请你返回设置完所有塔的高度后，可以达到的 <strong>最大</strong>&nbsp;总高度。如果没有合法的设置，返回 <code>-1</code>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><b>输入：</b>maximumHeight<span class=\"example-io\"> = [2,3,4,3]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>10</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们可以将塔的高度设置为：<code>[1, 2, 4, 3]</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><b>输入：</b>maximumHeight<span class=\"example-io\"> = [15,10]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>25</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们可以将塔的高度设置为：<code>[15, 10]</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><b>输入：</b>maximumHeight<span class=\"example-io\"> = [2,2,1]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>-1</span></p>\n\n<p><b>解释：</b></p>\n\n<p>无法设置塔的高度为正整数且高度互不相同。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= maximumHeight.length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= maximumHeight[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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