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{
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"question": {
"questionId": "3485",
"questionFrontendId": "3281",
"categoryTitle": "Algorithms",
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"title": "Maximize Score of Numbers in Ranges",
"titleSlug": "maximize-score-of-numbers-in-ranges",
"content": "<p>You are given an array of integers <code>start</code> and an integer <code>d</code>, representing <code>n</code> intervals <code>[start[i], start[i] + d]</code>.</p>\n\n<p>You are asked to choose <code>n</code> integers where the <code>i<sup>th</sup></code> integer must belong to the <code>i<sup>th</sup></code> interval. The <strong>score</strong> of the chosen integers is defined as the <strong>minimum</strong> absolute difference between any two integers that have been chosen.</p>\n\n<p>Return the <strong>maximum</strong> <em>possible score</em> of the chosen integers.</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> <span class=\"example-io\">start = [6,0,3], d = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The maximum possible score can be obtained by choosing integers: 8, 0, and 4. The score of these chosen integers is <code>min(|8 - 0|, |8 - 4|, |0 - 4|)</code> which equals 4.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">start = [2,6,13,13], d = 5</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The maximum possible score can be obtained by choosing integers: 2, 7, 13, and 18. The score of these chosen integers is <code>min(|2 - 7|, |2 - 13|, |2 - 18|, |7 - 13|, |7 - 18|, |13 - 18|)</code> which equals 5.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= start.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= start[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= d &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
"translatedTitle": "范围内整数的最大得分",
"translatedContent": "<p>给你一个整数数组 <code>start</code> 和一个整数 <code>d</code>,代表 <code>n</code> 个区间 <code>[start[i], start[i] + d]</code>。</p>\n\n<p>你需要选择 <code>n</code> 个整数,其中第 <code>i</code> 个整数必须属于第 <code>i</code> 个区间。所选整数的 <strong>得分</strong> 定义为所选整数两两之间的 <strong>最小 </strong>绝对差。</p>\n\n<p>返回所选整数的 <strong>最大可能得分 </strong>。</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><strong>输入:</strong> <span class=\"example-io\">start = [6,0,3], d = 2</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>可以选择整数 8, 0 和 4 获得最大可能得分,得分为 <code>min(|8 - 0|, |8 - 4|, |0 - 4|)</code>,等于 4。</p>\n</div>\n\n<p><strong class=\"example\">示例 2</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">start = [2,6,13,13], d = 5</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>可以选择整数 2, 7, 13 和 18 获得最大可能得分,得分为 <code>min(|2 - 7|, |2 - 13|, |2 - 18|, |7 - 13|, |7 - 18|, |13 - 18|)</code>,等于 5。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= start.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= start[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= d &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"Suppose that the answer is <code>x</code>. We can find a valid configuration of integers by sorting <code>start</code>, the first integer should be <code>start[0]</code>, then each subsequent integer should be the smallest one in <code>[start[i], start[i] + d]</code> that is greater than <code>last_chosen_value + x</code>.",
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