leetcode-problemset/leetcode-cn/originData/minimum-time-to-finish-the-race.json

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            "questionId": "2295",
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            "title": "Minimum Time to Finish the Race",
            "titleSlug": "minimum-time-to-finish-the-race",
            "content": "<p>You are given a <strong>0-indexed</strong> 2D integer array <code>tires</code> where <code>tires[i] = [f<sub>i</sub>, r<sub>i</sub>]</code> indicates that the <code>i<sup>th</sup></code> tire can finish its <code>x<sup>th</sup></code> successive lap in <code>f<sub>i</sub> * r<sub>i</sub><sup>(x-1)</sup></code> seconds.</p>\n\n<ul>\n\t<li>For example, if <code>f<sub>i</sub> = 3</code> and <code>r<sub>i</sub> = 2</code>, then the tire would finish its <code>1<sup>st</sup></code> lap in <code>3</code> seconds, its <code>2<sup>nd</sup></code> lap in <code>3 * 2 = 6</code> seconds, its <code>3<sup>rd</sup></code> lap in <code>3 * 2<sup>2</sup> = 12</code> seconds, etc.</li>\n</ul>\n\n<p>You are also given an integer <code>changeTime</code> and an integer <code>numLaps</code>.</p>\n\n<p>The race consists of <code>numLaps</code> laps and you may start the race with <strong>any</strong> tire. You have an <strong>unlimited</strong> supply of each tire and after every lap, you may <strong>change</strong> to any given tire (including the current tire type) if you wait <code>changeTime</code> seconds.</p>\n\n<p>Return<em> the <strong>minimum</strong> time to finish the race.</em></p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> tires = [[2,3],[3,4]], changeTime = 5, numLaps = 4\n<strong>Output:</strong> 21\n<strong>Explanation:</strong> \nLap 1: Start with tire 0 and finish the lap in 2 seconds.\nLap 2: Continue with tire 0 and finish the lap in 2 * 3 = 6 seconds.\nLap 3: Change tires to a new tire 0 for 5 seconds and then finish the lap in another 2 seconds.\nLap 4: Continue with tire 0 and finish the lap in 2 * 3 = 6 seconds.\nTotal time = 2 + 6 + 5 + 2 + 6 = 21 seconds.\nThe minimum time to complete the race is 21 seconds.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> tires = [[1,10],[2,2],[3,4]], changeTime = 6, numLaps = 5\n<strong>Output:</strong> 25\n<strong>Explanation:</strong> \nLap 1: Start with tire 1 and finish the lap in 2 seconds.\nLap 2: Continue with tire 1 and finish the lap in 2 * 2 = 4 seconds.\nLap 3: Change tires to a new tire 1 for 6 seconds and then finish the lap in another 2 seconds.\nLap 4: Continue with tire 1 and finish the lap in 2 * 2 = 4 seconds.\nLap 5: Change tires to tire 0 for 6 seconds then finish the lap in another 1 second.\nTotal time = 2 + 4 + 6 + 2 + 4 + 6 + 1 = 25 seconds.\nThe minimum time to complete the race is 25 seconds. \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= tires.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>tires[i].length == 2</code></li>\n\t<li><code>1 &lt;= f<sub>i</sub>, changeTime &lt;= 10<sup>5</sup></code></li>\n\t<li><code>2 &lt;= r<sub>i</sub> &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= numLaps &lt;= 1000</code></li>\n</ul>\n",
            "translatedTitle": "完成比赛的最少时间",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>tires</code>&nbsp;，其中&nbsp;<code>tires[i] = [f<sub>i</sub>, r<sub>i</sub>]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;种轮胎如果连续使用，第&nbsp;<code>x</code>&nbsp;圈需要耗时&nbsp;<code>f<sub>i</sub> * r<sub>i</sub><sup>(x-1)</sup></code>&nbsp;秒。</p>\n\n<ul>\n\t<li>比方说，如果&nbsp;<code>f<sub>i</sub> = 3</code>&nbsp;且&nbsp;<code>r<sub>i</sub> = 2</code>&nbsp;，且一直使用这种类型的同一条轮胎，那么该轮胎完成第&nbsp;<code>1</code>&nbsp;圈赛道耗时 <code>3</code>&nbsp;秒，完成第 <code>2</code>&nbsp;圈耗时&nbsp;<code>3 * 2 = 6</code>&nbsp;秒，完成第 <code>3</code>&nbsp;圈耗时&nbsp;<code>3 * 2<sup>2</sup> = 12</code>&nbsp;秒，依次类推。</li>\n</ul>\n\n<p>同时给你一个整数&nbsp;<code>changeTime</code>&nbsp;和一个整数&nbsp;<code>numLaps</code>&nbsp;。</p>\n\n<p>比赛总共包含&nbsp;<code>numLaps</code>&nbsp;圈，你可以选择 <strong>任意</strong>&nbsp;一种轮胎开始比赛。每一种轮胎都有 <strong>无数条</strong>&nbsp;。每一圈后，你可以选择耗费 <code>changeTime</code>&nbsp;秒 <strong>换成</strong>&nbsp;任意一种轮胎（也可以换成当前种类的新轮胎）。</p>\n\n<p>请你返回完成比赛需要耗费的 <strong>最少</strong>&nbsp;时间。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>tires = [[2,3],[3,4]], changeTime = 5, numLaps = 4\n<b>输出：</b>21\n<b>解释：</b>\n第 1 圈：使用轮胎 0 ，耗时 2 秒。\n第 2 圈：继续使用轮胎 0 ，耗时 2 * 3 = 6 秒。\n第 3 圈：耗费 5 秒换一条新的轮胎 0 ，然后耗时 2 秒完成这一圈。\n第 4 圈：继续使用轮胎 0 ，耗时 2 * 3 = 6 秒。\n总耗时 = 2 + 6 + 5 + 2 + 6 = 21 秒。\n完成比赛的最少时间为 21 秒。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>tires = [[1,10],[2,2],[3,4]], changeTime = 6, numLaps = 5\n<b>输出：</b>25\n<b>解释：</b>\n第 1 圈：使用轮胎 1 ，耗时 2 秒。\n第 2 圈：继续使用轮胎 1 ，耗时 2 * 2 = 4 秒。\n第 3 圈：耗时 6 秒换一条新的轮胎 1 ，然后耗时 2 秒完成这一圈。\n第 4 圈：继续使用轮胎 1 ，耗时 2 * 2 = 4 秒。\n第 5 圈：耗时 6 秒换成轮胎 0 ，然后耗时 1 秒完成这一圈。\n总耗时 = 2 + 4 + 6 + 2 + 4 + 6 + 1 = 25 秒。\n完成比赛的最少时间为 25 秒。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= tires.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>tires[i].length == 2</code></li>\n\t<li><code>1 &lt;= f<sub>i</sub>, changeTime &lt;= 10<sup>5</sup></code></li>\n\t<li><code>2 &lt;= r<sub>i</sub> &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= numLaps &lt;= 1000</code></li>\n</ul>\n",
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                "What is the maximum number of times we would want to go around the track without changing tires?",
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