{ "data": { "question": { "questionId": "2295", "questionFrontendId": "2188", "categoryTitle": "Algorithms", "boundTopicId": 1290375, "title": "Minimum Time to Finish the Race", "titleSlug": "minimum-time-to-finish-the-race", "content": "

You are given a 0-indexed 2D integer array tires where tires[i] = [fi, ri] indicates that the ith tire can finish its xth successive lap in fi * ri(x-1) seconds.

\n\n\n\n

You are also given an integer changeTime and an integer numLaps.

\n\n

The race consists of numLaps laps and you may start the race with any tire. You have an unlimited supply of each tire and after every lap, you may change to any given tire (including the current tire type) if you wait changeTime seconds.

\n\n

Return the minimum time to finish the race.

\n\n

 

\n

Example 1:

\n\n
\nInput: tires = [[2,3],[3,4]], changeTime = 5, numLaps = 4\nOutput: 21\nExplanation: \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
\n\n

Example 2:

\n\n
\nInput: tires = [[1,10],[2,2],[3,4]], changeTime = 6, numLaps = 5\nOutput: 25\nExplanation: \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
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "完成比赛的最少时间", "translatedContent": "

给你一个下标从 0 开始的二维整数数组 tires ，其中 tires[i] = [fi, ri] 表示第 i 种轮胎如果连续使用，第 x 圈需要耗时 fi * ri(x-1) 秒。

\n\n\n\n

同时给你一个整数 changeTime 和一个整数 numLaps 。

\n\n

比赛总共包含 numLaps 圈，你可以选择 任意 一种轮胎开始比赛。每一种轮胎都有 无数条 。每一圈后，你可以选择耗费 changeTime 秒 换成 任意一种轮胎（也可以换成当前种类的新轮胎）。

\n\n

请你返回完成比赛需要耗费的 最少 时间。

\n\n

 

\n\n

示例 1：

\n\n
输入：tires = [[2,3],[3,4]], changeTime = 5, numLaps = 4\n输出：21\n解释：\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
\n\n

示例 2：

\n\n
输入：tires = [[1,10],[2,2],[3,4]], changeTime = 6, numLaps = 5\n输出：25\n解释：\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
\n\n

 

\n\n

提示：

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