Package g2101_2200.s2188_minimum_time_to_finish_the_race

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    2188 - Minimum Time to Finish the Race.

    Hard

    You are given a 0-indexed 2D integer array tires where <code>tiresi = 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.

    • 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 3 seconds, its <code>2<sup>nd</sup></code> lap in 3 * 2 = 6 seconds, its <code>3<sup>rd</sup></code> lap in <code>3 * 2<sup>2</sup> = 12</code> seconds, etc.

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

    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.

    Return the minimum time to finish the race.

    Example 1:

    Input: tires = [2,3,3,4], changeTime = 5, numLaps = 4

    Output: 21

    Explanation:

    Lap 1: Start with tire 0 and finish the lap in 2 seconds.

    Lap 2: Continue with tire 0 and finish the lap in 2 \* 3 = 6 seconds.

    Lap 3: Change tires to a new tire 0 for 5 seconds and then finish the lap in another 2 seconds.

    Lap 4: Continue with tire 0 and finish the lap in 2 \* 3 = 6 seconds.

    Total time = 2 + 6 + 5 + 2 + 6 = 21 seconds.

    The minimum time to complete the race is 21 seconds.

    Example 2:

    Input: tires = [1,10,2,2,3,4], changeTime = 6, numLaps = 5

    Output: 25

    Explanation:

    Lap 1: Start with tire 1 and finish the lap in 2 seconds.

    Lap 2: Continue with tire 1 and finish the lap in 2 \* 2 = 4 seconds.

    Lap 3: Change tires to a new tire 1 for 6 seconds and then finish the lap in another 2 seconds.

    Lap 4: Continue with tire 1 and finish the lap in 2 \* 2 = 4 seconds.

    Lap 5: Change tires to tire 0 for 6 seconds then finish the lap in another 1 second.

    Total time = 2 + 4 + 6 + 2 + 4 + 6 + 1 = 25 seconds.

    The minimum time to complete the race is 25 seconds.

    Constraints:

    • <code>1 <= tires.length <= 10<sup>5</sup></code>

    • tires[i].length == 2

    • <code>1 <= f<sub>i</sub>, changeTime <= 10<sup>5</sup></code>

    • <code>2 <= r<sub>i</sub><= 10<sup>5</sup></code>

    • 1 &lt;= numLaps &lt;= 1000

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer minimumFinishTime(Array<IntArray> tires, Integer changeTime, Integer numLaps)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait