1870. Minimum Speed to Arrive on Time

https://leetcode.com/problems/minimum-speed-to-arrive-on-time

Description

You are given a floating-point number hour, representing the amount of time you have to reach the office. To commute to the office, you must take n trains in sequential order. You are also given an integer array dist of length n, where dist[i] describes the distance (in kilometers) of the ith train ride.

Each train can only depart at an integer hour, so you may need to wait in between each train ride.

• For example, if the 1st train ride takes 1.5 hours, you must wait for an additional 0.5 hours before you can depart on the 2nd train ride at the 2 hour mark.

Return the minimum positive integer speed (in kilometers per hour) that all the trains must travel at for you to reach the office on time, or -1 if it is impossible to be on time.

Tests are generated such that the answer will not exceed 107 and hour will have at most two digits after the decimal point.

Example 1:

**Input:** dist = [1,3,2], hour = 6
**Output:** 1
**Explanation:** At speed 1:
- The first train ride takes 1/1 = 1 hour.
- Since we are already at an integer hour, we depart immediately at the 1 hour mark. The second train takes 3/1 = 3 hours.
- Since we are already at an integer hour, we depart immediately at the 4 hour mark. The third train takes 2/1 = 2 hours.
- You will arrive at exactly the 6 hour mark.

Example 2:

**Input:** dist = [1,3,2], hour = 2.7
**Output:** 3
**Explanation:** At speed 3:
- The first train ride takes 1/3 = 0.33333 hours.
- Since we are not at an integer hour, we wait until the 1 hour mark to depart. The second train ride takes 3/3 = 1 hour.
- Since we are already at an integer hour, we depart immediately at the 2 hour mark. The third train takes 2/3 = 0.66667 hours.
- You will arrive at the 2.66667 hour mark.

Example 3:

**Input:** dist = [1,3,2], hour = 1.9
**Output:** -1
**Explanation:** It is impossible because the earliest the third train can depart is at the 2 hour mark.

Constraints:

• n == dist.length

• 1 <= n <= 105

• 1 <= dist[i] <= 105

• 1 <= hour <= 109

• There will be at most two digits after the decimal point in hour.

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