minimum-speed-to-arrive-on-time

Minimum Speed to Arrive on Time

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minSpeedOnTime

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

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

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

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 <code>-1</code> if it is impossible to be on time.

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

&nbsp;
Example 1:

<pre>
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.
</pre>

Example 2:

<pre>
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.
</pre>

Example 3:

<pre>
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.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == dist.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>1 &lt;= dist[i] &lt;= 105</code></li>
	<li><code>1 &lt;= hour &lt;= 109</code></li>
	<li>There will be at most two digits after the decimal point in <code>hour</code>.</li>
</ul>

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