# 1870. 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**.

### 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`.

### Approach

### Links

* Binarysearch
* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/minimum-speed-to-arrive-on-time/)
* ProgramCreek
* YouTube

### **Examples**

{% tabs %}
{% tab title="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.
  {% endtab %}

{% tab title="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.
  {% endtab %}

{% tab title="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.
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    public int minSpeedOnTime(int[] dist, double hour) {
        int n = dist.length, result = -1;
        if(n > 0) {
            int low = 1, high = 10000000;

            while(low <= high) {
                int mid = low + (high-low)/2;
                if(canReach(dist, hour, mid)) {
                    high = mid - 1;
                    result = mid;
                } else {
                    low = mid + 1;
                }
            }
        }
        
        return result;
    }
    
    private boolean canReach(int[] dist, double hour, int speed) {
        double time = 0.0;
        int n = dist.length;
        
        for(int i = 0; i < n-1; i++) {
            time += (int) Math.ceil(dist[i] * 1.0 / speed);
        }
        
        time += (dist[n-1] * 1.0 / speed);
        
        return time <= hour;
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*