Minimum Number of Refueling Stops

Statement

You need to find the minimum number of refueling stops that a car needs to make to cover a distance, target. For simplicity, assume that the car has to travel from west to east in a straight line. There are various fuel stations on the way, that are represented as a 2-D array of stations, i.e., stations[i] $= [d_i, f_i]$, where $d_i$ is the distance in miles of the $i^{th}$ gas station from the starting position, and $f_i$ is the amount of fuel in liters that it stores. Initially, the car starts with k liters of fuel. The car consumes one liter of fuel for every mile traveled. Upon reaching a gas station, the car can stop and refuel using all the petrol stored at the station. In case it cannot reach the target, the program simply returns $-1$.

Note: If the car reaches a station with $0$ fuel left, it can refuel from that station, and all the fuel from that station can be transferred to the car. If the car reaches the target with $0$ fuel left, it is still considered to have arrived.

For example:

• target: $15$
• start fuel: $2$