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. If it cannot reach the target, the program 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.

Constraints:

• $1 \leq$ target, k $\leq 10^9$
• $0 \leq$ stations.length $\leq 900$
• $1 \leq d_{i} < d_{i+1}<$ target
• $1 \leq f_{i} < 10^9$

Examples