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The Algorithms

Gas Station

There are n gas stations along a circular route, where the amount of gas
at the ith station is gas_quantities[i].

You have a car with an unlimited gas tank and it costs costs[i] of gas
to travel from the ith station to its next (i + 1)th station.
You begin the journey with an empty tank at one of the gas stations.

Given two integer arrays gas_quantities and costs, return the starting
gas station's index if you can travel around the circuit once
in the clockwise direction otherwise, return -1.
If there exists a solution, it is guaranteed to be unique


Implementation notes:
First, check whether the total gas is enough to complete the journey. If not, return -1.
However, if there is enough gas, it is guaranteed that there is a valid
starting index to reach the end of the journey.
Greedily calculate the net gain (gas_quantity - cost) at each station.
If the net gain ever goes below 0 while iterating through the stations,
start checking from the next station.


from dataclasses import dataclass

class GasStation:
    gas_quantity: int
    cost: int

def get_gas_stations(
    gas_quantities: list[int], costs: list[int]
) -> tuple[GasStation, ...]:
    This function returns a tuple of gas stations.

        gas_quantities: Amount of gas available at each station
        costs: The cost of gas required to move from one station to the next

        A tuple of gas stations

    >>> gas_stations = get_gas_stations([1, 2, 3, 4, 5], [3, 4, 5, 1, 2])
    >>> len(gas_stations)
    >>> gas_stations[0]
    GasStation(gas_quantity=1, cost=3)
    >>> gas_stations[-1]
    GasStation(gas_quantity=5, cost=2)
    return tuple(
        GasStation(quantity, cost) for quantity, cost in zip(gas_quantities, costs)

def can_complete_journey(gas_stations: tuple[GasStation, ...]) -> int:
    This function returns the index from which to start the journey
    in order to reach the end.

        gas_quantities [list]: Amount of gas available at each station
        cost [list]: The cost of gas required to move from one station to the next

        start [int]: start index needed to complete the journey

    >>> can_complete_journey(get_gas_stations([1, 2, 3, 4, 5], [3, 4, 5, 1, 2]))
    >>> can_complete_journey(get_gas_stations([2, 3, 4], [3, 4, 3]))
    total_gas = sum(gas_station.gas_quantity for gas_station in gas_stations)
    total_cost = sum(gas_station.cost for gas_station in gas_stations)
    if total_gas < total_cost:
        return -1

    start = 0
    net = 0
    for i, gas_station in enumerate(gas_stations):
        net += gas_station.gas_quantity - gas_station.cost
        if net < 0:
            start = i + 1
            net = 0
    return start

if __name__ == "__main__":
    import doctest