GasStation

Problem

https://leetcode.com/problems/gas-station/

There are n gas stations along a circular route, where the amount of gas at the i:sup:`th` station is gas[i].

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

Given two integer arrays gas and cost, 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.

Example 1:

Input: gas = [1,2,3,4,5], cost = [3,4,5,1,2]
Output: 3
Explanation:
Start at station 3 (index 3) and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 4. Your tank = 4 - 1 + 5 = 8
Travel to station 0. Your tank = 8 - 2 + 1 = 7
Travel to station 1. Your tank = 7 - 3 + 2 = 6
Travel to station 2. Your tank = 6 - 4 + 3 = 5
Travel to station 3. The cost is 5. Your gas is just enough to travel back to station 3.
Therefore, return 3 as the starting index.

Example 2:

Input: gas = [2,3,4], cost = [3,4,3]
Output: -1
Explanation:
You can't start at station 0 or 1, as there is not enough gas to travel to the next station.
Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 0. Your tank = 4 - 3 + 2 = 3
Travel to station 1. Your tank = 3 - 3 + 3 = 3
You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.
Therefore, you can't travel around the circuit once no matter where you start.

Constraints:

• n == gas.length == cost.length

• 1 <= n <= 10:sup:`5`

• 0 <= gas[i], cost[i] <= 10:sup:`4`

• The input is generated such that the answer is unique.

Solution

Create a surplus array, which stores the difference between gas and cost. If the sum of surplus is negative, then there is not enough gas to complete the circuit no matter the starting point. Otherwise, we can complete the circuit. Observe that if we cannot complete the circuit by i, then we cannot complete the circuit starting at any station in [start, i]. This is because the car had a non-empty tank until i. Thus, if there is a solution, it must be in [i + 1, n].

Pattern

Array, Greedy

Code

from typing import List


def canCompleteCircuit(gas: List[int], cost: List[int]) -> int:
    """Return the starting gas station index if we can complete the circuit, -1
    otherwise.
    """
    surplus = [g - c for g, c in zip(gas, cost)]

    if sum(surplus) < 0:
        return -1

    start = 0
    tank = 0
    for i, s in enumerate(surplus):
        tank += s
        if tank < 0:
            start = i + 1
            tank = 0

    return start

Test

>>> from GasStation import canCompleteCircuit
>>> gas = [1, 2, 3, 4, 5]
>>> cost = [3, 4, 5, 1, 2]
>>> canCompleteCircuit(gas, cost)
3
>>> gas = [2, 3, 4]
>>> cost = [3, 4, 3]
>>> canCompleteCircuit(gas, cost)
-1

GasStation.canCompleteCircuit(gas: List[int], cost: List[int]) → int

Return the starting gas station index if we can complete the circuit, -1 otherwise.