#+PROPERTY: STUDY_DECK_02
* TODO 0134. Gas Station :medium:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*0134. Gas Station][0134. Gas Station]]
:END:

There are ~n~ gas stations along a circular route, where the amount of gas at the ~i^{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^{th}~ 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~ 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:*


#+begin_src
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.
#+end_src


*Example 2:*


#+begin_src
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.
#+end_src


*Constraints:*

 - ~n == gas.length == cost.length~

 - ~1 <= n <= 10^{5}~

 - ~0 <= gas[i], cost[i] <= 10^{4}~

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

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def canCompleteCircuit(self, gas: List[int], cost: List[int]) -> int:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    int canCompleteCircuit(vector<int>& gas, vector<int>& cost) {
        
    }
};
#+end_src