# LC134 - Gas Station

## Problem

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

You have a car with an unlimited gas tank and it costs `cost[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` 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

**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.

## Solution

### Greedy

Time complexity is $$O(n)$$ and no extra space is used.

```python
def canCompleteCircuit(self, gas: List[int], cost: List[int]) -> int:
	# Total gas must be equal or more than total cost
	if sum(gas) < sum(cost):
		return -1
		
	total = 0
	start = 0
	
	for i in range(len(gas)):
		# running delta of price
		total += (gas[i] - cost[i])
		# that start didn't make it, shift
		if total < 0:
			total = 0
			start = i+1
	return start
```