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.

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