Question
Circular Gas Station Tour
There are n gas stations arranged in a circular route, where each station i provides gas[i] units of fuel.
You have a car with an unlimited-capacity fuel tank, but traveling from station i to station (i + 1) consumes cost[i] units of gas. You start your journey with an empty tank from one of these stations.
Given the two integer arrays gas and cost, return the 0-based index of the station from which you can complete a full clockwise circuit. If completing the circuit is impossible, return -1.
If a valid starting point exists, it is guaranteed to be unique.
Input
Input contains three lines:
First line contains a single integer n, representing the number of stations.
Second line contains n integers representing gas at each gas stations.
Third line contains n integers representing costs, cost[i] if the cost to travel from the ith station to its next (i + 1)th station.
First line contains a single integer n, representing the number of stations.
Second line contains n integers representing gas at each gas stations.
Third line contains n integers representing costs, cost[i] if the cost to travel from the ith station to its next (i + 1)th station.
Output
Print the starting gas station's index if you can travel around the circuit once in the clockwise direction, otherwise print -1.
Example
Input
5
1 2 3 4 5
3 4 5 1 2
Output
3
Explanation
gas = [1,2,3,4,5], cost = [3,4,5,1,2]
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.
Input
3
2 3 4
3 4 3
Output
-1
Explanation
gas = [2,3,4], cost = [3,4,3]
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.
5
1 2 3 4 5
3 4 5 1 2
Output
3
Explanation
gas = [1,2,3,4,5], cost = [3,4,5,1,2]
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.
Input
3
2 3 4
3 4 3
Output
-1
Explanation
gas = [2,3,4], cost = [3,4,3]
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.