Problem Description
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.
Key Insights
- The total amount of gas must be greater than or equal to the total cost to complete the circuit.
- If the current tank goes negative, the starting point must be adjusted to the next station.
- The problem can be solved in a single pass through the stations, ensuring O(n) time complexity.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we maintain a variable to track the total gas minus cost (net gain/loss) and another variable to track the current gas available during the journey. We iterate through each gas station, updating our total net gas and, if at any point the current gas becomes negative, we reset our starting index to the next station. If after one complete iteration the total net gas is non-negative, we can return the starting index; otherwise, we return -1. This approach efficiently determines the possible starting station in a single traversal.