Leetcode 134: Gas Station

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

You have a car with an unlimited gas tank and it costs cost[i] of gas to travel from station i to its next station (i+1). You begin the journey with an empty tank at one of the gas stations.

Return the starting gas station’s index if you can travel around the circuit once in the clockwise direction, otherwise return -1.

Note:

• If there exists a solution, it is guaranteed to be unique.
• Both input arrays are non-empty and have the same length.
• Each element in the input arrays is a non-negative integer.

Example 1:

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.

Example 2:

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.

Problem Analysis:

If sum of gas less than sum of cost, the travel can not be back to the original station.

So we consider in the condition: sum(gas) ≥ sum(cost), we need to find out which index should be the start station.

Suppose we travel from station i to station j, we sum the gas and cost, if sum(gas) < sum(cost), then we can find k, i ≤ k ≤ j, sum(gas) < sum(cost) from k to j. So skip these index, we can get the correct start index.

Solution:

class Solution {
public:
    int canCompleteCircuit(vector<int>& gas, vector<int>& cost) {
        int res = 0;
        int sum = 0;
        int current = 0;
        for (int i = 0; i < gas.size(); ++i) {
            current += gas[i] - cost[i];
            sum += gas[i] - cost[i];
            if (current < 0) {
                res = i + 1;
                current = 0;
            }
        }
        
        return sum >= 0 ? res : -1;
    }
};

Time Complexity: O(n)

Space Complexity: O(1)