Gas Station 解答

Problem

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, otherwise return -1.

Note:
The solution is guaranteed to be unique.

Solution

Key to the solution is a conclusion:

If sum of gas >= sum of costs, then there must exists one or more solution.

If sum of gas < sum of costs, then there is no solution.

So we can use method of exclusion here.

We need also note here that if A can not reach C in a the sequence of A-->B-->C, then B can not make it either.

public class Solution {
    public int canCompleteCircuit(int[] gas, int[] cost) {
        if (gas == null || cost == null)
            return -1;
        if (gas.length != cost.length)
            return -1;
        int start = 0;
        int sumRemaining = 0;
        int totalRemaining = 0;
        for (int i = 0; i < gas.length; i++) {
            int tmp = gas[i] - cost[i];
            if (sumRemaining >= 0) {
                sumRemaining += tmp;
            } else {
                start = i;
                sumRemaining = tmp;
            }
            totalRemaining += tmp;
        }
        if (totalRemaining < 0)
            return -1;
        return start;
    }
}