[LeetCode] - 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, otherwise return -1.

Note:
The solution is guaranteed to be unique.

这个题目的关键就是得想通一个问题，如果station[i...j]的耗油量小于补给量，那么i到j之间，也包括i和j的所有点都是不能作为起点的。这有点儿类似于maximum subarray的感觉。也就是说，如果一个区间的和小于零，再将这个和减去一个必然是正数的部分，这个和只能更小于零了。有点儿绕，需要仔细想清楚才行。这样做，就可以排除重复的check，达到线性的复杂的。

代码如下：

public class Solution {
    public int canCompleteCircuit(int[] gas, int[] cost) {
        if(gas==null || cost==null) return -1;
        int i = 0;
        while(i < gas.length) {
            int gasLeft=gas[i]-cost[i], j=i+1;
            while(gasLeft >= 0) {
                if(j%gas.length==i) return i;
                gasLeft += gas[j%gas.length]-cost[j%gas.length];
                j++;
            }
            i = j;
        }
        return -1;
    }
}