[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.

這個題目的關鍵就是得想通一個問題，如果station[i...j]的耗油量小於補給量，那麼i到j之間，也包括i和j的所有點都是不能作爲起點的。這有點兒類似於maximum subarray的感覺。也就是說，如果一個區間的和小於零，再將這個和減去一個必然是正數的部分，這個和只能更小於零了。有點兒繞，需要仔細想清楚才行。這樣做，就可以排除重複的check，達到線性的複雜的。

代碼如下：

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;
    }
}