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.

这道题最容易想到的方法就是从一个点出发，看看能不能走回到起点，如果可以返回起点的index, 不行的话再试下一个点。但是超时。

这个超时算法中有两点值得注意。

a) L13. 对于 int a 怎么计算 a 在 循环群[0,1,2,n-1]上的index?

b) L21-L22，可以使用一个变量记录是哪一步跳出的。然后判断是不是最后一步跳出的。

 1 class Solution(object):
 2     def canCompleteCircuit(self, gas, cost):
 3         """
 4         :type gas: List[int]
 5         :type cost: List[int]
 6         :rtype: int
 7         """
 8         n = len(gas)
 9         for i in range(n):
10             fule = 0
11             step = 0
12             for j in range(n):
13                 index = (i+j +1)%n -1
14                 fule += gas[index]
15                 step = j
16                 if fule < cost[index]:
17                     break
18                 else:
19                     fule -= cost[index]
20 
21                 if step == n-1:                        
22                     return i
23         return -1

一下三条原则摘自： http://bangbingsyb.blogspot.com/2014/11/leetcode-gas-station.html

性质1. 对于任意一个加油站i，假如从i出发可以环绕一圈，则i一定可以到达任何一个加油站。显而易见。

 1 class Solution(object):
 2     def canCompleteCircuit(self, gas, cost):
 3         """
 4         :type gas: List[int]
 5         :type cost: List[int]
 6         :rtype: int
 7         """
 8         n = len(gas)
 9         start = 0
10         netGasSum = 0
11         curGasSum = 0
12         
13         for i in range(n):
14             netGasSum += gas[i] - cost[i]
15             curGasSum += gas[i] - cost[i]
16             if curGasSum < 0:
17                 start = i+1
18                 curGasSum = 0;
19         
20         if netGasSum < 0:
21             return -1
22         return start

Leetcode 134 Gas Station