Description:
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.
Link:
https://leetcode.com/problems/gas-station/description/
解题方法:
一开始用的是O(N^2)的brute force,不能AC。
于是换一种O(N的方法):
有题目可知:
1、在第i个加油站时,gas[i] - cost[i] >= 0意味着车子可以从这个加油站经过,并且tank里可能剩油或者为空。
2、如果我们任意选择一个点start出发(也就是可以从第一个加油站出发),当走到A点时发现tank和A点的油加起来都不够走过A点,那么意味着我们从start点到A点之前的任意一个点出发,都不可能走过A点。
3、当出现以上情况时,如果车子能够循环跑一圈,意味着出发点必须在A点之后。此时应该把当前不够的油记录下来,让tank重置为0,即以A点以后的点为start继续跑,最后跑完(跑完最后一个加油站)看看tank里面剩下的油能不能把之前的坑填上,如果不能就返回-1,能就返回start。
Time Complexity:
O(N)
完整代码:
int canCompleteCircuit(vector<int>& gas, vector<int>& cost)
{
if(gas.size() == 0 || cost.size() == 0)
return -1;
int tank = 0, lack = 0, start = 0;
for(int i = 0; i < gas.size(); i++)
{
tank += gas[i] - cost[i];
if(tank < 0)
{
lack += tank;
start = i + 1;
tank = 0;
}
}
return lack + tank >= 0 ? start : -1;
}