Leetcode 134（Gas Station）

Question

There are N gas stations along a circular route, where the amount of gas at station ii is gas[i]gas[i].

You have a car with an unlimited gas tank and it costs cost[i]cost[i] of gas to travel from station ii to its next station (i+1)(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.

有NN个地方排列成环状，每个地方可以添加固定数量的油，从一个地方到另一个地方需要消耗固定数量的油。问从哪个地方出发可以保证能环游这NN个地方。

Analysis

一个暴力的方法是遍历每个节点，一次判断这个节点是否满足，直到选出最先找到的那个合适节点或者返回失败。但是这种方法时间复杂度为O(n2)O(n^{2})，而且leetcode会报Time Limited Error。

另外一种方法是从第一个节点开始遍历，直到找到无法满足的那个地方为止，则遍历起点到终止点得任何一个地方都无法满足条件（可用反证法证明）。则把终止点得下一个节点作为出发点向后遍历，照上面方法继续遍历。如果遍历到最后一个节点扔无法成功，则返回-1，否则可加的油量大于遍历所需的耗油量，则一定可以遍历成功。

Code

int canCompleteCircuit(int* gas, int gasSize, int* cost, int costSize) {

int gasSum=0;

int costSum=0;

int total=0;

int sum=0;

int result=0;

if (gasSize==0) return 0;

for(int i=0;i<=gasSize-1;++i){

sum+=gas[i]-cost[i];

total+=gas[i]-cost[i];

costSum=costSum+cost[i];

if(sum<0){

result=i+1;

sum=0;

}

}

if(total<0) return -1;

else return result;

}