Gas Station 解答

Problem

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.

Solution

Key to the solution is a conclusion:

If sum of gas >= sum of costs, then there must exists one or more solution.

If sum of gas < sum of costs, then there is no solution.

So we can use method of exclusion here.

We need also note here that if A can not reach C in a the sequence of A-->B-->C, then B can not make it either.

 1 public class Solution {
 2     public int canCompleteCircuit(int[] gas, int[] cost) {
 3         if (gas == null || cost == null)
 4             return -1;
 5         if (gas.length != cost.length)
 6             return -1;
 7         int start = 0;
 8         int sumRemaining = 0;
 9         int totalRemaining = 0;
10         for (int i = 0; i < gas.length; i++) {
11             int tmp = gas[i] - cost[i];
12             if (sumRemaining >= 0) {
13                 sumRemaining += tmp;
14             } else {
15                 start = i;
16                 sumRemaining = tmp;
17             }
18             totalRemaining += tmp;
19         }
20         if (totalRemaining < 0)
21             return -1;
22         return start;
23     }
24 }