[LeetCode] 134. Gas Station

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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 in the clockwise direction, otherwise return -1.

Note:

  • If there exists a solution, it is guaranteed to be unique.
  • Both input arrays are non-empty and have the same length.
  • Each element in the input arrays is a non-negative integer.

Example 1:

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Input:
gas  = [1,2,3,4,5]
cost = [3,4,5,1,2]

Output: 3

Explanation:
Start at station 3 (index 3) and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 4. Your tank = 4 - 1 + 5 = 8
Travel to station 0. Your tank = 8 - 2 + 1 = 7
Travel to station 1. Your tank = 7 - 3 + 2 = 6
Travel to station 2. Your tank = 6 - 4 + 3 = 5
Travel to station 3. The cost is 5. Your gas is just enough to travel back to station 3.
Therefore, return 3 as the starting index.

Example 2:

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Input:
gas  = [2,3,4]
cost = [3,4,3]

Output: -1

Explanation:
You can't start at station 0 or 1, as there is not enough gas to travel to the next station.
Let's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4
Travel to station 0. Your tank = 4 - 3 + 2 = 3
Travel to station 1. Your tank = 3 - 3 + 3 = 3
You cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.
Therefore, you can't travel around the circuit once no matter where you start.

Explanation

  1. In order to loop all elements, total gas must equal or greater than total cost, then the start can exist.

  2. If we start from index 0, if current gas is equal or greater than current cost, then we can move forward. After we successfully move forward, we use the remaining gas plus the current gas minus the current cost to get the difference. If the difference is less than 0, that means we cannot start from any indexes between index 0 and current index inclusive. For example, we start from index 0, now when we are on index i, and curGas + gas[i] - cost[i] < 0, we know that after index i-1, curGas >= 0, after index i-2, old_curGas >= 0, etc. Any index before i will only bring positive curGas, so if at index i and the difference is negative, then we the start cannot be any index between 0 and i inclusive, so we update start = i + 1. When finish looping, we return start if the total gas is equal or greater than total cost.

Solution

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class Solution {
    public int canCompleteCircuit(int[] gas, int[] cost) {
        int start = 0;
        int totalDiff = 0, curGas = 0;

        for (int i = 0; i < gas.length; i++) {
            curGas += gas[i] - cost[i];
            totalDiff += gas[i] - cost[i];
            if (curGas < 0) {
                start = i+1;
                curGas = 0;
            }
        }
        if (totalDiff < 0) {
            return -1;
        } else {
            return start;
        }
    }
}