134. Gas Station.md

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:

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:

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.

Solution 1 :Brute Force

class Solution {
    public int canCompleteCircuit(int[] gas, int[] cost) {
        if(cost.length==1) return (cost[0]<=gas[0])?0:-1;
        for(int i=0;i<gas.length;i++){
            if(gas[i]<=cost[i]) continue;
            if(canTravel(gas,cost,i)) return i;
        }
        return -1;
    }
    public boolean canTravel(int[] gas,int cost[],int current){
        int currentGas=0;
        boolean first=true;
        int lastStop=0;
        if(current==0) lastStop=cost.length-1;
        else lastStop=current-1;
        for(int i=(current%gas.length); first || i!=current;i=(i+1)%gas.length){
            currentGas+=gas[i];
            if(currentGas<cost[i]) return false;
            if(i==lastStop && currentGas>=cost[i]) return true;
            currentGas-=cost[i];
            first=false;
           // System.out.println(currentGas);
        }
        if(current==0 && cost[cost.length-1]>currentGas) return false;
        if(cost[current-1]>currentGas) return false;
        return true;
    }
}

Solution 2 :

/*
What we are gonna do is we start from first station and as soon as out tank goes in negative we know we can't travel to next node . So we start from i+1 station because their is not point in starting from next station because lets say we were we have travelled to s1 s2 s3 and then we go negative on s4 so we know everything was well on s1 s2 s3 and something is wrong with s4 so if we start at s2 that's just substracting gas from s1 and Jab s1 ke sath defiect ho gya toh s1 k bina toh hoga hi. So we will start from s5. And we will only check until end of array. We will first find if we really can travel all the station and we if can then we know there must be a start station and if the start station is not s1 s2 s3 s4 then it must be after that.
*/
class Solution {
    public int canCompleteCircuit(int[] gas, int[] cost) {
        int result=0;
        int tank=0;
        int sumGas=0;
        int sumCost=0;
        for(int i=0;i<gas.length;i++){
            sumCost+=cost[i];
            sumGas+=gas[i];
            tank+=gas[i]-cost[i];
            if(tank<0){
                result=i+1;
                tank=0;
            }
        }
        return sumGas-sumCost<0?-1:result;
    }
}