LeetCode Q134: Gas Station

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.

	class Solution {
	public:
	int canCompleteCircuit(vector<int>& gas, vector<int>& cost) {
	int i, j;
	/*
	* If start from i, stop before station x -> no station k from i + 1 to x - 1 can reach x.
	* Bcoz if so, i can reach k and k can reach x, then i reaches x. Contradiction.
	* Thus i can jump directly to x instead of i + 1, bringing complexity from O(n^2) to O(n).
	*/
	// start from station i
	for(i=0; i<cost.size(); i=i+j+1){
	int r=0;
	for(j=0; j<cost.size(); j++){
	int k=(i+j)%cost.size();
	r=r+gas[k]-cost[k];
	if(r<0)
	break;
	}
	if(j==cost.size())
	return i;
	}
	return -1;
	}
	};

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