What is the optimal time complexity of solving Gas Station?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Gas Station?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Gas Station?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Gas Station?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Gas Station

Learn how to solve the 'Gas Station' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

There are n gas stations along a circular route, where the amount of gas at the ith station is gas[i]. You have a car with an unlimited gas tank and it costs cost[i] of gas to travel from the ith station to its next (i + 1)th station. 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. If there exists a solution, it is guaranteed to be unique.

Write a function canCompleteCircuit(gas: List[int], cost: List[int]) -> int.

Constraints

•n == len(gas) == len(cost)
•1 <= n <= 10^5
•0 <= gas[i], cost[i] <= 10^4

Examples

Example 1

Input

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

Output

Explanation

Start at station 3. tank = 4. Go to 4: cost 1, tank = 4-1+5 = 8. Go to 0: cost 2, tank = 8-2+1=7. Go to 1: cost 3, tank = 7-3+2=6. Go to 2: cost 4, tank = 6-4+3=5. Go to 3: cost 5, tank = 5-5=0. We reached back to station 3.

Example 2

Input

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

Output

-1

Explanation

No station can complete the circuit.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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