LeetCode 134: Gas Station — Python Solution

Solve LeetCode 134: Gas Station in Python with a greedy restart approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

If total fuel is insufficient no start works. While scanning, a negative running tank invalidates every start since the previous candidate, so restart after it.

Algorithm

1. If total fuel is insufficient no start works. While scanning, a negative running tank invalidates every start since the previous candidate, so restart after it.
2. Maintain this invariant: The current candidate can reach every station processed since it was chosen.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def canCompleteCircuit(self, gas, cost):
        if sum(gas) < sum(cost):
            return -1
        start = tank = 0
        for i, (fuel, price) in enumerate(zip(gas, cost)):
            tank += fuel - price
            if tank < 0:
                start, tank = i + 1, 0
        return start

Why this is correct

The proof follows the maintained state: The current candidate can reach every station processed since it was chosen. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

A valid start may be the final station; the total balance decides impossibility.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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