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Nov 29, 2024
4 min read

LeetCode 134: Gas Station

Leetcode 134: Gas Station solution in Python

Problem Description

LeetCode Problem 134

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.

Given two integer arrays gas and cost, 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.

 

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.

 

Constraints:

  • n == gas.length == cost.length
  • 1 <= n <= 105
  • 0 <= gas[i], cost[i] <= 104

Difficulty: Medium

Tags: array, greedy

Rating: 90.91%

Solution Approach

The solution uses two key insights:

  • Total Gas vs Total Cost: If the total gas available is less than the total cost needed, it’s impossible to complete the circuit. This is our first check.
  • Greedy Approach: If we can’t reach a station j from station i, then we can’t reach station j from any station between i and j-1.

Solution

Here’s my Python solution to this problem:

class Solution:
    def canCompleteCircuit(self, gas: List[int], cost: List[int]) -> int:
        if sum(gas) < sum(cost): return -1

        curr_g = 0
        start = 0

        for i in range(len(gas)):
            curr_g += gas[i] - cost[i]
            if curr_g < 0:
                start = i + 1
                curr_g = 0

        return start

Complexity Analysis

The solution has the following complexity characteristics:

  • Time Complexity: O(n)O(n)
  • Space Complexity: O(1)O(1)