Gas Station

arraygreedy

Problem Statement

There are n gas stations along a circular route, where the amount of gas at the i ^th station is gas[i] .

You have a car with an unlimited gas tank and it costs cost[i] of gas to travel from the i ^th 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 .

Examples

Example 1

Input: gas = [1,2,3,4,5], cost = [3,4,5,1,2]
Output: 3
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
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 <= 10 ^5

0 <= gas[i], cost[i] <= 10 ^4

The input is generated such that the answer is unique.

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy