[Solved] You have a circular route with gas stations, each providing some gas and requiring some cost to travel to... Which algorithmic approach guarantees finding the correct starting station efficiently? | Greedy Algorithms

Greedy Algorithms - Gas Station (Circular)

You have a circular route with gas stations, each providing some gas and requiring some cost to travel to the next station. You want to find a starting station to complete the full circle without running out of gas. Which algorithmic approach guarantees finding the correct starting station efficiently?

ADivide and conquer by splitting the circle into halves and solving recursively

BDynamic Programming to store maximum gas reachable from each station

CBrute force by simulating the trip starting from each station until success or failure

DGreedy approach that checks total gas vs total cost and resets start when tank goes negative

Step-by-Step Solution

Solution:

Step 1: Understand problem constraints
The problem requires finding a single start station to complete a circular route without running out of gas, which can be solved efficiently by a greedy approach.
Step 2: Identify the correct approach
The greedy method that first checks if total gas is at least total cost ensures a solution exists, then resets the start whenever the tank goes negative, guaranteeing an O(n) solution.
Final Answer:
Option D -> Option D
Quick Check:
Greedy reset approach is optimal and widely accepted [OK]

Quick Trick: Check total gas vs cost, then reset start on negative tank [OK]

Common Mistakes:

MISTAKES

Thinking brute force is efficient enough
Using DP which is unnecessary
Trying divide and conquer which doesn't fit circular nature

Trap Explanation:

PITFALL

Brute force looks correct but is inefficient; DP and divide and conquer don't naturally fit the circular greedy property.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the classic greedy pattern for circular gas station problem.

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More Greedy Algorithms Quizzes

Which algorithmic approach guarantees finding the correct starting station efficiently?

Step 1: Understand problem constraints

Step 2: Identify the correct approach

Final Answer:

Quick Check:

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