Total Distance Traveled - Solution & Explanation

Problem Overview: You are given two integers: mainTank and additionalTank. A truck consumes 1 liter of fuel for every 10 km traveled. Each time the truck uses 5 liters from the main tank, you can transfer 1 liter from the additional tank to the main tank (if available). The goal is to compute the total distance the truck can travel.

Approach 1: Simulation Approach (Time: O(n), Space: O(1))

This method follows the exact process described in the problem using simulation. You repeatedly consume fuel from the main tank while tracking how many liters have been used. After every 5 liters consumed, check whether the additional tank still has fuel. If it does, transfer 1 liter to the main tank and continue driving. The loop continues until the main tank becomes empty. The final distance equals the total liters consumed multiplied by 10. This approach mirrors the real-world process step by step and is useful when verifying the mechanics of the rule or when constraints are small.

Approach 2: Direct Calculation Approach (Time: O(1), Space: O(1))

The fuel transfer rule reveals a mathematical pattern. For every 5 liters consumed from the main tank, you gain 1 extra liter from the additional tank. However, the last few liters may not complete another group of 5, so they do not trigger another transfer. The number of possible transfers is therefore (mainTank - 1) / 4 using integer division. This works because each transfer effectively increases usable fuel before the next group of five is completed. The actual number of transferred liters is limited by additionalTank, so the formula becomes extra = min(additionalTank, (mainTank - 1) // 4). The total usable fuel becomes mainTank + extra, and the final distance is that value multiplied by 10.

This approach relies on recognizing the repeating pattern rather than explicitly simulating each step. It uses simple math and constant-time arithmetic, which makes it significantly cleaner and faster.

Recommended for interviews: The direct calculation approach is usually what interviewers expect. Simulation demonstrates that you understand the mechanics of the rule, but recognizing the mathematical pattern and reducing the solution to O(1) time shows stronger problem-solving and optimization skills.