Total Distance Traveled - Practice Coding Problems

Total Distance Traveled - Problem

Math Simulation Easy

Imagine you're a truck driver on a long cross-country journey with a unique dual-tank fuel system! Your truck has two separate fuel tanks: a main tank that powers the engine, and an additional tank that serves as a backup reservoir.

Here's how this fascinating system works:

🚛 Your truck gets 10 km per liter of fuel efficiency
⛽ The engine only runs on fuel from the main tank
🔄 Every time you consume exactly 5 liters from the main tank, the system automatically transfers 1 liter from the additional tank to the main tank (if available)
⚡ The fuel transfer is instantaneous and happens immediately when you hit each 5-liter consumption milestone

Given the initial fuel amounts in both tanks, your goal is to calculate the maximum total distance you can travel before running out of fuel completely.

Example: If you start with 5 liters in the main tank and 10 liters in the additional tank, you'll travel 50 km using the initial 5 liters, then receive 1 liter from the additional tank, allowing you to continue your journey!

Input & Output

example_1.py — Basic Case

$ Input: mainTank = 5, additionalTank = 10

› Output: 60

💡 Note: We start with 5L in main tank. After consuming all 5L (traveling 50km), we trigger one transfer of 1L from additional tank. This 1L allows us to travel 10 more km, giving us a total of 60km.

example_2.py — Multiple Transfers

$ Input: mainTank = 1, additionalTank = 2

› Output: 10

💡 Note: We have only 1L in main tank, so we can travel 10km. Since we consumed less than 5L total, no transfer from additional tank occurs. The additional tank fuel remains unused.

example_3.py — No Additional Fuel

$ Input: mainTank = 25, additionalTank = 0

› Output: 250

💡 Note: With 25L in main tank and 0L in additional tank, we can only use the main tank fuel. 25L × 10km/L = 250km total distance.

Constraints

1 ≤ mainTank, additionalTank ≤ 1000
The truck's fuel efficiency is always 10 km per liter
Transfer only occurs when exactly 5 liters total have been consumed from the main tank
Each transfer moves exactly 1 liter from additional to main tank

Visualization

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Understanding the Visualization

Journey Begins

Truck starts with fuel in both main and additional tanks

Fuel Consumption

Engine consumes fuel from main tank at 10km per liter

Transfer Trigger

Every 5 liters consumed triggers automatic 1L transfer

Journey Continues

Process repeats until no more fuel can be transferred

Journey Ends

Calculate total distance when main tank is finally empty

Key Takeaway

🎯 Key Insight: Instead of simulating every liter, we can mathematically calculate the total transfers by recognizing that every 5 liters consumed from the main tank triggers exactly 1 liter transfer from the additional tank!

Asked in

a Amazon 45 G Google 32 ⊞ Microsoft 28 f Meta 22

The optimal approach uses mathematical calculation to determine fuel transfers in batches rather than simulating liter by liter. By iteratively calculating how many complete 5-liter cycles can trigger transfers, we achieve O(log n) time complexity while the brute force simulation requires O(n) time. The key insight is that every 5 liters consumed triggers exactly 1 liter transfer, allowing us to batch these operations efficiently.

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Optimization (Optimal)	O(log(additionalTank))	O(1)	Calculate transfers in batches using division and modulo operations
Brute Force Simulation	O(mainTank + additionalTank)	O(1)	Simulate the journey liter by liter, tracking fuel transfers

Mathematical Optimization (Optimal) — Algorithm Steps

Calculate total fuel that can be consumed (main + transferred fuel)
Determine how many transfers will occur based on fuel consumption
Use the formula: transfers = min(additionalTank, (mainTank + transfers) / 5)
Solve iteratively or use mathematical insight to find the answer
Multiply total consumable fuel by 10 to get distance

Visualization

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Step-by-Step Walkthrough

Initial Calculation

Start with main tank fuel as base

Batch Transfers

Calculate how many complete 5L→1L transfers possible

Convergence

Iterate until no more transfers can be made

Final Distance

Multiply total fuel by 10 km/L

Code -

solution.c — C

#include <stdio.h>

int min(int a, int b) {
    return (a < b) ? a : b;
}

int distanceTraveled(int mainTank, int additionalTank) {
    int totalConsumed = mainTank;
    
    while (1) {
        int transfers = min(additionalTank, totalConsumed / 5);
        int newTotal = mainTank + transfers;
        
        if (newTotal == totalConsumed) {
            break;
        }
        
        totalConsumed = newTotal;
    }
    
    return totalConsumed * 10;
}

int main() {
    int mainTank, additionalTank;
    scanf("%d %d", &mainTank, &additionalTank);
    printf("%d\n", distanceTraveled(mainTank, additionalTank));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(log(additionalTank))

In worst case, we might need a few iterations to converge to the answer, but typically runs in O(1)

⚡ Linearithmic

Space Complexity

O(1)

Only using a constant amount of extra space

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Optimization (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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