Truck Tour Hackerrank Solution: Your Guide to Mastering the Challenge

Are you ready to test your coding skills with a fun and engaging challenge? The Truck Tour problem on HackerRank is a classic example of a dynamic programming problem that requires you to think strategically about finding the optimal solution. In this article, we’ll delve into the heart of the Truck Tour problem, breaking down the solution step-by-step and providing you with the tools and insights you need to conquer it.

Understanding the Truck Tour Problem

Imagine you’re on a road trip across a vast country, and your truck has a limited fuel capacity. You need to plan your journey carefully to ensure you can reach your destination without running out of gas. You’re given a list of petrol pumps along the route, each with a certain amount of fuel available and a distance from the starting point. Your goal is to find the shortest possible circular route that allows you to visit all the petrol pumps and return to the starting point, ensuring you never run out of fuel.

The Key to Cracking the Code

The Truck Tour problem is a prime example of a dynamic programming puzzle. This approach involves breaking down the problem into smaller, overlapping subproblems and solving them recursively. In this case, we’ll focus on finding the starting point of the optimal circular route.

Here’s how you can approach the Truck Tour problem:

Step-by-Step Solution

1. Calculate Net Fuel at Each Pump:

   • For each petrol pump, determine the net fuel available by subtracting the distance to the next pump from the fuel available at the current pump.

2. Identify a Potential Starting Point:

   • Start with the first petrol pump as a potential starting point.
   • Keep a running total of the net fuel available at each pump.

3. Iterate and Evaluate:

   • If the running fuel total becomes negative at any point, discard the current starting point and move to the next pump.
   • Continue this process, starting from each pump in the list.

4. Finding the Optimal Route:

   • If you reach a point where the running fuel total remains non-negative for the entire circuit, you’ve found the optimal starting point for your circular route.

Let’s illustrate this with a simple example:

Petrol Pump | Fuel | Distance to Next Pump
----------------------------------------
1           | 5    | 4
2           | 1    | 2
3           | 2    | 5
4           | 6    | 3

Calculations:

• Pump 1: Net Fuel = 5 – 4 = 1 (Starting Point)
• Pump 2: Net Fuel = 1 – 2 = -1 (Fuel is not enough to reach the next pump)
• Pump 3: Net Fuel = 2 – 5 = -3 (Fuel is not enough to reach the next pump)
• Pump 4: Net Fuel = 6 – 3 = 3 (Fuel is enough to reach the next pump)

Result:

The optimal starting point for the circular route is Pump 4, as the running fuel total remains non-negative throughout the circuit.

Code Implementation (Python):

def truck_tour(petrol_pumps):
    n = len(petrol_pumps)
    start = 0
    current_fuel = 0
    total_fuel = 0

    for i in range(n):
        current_fuel += petrol_pumps[i][0] - petrol_pumps[i][1]
        total_fuel += petrol_pumps[i][0] - petrol_pumps[i][1]

        if current_fuel < 0:
            start = i + 1
            current_fuel = 0

    if total_fuel >= 0:
        return start
    else:
        return -1

Understanding the Code:

• The petrol_pumps list represents the fuel available and the distance to the next pump for each pump.
• start keeps track of the potential starting point.
• current_fuel stores the running fuel total.
• total_fuel keeps track of the total net fuel available across the entire circuit.

The Algorithm Explained:

1. The code initializes start to 0, indicating the first pump as the initial potential starting point.
2. It iterates through the list of pumps, calculating the net fuel for each pump and updating current_fuel and total_fuel.
3. If current_fuel becomes negative, it means we need a new starting point. Therefore, start is updated to the next pump, and current_fuel is reset to 0.
4. If total_fuel is non-negative after the iteration, we’ve found a feasible solution, and start indicates the optimal starting point.
5. If total_fuel is negative, it indicates there’s no valid starting point, and the function returns -1.

FAQ

Q1: What are the time and space complexities of this solution?

A: The time complexity of this solution is O(N), where N is the number of petrol pumps. This is because we iterate through the list of pumps only once. The space complexity is O(1), as we’re using a constant amount of extra space regardless of the input size.

Q2: Can we solve this problem without dynamic programming?

A: While brute force approaches are possible, they would involve trying all possible starting points, leading to a time complexity of O(N^2) or even higher. Dynamic programming provides a more efficient and elegant solution.

Q3: What are some real-world applications of this problem?

A: The Truck Tour problem has applications in various areas, such as:

• Resource Optimization: Finding the optimal sequence for accessing resources in a system.
• Routing Problems: Planning delivery routes for vehicles with limited capacity.
• Network Analysis: Identifying the most efficient paths for data transmission.

Let’s recap:

The Truck Tour problem is a fun and challenging dynamic programming puzzle that encourages you to think strategically about optimization. By breaking down the problem into smaller subproblems and applying a step-by-step approach, you can conquer this problem and gain valuable insights into algorithmic thinking.

Ready to put your skills to the test? Head over to HackerRank and try out the Truck Tour challenge.