Total Distance Traveled

Easy

Asked by:

11 views

Topics:

Greedy Algorithms

A truck has two fuel tanks. You are given two integers, mainTank representing the fuel present in the main tank in liters and additionalTank representing the fuel present in the additional tank in liters.

The truck has a mileage of 10 km per liter. Whenever 5 liters of fuel get used up in the main tank, if the additional tank has at least 1 liters of fuel, 1 liters of fuel will be transferred from the additional tank to the main tank.

Return the maximum distance which can be traveled.

Note: Injection from the additional tank is not continuous. It happens suddenly and immediately for every 5 liters consumed.

Example 1:

Input: mainTank = 5, additionalTank = 10
Output: 60
Explanation: 
After spending 5 litre of fuel, fuel remaining is (5 - 5 + 1) = 1 litre and distance traveled is 50km.
After spending another 1 litre of fuel, no fuel gets injected in the main tank and the main tank becomes empty.
Total distance traveled is 60km.

Example 2:

Input: mainTank = 1, additionalTank = 2
Output: 10
Explanation: 
After spending 1 litre of fuel, the main tank becomes empty.
Total distance traveled is 10km.

Constraints:

1 <= mainTank, additionalTank <= 100

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What are the data types and possible ranges for the position and fuel arrays? Can fuel values be negative or zero?
Is it guaranteed that the position array is sorted, and if so, is it sorted in ascending or descending order?
If the fuel runs out during the journey (i.e., `fuel[i]` becomes zero or negative before reaching the end), should the function return the distance traveled up to that point, or should it be treated as an error?
Are the position and fuel arrays always of the same length, and is that length always greater than zero?
If the fuel is insufficient to reach the end, even if the current fuel is optimally spent, should the function return the maximum possible distance traveled or indicate an error condition?

Brute Force Solution

Approach

The brute force approach to calculating total distance traveled directly simulates the journey. We will examine the positions in order and calculate the distance between each consecutive pair. The total distance is simply the sum of all these individual distances.

Here's how the algorithm would work step-by-step:

Begin with the starting location.
Move to the next location in the sequence and calculate the distance between the starting location and this new location.
Add this calculated distance to our running total.
Now, move to the subsequent location and calculate the distance between your current location and this new location.
Again, add this calculated distance to the running total.
Keep repeating this process of moving to the next location, calculating the distance from the previous one, and adding it to the total, until you have visited every location in the sequence.
The final value of the running total is the total distance traveled.

Code Implementation

def total_distance_traveled_brute_force(locations):
    total_distance = 0.0

    # Handle edge case where there are no locations
    if not locations:
        return total_distance

    previous_location = locations[0]

    # Iterate through locations, starting from the second location
    for current_location in locations[1:]:

        # Calculate the distance between previous and current locations
        distance = ((current_location[0] - previous_location[0])**2 +
                    (current_location[1] - previous_location[1])**2)**0.5

        # Accumulate the distance to the total
        total_distance += distance
        previous_location = current_location

    return total_distance

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the list of positions once. For each position, it calculates the distance to the next position and adds it to the total. Since the number of distance calculations is directly proportional to the number of positions (n), the time complexity is O(n).

Space Complexity

O(1) – The described brute force approach calculates the total distance traveled by iterating through the locations and summing the distances between consecutive locations. The only extra memory used consists of a few variables to store the current location, the previous location, and the accumulated total distance. Since the number of extra variables does not depend on the number of locations (N), the space complexity is constant.

Optimal Solution

Approach

The best way to calculate the total distance traveled involves summing the distances between consecutive points. The key is to consider the order of the points to ensure we are always moving forward, not backward, along the path. We achieve this by visiting the points in the order they are given.

Here's how the algorithm would work step-by-step:

Start with a running total of zero to store the total distance.
Begin at the first point in the journey.
Calculate the distance between the current point and the next point.
Add this distance to the running total.
Move to the next point, making it the current point.
Repeat the distance calculation and addition until you reach the last point.
The final running total represents the total distance traveled.

Code Implementation

import math

def total_distance_traveled(points):
    total_distance = 0.0

    # Initialize the current point with the starting coordinates.
    current_point_index = 0

    # Iterate through the points to calculate distances.
    while current_point_index < len(points) - 1:
        # Ensure we always move forward.
        point_x1, point_y1 = points[current_point_index]
        point_x2, point_y2 = points[current_point_index + 1]

        # Calculate distance between current and next points.
        distance = math.sqrt((point_x2 - point_x1)**2 + (point_y2 - point_y1)**2)

        # Accumulate the total distance.
        total_distance += distance

        current_point_index += 1

    return total_distance

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the given array of points exactly once to calculate the distance between consecutive points. For an array of size n, there are (n-1) distance calculations. Each distance calculation involves constant-time operations. Therefore, the total number of operations is proportional to n, resulting in a time complexity of O(n).

Space Complexity

O(1) – The algorithm maintains a running total for the distance and iterates through the points. It only uses a constant amount of extra space to store variables like the running total and indices for iterating through the list of points. No additional data structures that scale with the input size (N, the number of points) are created. Therefore, the space complexity is constant.

Edge Cases

Case	How to Handle
Null or empty input array for positions	Return 0.0 as no distance can be calculated without positions.
Input array with only one position	Return 0.0 because there is no movement from a single point.
Positions array contains duplicate adjacent values	The distance between these duplicate values should be zero, so handle it as is.
Large number of positions causing floating-point precision issues	Use double precision to minimize precision loss during calculations, but be aware of limitations.
Positions array contains very large or very small numbers (close to MAX_DOUBLE/MIN_DOUBLE)	Ensure calculations do not result in overflow or underflow by checking limits before adding the result.
Positions are in strictly decreasing order	The absolute value function correctly calculates the positive distance in each segment.
Input array contains NaN or Infinity values	Check for NaN or Infinity values in the input and return NaN if they are present, or handle the exception.
Positions array is extremely large, potentially causing memory issues	Iterate through the array only once, calculating distances on the fly to minimize memory usage.

Null or empty input array for positions

How to Handle:

Return 0.0 as no distance can be calculated without positions.

Input array with only one position

How to Handle:

Return 0.0 because there is no movement from a single point.

Positions array contains duplicate adjacent values

How to Handle:

The distance between these duplicate values should be zero, so handle it as is.

Large number of positions causing floating-point precision issues

How to Handle:

Use double precision to minimize precision loss during calculations, but be aware of limitations.

Positions array contains very large or very small numbers (close to MAX_DOUBLE/MIN_DOUBLE)

How to Handle:

Ensure calculations do not result in overflow or underflow by checking limits before adding the result.

Positions are in strictly decreasing order

How to Handle:

The absolute value function correctly calculates the positive distance in each segment.

Input array contains NaN or Infinity values

How to Handle:

Check for NaN or Infinity values in the input and return NaN if they are present, or handle the exception.

Positions array is extremely large, potentially causing memory issues

How to Handle:

Iterate through the array only once, calculating distances on the fly to minimize memory usage.