Tire Durability Spare Tire

EasyPython

Problem

In an ION fleet simulation, a vehicle has a fixed number of wheels and may rotate or replace tires whenever necessary. Given the durability of every available tire, including spares, calculate the maximum distance the vehicle can travel.

Assume tire changes and rotations take no time, every mounted tire contributes equally to the vehicle's travel, and a tire cannot be mounted on more than one wheel at the same time. The vehicle may travel fractional kilometers.

Formal Specification

Implement max_distance(durabilities, wheel_count), where:

durabilities is a list of nonnegative numbers representing each tire's remaining durability in kilometers.
wheel_count is a positive integer representing the number of wheels that must be covered.
Return a number representing the maximum possible travel distance.

A valid strategy may distribute the required wheel usage across all available tires. The four-tire example with durability [4, 4, 4, 4, 10] has total durability 26, so traveling 26 / 4 = 6.5 kilometers is possible.

Constraints

1 <= wheel_count <= len(durabilities)
1 <= len(durabilities) <= 10^5
0 <= durabilities[i] <= 10^9
Tire rotation and replacement have no cost
Fractional kilometers are allowed

Function Signature

def max_distance(durabilities, wheel_count):

Formal Specification

Implement max_distance(durabilities, wheel_count), where:

durabilities is a list of nonnegative numbers representing each tire's remaining durability in kilometers.
wheel_count is a positive integer representing the number of wheels that must be covered.
Return a number representing the maximum possible travel distance.