running dog with alarm clock

dog.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

# Copyright (c) 2012 Martin Ueding <dev@martin-ueding.de>

"""
Based on a Question from "Physics - Stack Exchange".

http://physics.stackexchange.com/questions/20083/riddle-about-speed
"""

# Position, speed.
dog = [0, 5]

# The timer on the dog's back.
timer = 0

# Global time.
t = 0

# Time interval for simulation.
dt = 0.0001

# List of waves.
waves = []

# Count of iterations.
i = 0

while True:
    if timer > 10:
        timer -= 10
        # Spawn a new wave a meter behind the dog.
        waves.append([dog[0]-1, 340])

    in_front = 0

    for wave in waves:
        # Check whether the wave is front of the dog.
        in_front_of_dog = wave[0] > dog[0]

        # Delete waves that are behind the dog and slower than the dog. Those
        # waves could never reach the dog anyway.
        if not in_front_of_dog:
            if wave[1] < dog[1]:
                waves.remove(wave)

        # Move the wave.
        wave[0] += wave[1] * dt

        # Check whether the wave is still in front of the (now moved) dog.
        still_in_front_of_dog = wave[0] > (dog[0] + dog[1]*dt)

        # Count the number of waves that are still in front of the dog.
        if still_in_front_of_dog:
            in_front += 1

        # If the wave passed the dog, he would head it and therefore double his
        # speed.
        if in_front_of_dog ^ still_in_front_of_dog:
            if in_front_of_dog:
                print "Dog catches wave."
            else:
                print "Wave catches dog."

            print "t = %.1f, position = %.1f, speed = %.1f, waves in front = %d" % (t, dog[0], dog[1], in_front)
            print "Waves at", ', '.join(["%.1f" % x for x in sorted([x[0] for x in waves])])
            print
            dog[1] *= 2

    # Move the dog.
    dog[0] += dog[1] * dt

    # Increase the time.
    timer += dt
    t += dt
    i += 1

    # Stop when there are no waves in front of the dog left. The t > 100 is a
    # safeguard before the first alarm goes off.
    if t > 100 and len(waves) == 0:
        break


print "Final speed of the dog:", dog[1]

out.txt

Wave catches dog.
t = 10.0, position = 50.0, speed = 5.0, waves in front = 1
Waves at 50.0

Wave catches dog.
t = 20.0, position = 150.0, speed = 10.0, waves in front = 2
Waves at 150.0, 3450.1

Wave catches dog.
t = 30.0, position = 350.0, speed = 20.0, waves in front = 3
Waves at 350.0, 3550.1, 6850.1

Wave catches dog.
t = 40.0, position = 750.0, speed = 40.0, waves in front = 4
Waves at 750.1, 3750.1, 6950.1, 10250.2

Wave catches dog.
t = 50.0, position = 1550.1, speed = 80.0, waves in front = 5
Waves at 1550.1, 4150.2, 7150.3, 10350.3, 13650.3

Wave catches dog.
t = 60.0, position = 3150.3, speed = 160.0, waves in front = 6
Waves at 3150.4, 4950.7, 7550.8, 10550.9, 13750.9, 17050.9

Wave catches dog.
t = 60.0, position = 3150.5, speed = 320.0, waves in front = 6
Waves at 3150.5, 4950.8, 7550.9, 10551.0, 13751.0, 17051.0

Dog catches wave.
t = 66.0, position = 6991.1, speed = 640.0, waves in front = 4
Waves at 6991.1, 9591.3, 12591.3, 15791.4, 19091.4

Dog catches wave.
t = 68.8, position = 10531.6, speed = 1280.0, waves in front = 3
Waves at 10531.7, 13531.8, 16731.8, 20031.8

Dog catches wave.
t = 70.1, position = 13991.2, speed = 2560.0, waves in front = 2
Waves at 13991.3, 17191.3, 20491.3

Dog catches wave.
t = 70.8, position = 17418.5, speed = 5120.0, waves in front = 1
Waves at 17418.9, 20718.9

Dog catches wave.
t = 71.1, position = 20831.5, speed = 10240.0, waves in front = 0
Waves at 20832.2

Final speed of the dog: 20480