simulating a bullet problem

from collections import namedtuple, Counter
from itertools import permutations
from random import random

Bullet = namedtuple("Bullet", ("time", "speed"))



def ctime(bullet1, bullet2):
    """ time bullet1 will collide with bullet2, or None if no collision."""
    # swap bullets so that bullet2 is fired second
    if bullet2.time < bullet1.time: bullet1,bullet2 = bullet2,bullet1

    if bullet2.speed <= bullet1.speed: return None

    # where is bullet1 when bullet2 is fired?
    b1startPos = (bullet2.time - bullet1.time)*bullet1.speed
    # how long will it take bullet2 to catch up?
    catchUpTime = b1startPos/(bullet2.speed - bullet1.speed)

    return catchUpTime + bullet2.time

def sim(bullets):
    """Input: list of bullets. Output: list of surviving bullets."""
    while True:
        n = len(bullets)
        ctimes = [ctime(bullets[i],bullets[i+1]) for i in xrange(n-1)]
        collisions = [(i,c) for (i,c) in enumerate(ctimes) if c != None]
        if not collisions: return bullets
        nextCollision = min(collisions, key=lambda (i,c): c)
        indexNextCollision = nextCollision[0]
        bullets = bullets[:indexNextCollision]+bullets[indexNextCollision+2:]
    return bullets

def monte(n, trials):
    """ returns number of times (out of trials) that all bullets died."""
    deaths = 0
    for i in xrange(trials):
        bullets = [Bullet(i,random()) for i in xrange(n)]
        if len(sim(bullets)) == 0: deaths += 1
    return deaths

def simulatePermutations(n):
    """ returns Counter of how many bullets survived in each of n! trials,
    each trial being one permutation of n randomly chosen speeds. """
    speeds = [random() for i in xrange(n)]
    def results():
        for speedperm in permutations(speeds):
            bullets = [Bullet(i,s) for (i,s) in enumerate(speedperm)]
            yield sim(bullets)
    return Counter(map(len, results()))