优惠券收集者。如何改进代码以获得更好的运行时？

Question

这是一个优惠券收集器代码，用于分析运行时间。我需要一些关于如何提高这段代码的运行时间的建议？我使用过数据结构字典，但是有没有其他的数据结构可以更快地执行呢。在

import random
import numpy as np
import matplotlib.pyplot as plt 
from array import *
import timeit

trailList = {}

def couponcollector(n):
    numDic = {}
    trails = 0
    while len(numDic) < n:
        num = np.random.random_integers(n);
        trails = trails + 1
        if num not in numDic.keys():
            numDic[num] = 1

    return trails


def starter(n,m):
    summ = 0
    for i in range(0,m):
        r = couponcollector(n)
        summ = summ + r
        if trailList.has_key(r):
            trailList[r] = trailList[r] + 1
        else:
            trailList[r] = 1
    print trailList
    #print "Expected Trails"
    #print summ/300


nvalues= []
runtimes = []
runtimes1 = []
runtimes2 = []
runtimes3 = []
runtimes4 = []
#color = {300: 'blue', 1000: 'green', 5000: 'red', 10000: 'black'}
def runtimer():
    for n in range(300,20000,4000):
        nvalues.append(n)
        #stmt = 'starter(' + str(n)+','+str(300) + ')'
        #stmt1 = 'starter(' + str(n)+','+str(800) + ')'
        stmt2 = 'starter(' + str(n)+','+str(1000) + ')'
        stmt3 = 'starter(' + str(n)+','+str(3000) + ')'
        stmt4= 'starter(' + str(n)+','+str(5000) + ')'
        print(nvalues)
        #runtimes.append(timeit.timeit(stmt, setup="from __main__ import starter", number = 1))
        #runtimes1.append(timeit.timeit(stmt1, setup="from __main__ import starter", number = 1))
        runtimes2.append(timeit.timeit(stmt2, setup="from __main__ import starter", number = 1))
        print runtimes2
        runtimes3.append(timeit.timeit(stmt3, setup="from __main__ import starter", number = 1))
        runtimes4.append(timeit.timeit(stmt4, setup="from __main__ import starter", number = 1))

    fig = plt.figure()
    #plt.plot(nvalues, runtimes, c='blue', label='m = 300')
    #plt.plot(nvalues, runtimes1, c='green', label='m = 800')
    plt.plot(nvalues, runtimes2, c='red', label='m = 1000')
    plt.plot(nvalues, runtimes3, c='blue', label='m = 3000')
    plt.plot(nvalues, runtimes4, c='green', label='m = 5000')
    plt.ylabel('Runtimes')
    plt.xlabel('Coupon Collector Domain Size')
    plt.title('Plot of Coupon Collector runtimes')
    plt.legend(loc='upper left')
    plt.grid(True)
    fig.savefig('ccFinal.png')
runtimer()