我在自学数据结构,并试图测量将append方法实现到数组数据结构的有效和低效方法之间的时间复杂度差异。也就是说,根据我在纸上做的一些数学计算,无效的方法应该是O(n)=n^2,有效的方法应该是O(n)=n
问题是,当我运行模拟并将这两种情况绘制在一张图上时,效率低下的方法会按预期执行,但效率低下的方法会执行O(n)=1。我做错什么了吗
import datetime
import time
import random
import matplotlib.pyplot as plt
import numpy as np
# Inefficient append
class PyListInef:
def __init__(self):
self.items = []
def append(self, item):
# Inefficient append -> appending n items to the list causes a O(n) = n^2, since for each i for i in 1, 2, 3...n
# we need i * k operations in order to append every element to the new list. Then, by weak induction we prove
# that the number of required operations is n(n+1)/2 which implies O(n) = n^2
self.items = self.items + [item]
# Using magic method for our PyList to be an iterable object.
def __iter__(self):
for c in self.items:
yield c
# Efficient append:
class PyList:
def __init__(self):
self.items = []
def append(self, item):
self.items.append(item)
def __iter__(self):
for c in self.items:
yield c
# The inefficient append running time
lst = PyListInef()
time_dict_inef = dict()
time_dict_ef = dict()
series = np.linspace(1, 301, 300)
time.sleep(2)
for i in range(300):
starttime = time.time()
for j in range(i):
lst.append(series[j])
elapsed_time = time.time() - starttime
time_dict_inef[i] = elapsed_time * 100000
# The efficient append running time
lst = PyList()
time.sleep(2)
for i in range(300):
starttime = time.time()
for j in range(i):
lst.append(series[j])
elapsed_time = time.time() - starttime
time_dict_ef[i] = elapsed_time * 100000
plt.figure(figsize = (14,7))
plt.plot(time_dict_inef.keys(), time_dict_inef.values())
plt.plot(time_dict_ef.keys(), time_dict_ef.values())
plt.xlabel('Number of elements to append')
plt.ylabel('Elapsed time (microseconds)')
plt.title('Comparison between efficient appending vs inefficient appending in a list data structure')
plt.show()
你能帮我指出我做错了什么吗
time.time()
的分辨率有限。您的“高效附加”计时足够快,通常在time.time()
分辨率的一个刻度之前完成。请注意,在黄色图表中显示了两个精确的时间:0个刻度和1个刻度。图右侧的1次勾选次数更频繁,因为即使时间短于一次勾选,较长的时间也意味着在运行期间发生勾选的概率更高。如果您使用更大的输入运行,您最终会看到2个刻度和更高的刻度。(还要注意的是,100000中没有足够的0,因此您的计时时间缩短了10倍。)相关问题 更多 >
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