ex1(p20)

代码如下：

import random

def Darts(n):
k=0
i=1
while i<=n:
x=random.uniform(0,1)
#y=random.uniform(0,1)
y=x
if(x**2+y**2<=1):
k+=1
i+=1
return 4*k/n

print(Darts(10000000))
print(Darts(100000000))
print(Darts(100000000))

结果如下：

物理意义：计算2*sqrt（2）  #如果结果输出的是2*k/n，则计算的是无理数sqrt（2）的近似值

ex2(p23)

代码如下：

import random
import math

def F(x):
return math.sqrt(1-x**2)

def CalPI(n):
k=0
i=1
while i<=n:
i+=1
x=random.uniform(0,1)
y=random.uniform(0,1)
if (y<=F(x)):
k+=1
return 4*k/n

print("when n=10000000,PI=%.10f"%CalPI(10000000))
print("when n=100000000,PI=%.10f"%CalPI(100000000))
print("when n=1000000000,PI=%.10f"%CalPI(1000000000))

结果如下：

ex3（p23）

代码如下：

import random
import math

def F(x):
return x-1

def CalCalculus(a,b,c,d,n,function):
k_positive=0
k_negtive=0
i=1
while i<=n: i+=1 x=random.uniform(a,b) y=random.uniform(c,d) if (y>=0 and y<=function(x)): k_positive+=1 elif(y<0 and y>function(x)):
k_negtive+=1
return (b-a)*(d-c)*(k_positive-k_negtive)/n

if __name__=="__main__":
function=F
str=input("please input a,b,c,d:");
ceof=list(str.split(" "))
ceof=[int(i) for i in ceof]
print(ceof)
print("when n=1000000,res=%.10f"%CalCalculus(ceof[0],ceof[1],ceof[2],ceof[3],1000000,function))
print("when n=10000000,res=%.10f"%CalCalculus(ceof[0],ceof[1],ceof[2],ceof[3],10000000,function))
print("when n=100000000,res=%.10f"%CalCalculus(ceof[0],ceof[1],ceof[2],ceof[3],100000000,function))

结果如下：

p24 Ex4

ex4(p36)

代码如下：

# -*- coding: utf-8 -*-
"""
__title__ = ''
__author__ = 'jing'
__mtime__ = '2017/9/20'
# code is far away from bugs with the god animal protecting
I love animals. They taste delicious.
┏┓ ┏┓
┏┛┻━━━┛┻┓
┃ ☃ ┃
┃ ┳┛ ┗┳ ┃
┃ ┻ ┃
┗━┓ ┏━┛
┃ ┗━━━┓
┃ 神兽保佑 ┣┓
┃　永无BUG！ ┏┛
┗┓┓┏━┳┓┏┛
┃┫┫ ┃┫┫
┗┻┛ ┗┻┛
"""
import random
import math

def CalSetCount(setN):
setTemp=set()
k=0
a=random.choice(setN)
while a not in setTemp:
k+=1
setTemp.add(a)
a = random.choice(setN)
return k

if __name__=="__main__":
n=int(input("please enter n(the numbers of set):"))
while n!=0:
setN=range(0,n)
i=0
kList=[]
while i<1000:
i+=1
kList.append(CalSetCount(setN))
print("The estimated value of n is %.f"%(2.0*((sum(kList)/1000)**2)/math.pi))
n = int(input("please enter n(the numbers of set):"))

结果如下：

随着n值的增大，误差存在着波动性，但整体趋势是越来越小的

p54

p64 ex

import random

count=1

def Search(val,ptr,x,i):
global count
count=1
while x>val[i]:
i=ptr[i]
count=count+1
return i

def A(val,ptr,x,head):
return Search(val,ptr,x,head)

def B(val,ptr,x,head):
i=head
max=val[i]
for j in range(4):
y=val[j]
if max<y and y<=x:
i=j
max=y
return Search(val,ptr,x,i)

def C(val,ptr,x,head):
i=head
max=val[i]
for k in range(4):
j=random.randint(0,15)
y=val[j]
if max<y and y<=x:
i=j
max=y
return Search(val,ptr,x,i)

def D(val,ptr,x,head):
i=random.randint(0,15)
y=val[i]
if xy:
return Search(val,ptr,x,ptr[i])
else:
return i

val=[5,7,3,0,4,11,17,14,9,20,21,25,23,30,34,31]
ptr=[1,8,4,2,0,7,9,6,5,10,12,13,11,15,-1,14] #the maxnum's index equats to -1

head=3
x=11
print("C:x=11's position is %d.Compared %d times\n"%(C(val,ptr,x,head),4+count))
print("A:x=11's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))
print("B:x=11's position is %d.Compared %d times\n"%(B(val,ptr,x,head),4+count))
print("D:x=11's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))

x=30
print("C:x=30's position is %d.Compared %d times\n"%(C(val,ptr,x,head),4+count))
print("A:x=30's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))
print("B:x=30's position is %d.Compared %d times\n"%(B(val,ptr,x,head),4+count))
print("D:x=30's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))