ex1(p20)
代码如下：
1 import random 2 3 def Darts(n): 4 k=0 5 i=1 6 while i<=n: 7 x=random.uniform(0,1) 8 #y=random.uniform(0,1) 9 y=x10 if(x**2+y**2<=1):11 k+=112 i+=113 return 4*k/n14 15 print(Darts(10000000))16 print(Darts(100000000))17 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：
1 import random 2 import math 3 4 def F(x): 5 return math.sqrt(1-x**2) 6 7 def CalPI(n): 8 k=0 9 i=110 while i<=n:11 i+=112 x=random.uniform(0,1)13 y=random.uniform(0,1)14 if (y<=F(x)):15 k+=116 return 4*k/n17 18 print("when n=10000000,PI=%.10f"%CalPI(10000000))19 print("when n=100000000,PI=%.10f"%CalPI(100000000))20 print("when n=1000000000,PI=%.10f"%CalPI(1000000000)) 结果如下：
ex3（p23）
代码如下：
1 import random 2 import math 3 4 def F(x): 5 return x-1 6 7 def CalCalculus(a,b,c,d,n,function): 8 k_positive=0 9 k_negtive=010 i=111 while i<=n:12 i+=113 x=random.uniform(a,b)14 y=random.uniform(c,d)15 if (y>=0 and y<=function(x)):16 k_positive+=117 elif(y<0 and y>function(x)):18 k_negtive+=119 return (b-a)*(d-c)*(k_positive-k_negtive)/n20 21 if __name__=="__main__":22 function=F23 str=input("please input a,b,c,d:");24 ceof=list(str.split(" "))25 ceof=[int(i) for i in ceof]26 print(ceof)27 print("when n=1000000,res=%.10f"%CalCalculus(ceof[0],ceof[1],ceof[2],ceof[3],1000000,function))28 print("when n=10000000,res=%.10f"%CalCalculus(ceof[0],ceof[1],ceof[2],ceof[3],10000000,function))29 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：
1 # -*- coding: utf-8 -*- 2 """ 3 __title__ = '' 4 __author__ = 'jing' 5 __mtime__ = '2017/9/20' 6 # code is far away from bugs with the god animal protecting 7 I love animals. They taste delicious. 8 ┏┓ ┏┓ 9 ┏┛┻━━━┛┻┓10 ┃ ☃ ┃11 ┃ ┳┛ ┗┳ ┃12 ┃ ┻ ┃13 ┗━┓ ┏━┛14 ┃ ┗━━━┓15 ┃ 神兽保佑 ┣┓16 ┃ 永无BUG！ ┏┛17 ┗┓┓┏━┳┓┏┛18 ┃┫┫ ┃┫┫19 ┗┻┛ ┗┻┛20 """21 import random22 import math23 24 def CalSetCount(setN):25 setTemp=set()26 k=027 a=random.choice(setN)28 while a not in setTemp:29 k+=130 setTemp.add(a)31 a = random.choice(setN)32 return k33 34 if __name__=="__main__":35 n=int(input("please enter n(the numbers of set):"))36 while n!=0:37 setN=range(0,n)38 i=039 kList=[]40 while i<1000:41 i+=142 kList.append(CalSetCount(setN))43 print("The estimated value of n is %.f"%(2.0*((sum(kList)/1000)**2)/math.pi))44 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
1 import random 2 3 count=1 4 5 def Search(val,ptr,x,i): 6 global count 7 count=1 8 while x>val[i]: 9 i=ptr[i]10 count=count+111 return i12 13 def A(val,ptr,x,head):14 return Search(val,ptr,x,head)15 16 def B(val,ptr,x,head):17 i=head18 max=val[i]19 for j in range(4):20 y=val[j]21 if maxy:43 return Search(val,ptr,x,ptr[i])44 else:45 return i46 47 48 49 val=[5,7,3,0,4,11,17,14,9,20,21,25,23,30,34,31]50 ptr=[1,8,4,2,0,7,9,6,5,10,12,13,11,15,-1,14] #the maxnum's index equats to -151 52 head=353 x=1154 print("C:x=11's position is %d.Compared %d times\n"%(C(val,ptr,x,head),4+count))55 print("A:x=11's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))56 print("B:x=11's position is %d.Compared %d times\n"%(B(val,ptr,x,head),4+count))57 print("D:x=11's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))58 59 x=3060 print("C:x=30's position is %d.Compared %d times\n"%(C(val,ptr,x,head),4+count))61 print("A:x=30's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))62 print("B:x=30's position is %d.Compared %d times\n"%(B(val,ptr,x,head),4+count))63 print("D:x=30's position is %d.Compared %d times\n"%(A(val,ptr,x,head),count))
