算法设计与分析-HomeWork

Posted 2020-10-06 Run_For_Love一朝一夕一点一滴

 

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=x
10         if(x**2+y**2<=1):
11             k+=1
12         i+=1
13     return 4*k/n
14 
15 print(Darts(10000000))
16 print(Darts(100000000))
17 print(Darts(100000000))

View Code

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=1
10     while i<=n:
11         i+=1
12         x=random.uniform(0,1)
13         y=random.uniform(0,1)
14         if (y<=F(x)):
15             k+=1
16     return 4*k/n
17 
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))

View Code

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=0
10     i=1
11     while i<=n:
12         i+=1
13         x=random.uniform(a,b)
14         y=random.uniform(c,d)
15         if (y>=0 and y<=function(x)):
16             k_positive+=1
17         elif(y<0 and y>function(x)):
18             k_negtive+=1
19     return (b-a)*(d-c)*(k_positive-k_negtive)/n
20 
21 if __name__=="__main__":
22     function=F
23     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))

View Code

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 random
22 import math
23 
24 def CalSetCount(setN):
25     setTemp=set()
26     k=0
27     a=random.choice(setN)
28     while a not in setTemp:
29         k+=1
30         setTemp.add(a)
31         a = random.choice(setN)
32     return k
33 
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=0
39         kList=[]
40         while i<1000:
41             i+=1
42             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):"))

View Code

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+1
11     return i
12 
13 def A(val,ptr,x,head):
14     return Search(val,ptr,x,head)
15 
16 def B(val,ptr,x,head):
17     i=head
18     max=val[i]
19     for j in range(4):
20         y=val[j]
21         if max<y and y<=x:
22             i=j
23             max=y
24     return Search(val,ptr,x,i)
25 
26 def C(val,ptr,x,head):
27     i=head
28     max=val[i]
29     for k in range(4):
30         j=random.randint(0,15)
31         y=val[j]
32         if max<y and y<=x:
33             i=j
34             max=y
35     return Search(val,ptr,x,i)
36 
37 def D(val,ptr,x,head):
38     i=random.randint(0,15)
39     y=val[i]
40     if x<y:
41         return Search(val,ptr,x,head)
42     elif x>y:
43         return Search(val,ptr,x,ptr[i])
44     else:
45         return i
46 
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 -1
51 
52 head=3
53 x=11
54 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=30
60 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))