Some questions from the Zhejiang University edition of "Python Programming" question set

1. Chapter 4-15 Exchange coins (20 cents)
   Change a change into coins of 5 cents, 2 cents and 1 cent. It is required to have at least one coin of each kind. How many different ways are there?
   Input format:
   Enter the amount of change to be exchanged x∈(8,100) in one line.
   Output format:
   It is required to output various exchange methods according to the number of 5 cents, 2 cents and 1 cent coins in descending order. Each line outputs a replacement method, and the format is: "fen5: the number of 5-cent coins, fen2: the number of 2-cent coins, fen1: the number of 1-cent coins, total: the total number of coins." The last line outputs "count = number of substitutions".
   Input example:

   13
   

   Output sample:

   fen5:2, fen2:1, fen1:1, total:4
   fen5:1, fen2:3, fen1:2, total:6
   fen5:1, fen2:2, fen1:4, total:7
   fen5:1, fen2:1, fen1:6, total:8
   count = 4
   

   x=int(input())
   if 8<x and x<100:
       fen5=0;fen2=0;fen1=0;count=0
       fen5=int(x/5) #最多多少个5
       ##根据题目要求由内到外循环，依次求得满足条件的最大的5的个数
       while fen5>0:
           fen2=int(x/2) #最多多少个2
           while fen2>0:
               fen1=x ##最多多少个1 
               while fen1>0:
                   if fen5*5+fen2*2+fen1*1==x:
                       print("fen5:{}, fen2:{}, fen1:{}, total:{}".format(fen5,fen2,fen1,fen1+fen2+fen5))
                       count=count+1
                   fen1=fen1-1
               fen2=fen2-1
           fen5=fen5-1
       print("count = {}".format(count))
   

2. Chapter 4-18 Monkeys choose a king (20 points)
   A group of monkeys want to choose a new monkey king. The method of selecting the new monkey king is: let N candidate monkeys form a circle, and number them sequentially from 1 to N starting from a certain position. Counting starts from No. 1, and counts from 1 to 3 in each round. Any monkey that counts 3 will exit the circle, and then the same counting will start from the next monkey. This cycle continues until the last remaining monkey is chosen as the monkey king. May I ask which monkey was originally elected as the Monkey King?
   Input format:
   Enter a positive integer N (≤1000) in one line.
   Output format:
   Output the number of the selected monkey king in one line.
   Input example:

   11
   

   Output sample:

   7
   

   N=int(input())
   if N<=1000:
       #首先分配编号，设置每个猴子在的标记，如果淘汰，则换标记
       l=['n']
       for i in range(N):
           l.append('y') #y表示在，n表示淘汰，为了契合题目，从列表索引1开始
       count=0     
       while(l.count('y')>1): #如果还有一个以上的猴子则继续报数
           ##模仿规则，报数淘汰报数为3的猴               
           for i in range(1,N+1):
               if l[i]=='y':
                   count=count+1
                   if count == 3:                 
                       l[i]='n'
                       count=0
       idx=l.index('y')
       print(idx)
   

3. Chapter 4-30 Find a complete number (20 points)
   The so-called perfect number is that the number is exactly equal to the sum of factors except itself. For example: 6=1+2+3, where 1, 2, and 3 are the factors of 6. This question requires writing a program to find all perfect numbers between any two positive integers m and n.
   Input format:
   Input two positive integers m and n (1<m≤n≤10000) in one line, separated by spaces.
   Output format:
   Output line by line the factor accumulation form of each perfect number within a given range. Each perfect number occupies one line. The format is "perfect number = factor 1 + factor 2 + ... + factor k", where the perfect number occupies one line. and factors are given in increasing order. If there is no perfect number in the interval, "None" is output.
   Input example:

   2 30
   

   Output sample:

   6 = 1 + 2 + 3
   28 = 1 + 2 + 4 + 7 + 14
   

   import math
   m,n=map(int,input().split())
   if 1 < m and m <= n and n <= 10000:
       flag=False
       for i in range(m,n+1):
           l=[1]
           for j in range(2,int(math.sqrt(i))+1):
               if i%j==0:
                   l.append(j)
                   if j*j!=i:
                       l.append(i//j)
           if sum(l)==i:
               flag=True
               l.sort()
               print("{} = {}".format(i,l[0]),end="")
               for j in l[1:]:
                   print(" + {}".format(j),end="")
               print()
       if(flag == 0):
           print("None")
   

4. Chapter 5-11 Dictionary merging (40 points)
   Dictionary merging. The input is represented by two dictionaries as strings, and the merged dictionary is output. The key of the dictionary is represented by a letter or number. Note: 1 and '1' are different keywords!
   Input format:
   Enter the first dictionary string in the first line and enter the second dictionary string in the second line.
   Output format:
   Output the merged dictionary in one line, and the output is in lexicographic order. The ASCII value of "1" is 49, which is greater than 1. When sorting, 1 is in front, "1" is in the back, and the same is true for others.
   Input example 1:

   {1:3,2:5}
   {1:5,3:7} 
   

   Output sample 1:

   {1:8,2:5,3:7}
   

   Input example 2:

   {"1":3,1:4}
   {"a":5,"1":6}
   

   Output sample 2:

   {1:4,"1":9,"a":5}
   

   dic1=eval(input())
   dic2=eval(input())
   
   for k2,v2 in dic2.items():
       if dic1.get(k2) == None:
           dic1[k2]=v2
       else:
           dic1[k2]=dic1[k2]+v2
   print("{",end="")
   l1=[i for i in dic1.keys() if type(i)==type(1)]
   l2=[i for i in dic1.keys() if type(i)==type('a')]
   l1.sort()
   l2.sort()
   cnt=0
   ##这里的重点就是控制输出
   for i in l1+l2:
       cnt=cnt+1
       if type(i)==type(1):
           print("{}:{}".format(i,dic1[i]),end="")
       elif type(i)==type('a'):
           print('"{}":{}'.format(i,dic1[i]),end="")
       if cnt<len(dic1):
           print(",",end="")
   print("}")