full-speed-python 习题解答(三)

full-speed-python书籍地址：https://github.com/joaoventura/full-speed-python

参考链接：https://www.chzzz.club/post/13.html

4.1 Exercise with the math module

1.Find the greatest common divisor of the following pairs of numbers: (15, 21), (152,
200), (1988, 9765).
2.Compute the base-2 logarithm of the following numbers: 0, 1, 2, 6, 9, 15.
3.Use the “input” function to ask the user for a number and show the result of the
sine, cosine and tangent of the number. Make sure that you convert the user input
from string to a number (use the int() or the float() function).
```
  import math
  print(math.gcd(15,21),math.gcd(152,200),math.gcd(1988,9765))
  print(math.log(1,2),math.log(2,2),math.log(6,2),math.log(9,2),math.log(15,2))
  a=int(input())
  print(math.sin(a),math.cos(a),math.tan(a))
```
3 8 7
0.0 1.0 2.584962500721156 3.1699250014423126 3.9068905956085187
10
-0.5440211108893698 -0.8390715290764524 0.6483608274590866

4.2 Exercise with functions

1.Implement the “add2” function that receives two numbers as arguments and returns
the sum of the numbers. Then implement the “add3” function that receives and
sums 3 parameters.
2.Implement a function that returns the greatest of two numbers given as parameters.
Use the “if” statement to compare both numbers: https://docs.python.org/3/
tutorial/controlflow.html#if-statements.
3.Implement a function named “is_divisable” that receives two parameters (named
“a” and “b”) and returns true if “a” can be divided by “b” or false otherwise. A
number is divisable by another when the remainder of the division is zero. Use the
modulo operator (“%”).
4.Create a function named “average” that computes the average value of a list passed
as parameter to the function. Use the “sum” and “len” functions.
```
  def add_two(a,b):
      print('Function got value:',a,b)
      return a+b
  def add_thr(a,b,c):
      print('Function got value:',a,b,c)
      return a+b+c
  sum_two = add_two(1,2)
  sum_thr = add_thr(1,2,3)
  print('sum_two:',sum_two,'sum_three:',sum_thr)

  def comp(num_1,num_2):
      if num_1 > num_2:
          return num_1
      else:
          return num_2
  greatest = comp(3,4)  
  print('the greatest one:',greatest)

  def is_divisible(a,b):
      if a%b == 0:
          return True
      else:
          return False
  print(is_divisible(8,3))    

  def average(alist):
      ave = sum(alist)/len(alist)
      return ave
  print(average([1,2,3,4]))
```
Function got value: 1 2
Function got value: 1 2 3
sum_two: 3 sum_three: 6
the greatest one: 4
False
2.5

4.4 Exercise with recursive functions

1.Implement the factorial function and test it with several different values. Crosscheck
with a calculator.
2.Implement a recursive function to compute the sum of the n first integer numbers
(where n is a function parameter). Start by thinking about the base case (the sum
of the first 0 integers is?) and then think about the recursive case.
3.The Fibonnaci sequence is a sequence of numbers in which each number of the
sequence matches the sum of the previous two terms. Given the following recursive
definition implement fib(n).
fib(n) =0,if x = 0;
=1,if x =1;
=fib(n-1)+fib(n-2) otherwise.
Check your results for the first numbers of the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21,
34, 55, 89, …

    def factorial(x):
        if x == 0:
            return 1
        else:
            return x * factorial(x-1)
    print('5的递归结果',factorial(5))  

    def sum_first(n):
        if n == 0:
            return 0
        else:
            return n + sum_first(n-1)
    print('the sum of n first integer：',sum_first(5))    

    def fib(n):
        if n == 0:
            return 0
        if n == 1:
            return 1
        else:
            return fib(n-1)+fib(n-2)
    for i in range(12):
        print(fib(i))

5的递归结果 120
the sum of n first integer： 15
0
1
1
2
3
5
8
13
21
34
55
89

full-speed-python 习题解答(三)

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