Python中的 gcd()

最高公因数 (HCF) 也称为 gcd，可以使用数学模块提供的单个函数在Python中计算，因此可以在许多情况下使任务更容易。

计算 gcd 的朴素方法

1. 使用递归：

# Python code to demonstrate naive
# method to compute gcd ( recursion )
  
def hcfnaive(a,b):
    if(b==0):
        return a
    else:
        return hcfnaive(b,a%b)
  
a = 60
b= 48
  
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (hcfnaive(60,48))

输出：

The gcd of 60 and 48 is : 12

2. 使用循环

# Python code to demonstrate naive
# method to compute gcd ( Loops )
  
  
def computeGCD(x, y):
  
    if x > y:
        small = y
    else:
        small = x
    for i in range(1, small+1):
        if((x % i == 0) and (y % i == 0)):
            gcd = i
              
    return gcd
  
a = 60
b= 48
  
# prints 12
print ("The gcd of 60 and 48 is : ",end="")
print (computeGCD(60,48))

输出：

The gcd of 60 and 48 is : 12

3. 使用欧几里得算法

   # Python code to demonstrate naive
   # method to compute gcd ( Euclidean algo )
     
     
   def computeGCD(x, y):
     
      while(y):
          x, y = y, x % y
     
      return x
     
   a = 60
   b= 48
     
   # prints 12
   print ("The gcd of 60 and 48 is : ",end="")
   print (computeGCD(60,48))
   

   输出：

   The gcd of 60 and 48 is : 12
   

   使用Python的 math.gcd()函数
   
   使用 gcd() 可以只用一行计算相同的 gcd。

   math.gcd( x, y )
   Parameters : 
   x :  Non-negative integer whose gcd has to be computed.
   y : Non-negative integer whose gcd has to be computed.
   Return Value : 
   This method will return an absolute/positive integer value after 
   calculating the GCD of given parameters x and y.
   Exceptions : 
   When Both x and y are 0, function returns 0, If any number is a character ,
   Type error is raised.
   

   # Python code to demonstrate gcd()
   # method to compute gcd
     
   import math
     
   # prints 12
   print ("The gcd of 60 and 48 is : ",end="")
   print (math.gcd(60,48))
   

   输出：

   The gcd of 60 and 48 is : 12
   

   常见异常
   
   此函数中的一些常见异常是：
   • 两个数都是0，gcd是0
   • 如果只有一个数字不是数字，则会引发类型错误。

   # Python code to demonstrate gcd()
   # method exceptions
     
   import math
     
   # prints 0
   print ("The gcd of 0 and 0 is : ",end="")
   print (math.gcd(0,0))
     
   # Produces error
   print ("The gcd of a and 13 is : ",end="")
   print (math.gcd('a',13))
   

   输出：

   The gcd of 0 and 0 is : 0
   The gcd of a and 13 is : 
   

   运行时错误：

   Traceback (most recent call last):
     File "/home/94493cdfb3c8509146254862d12bcc97.py", line 12, in 
       print (math.gcd('a',13))
   TypeError: 'str' object cannot be interpreted as an integer