Python - 最大公约数算法

# Python 3.6

# 最大公约数，最大公因子
# Greatest Common Divisor

# 辗转相除法
def gcd(num1: object, num2: object) -> object:
    print('num1={},num2={},r={}'.format( num1, num2, num1 % num2 ) )
    if num1 % num2 == 0:
        return num2
    return gcd(num2, num1 % num2)

# 更相减损术（递归）
def gcd2(num1, num2):
    bignum = num1 if num1 >= num2 else num2
    smallnum = num2 if num1 > num2 else num1
    difference = bignum-smallnum   # 差
    print('num1={},num2={},difference={}'.format(bignum, smallnum, difference))
    if smallnum == difference :
        return difference
    return gcd2(smallnum, difference);

# 更相减损术 （循环）
def gcd3(m, n):
    res=m-n
    while res != n:
        print('num1={},num2={},difference={}'.format(m, n, res))
        m = n if n >= res else res
        n = n if n <= res else res
        res = m - n
    return n

print('-'*100)
print(gcd2(9876,8756))
print('-'*100)
print(gcd2(9876, 8756))

 

PyCharm中，使用Shift+F9,得到如下结果：　　

Connected to pydev debugger (build 181.4892.64)
num1=9876,num2=8756,r=1120
num1=8756,num2=1120,r=916
num1=1120,num2=916,r=204
num1=916,num2=204,r=100
num1=204,num2=100,r=4
num1=100,num2=4,r=0
4
----------------------------------------------------------------------------------------------------
num1=9876,num2=8756,difference=1120
num1=8756,num2=1120,difference=7636
num1=7636,num2=1120,difference=6516
num1=6516,num2=1120,difference=5396
num1=5396,num2=1120,difference=4276
num1=4276,num2=1120,difference=3156
num1=3156,num2=1120,difference=2036
num1=2036,num2=1120,difference=916
num1=1120,num2=916,difference=204
num1=916,num2=204,difference=712
num1=712,num2=204,difference=508
num1=508,num2=204,difference=304
num1=304,num2=204,difference=100
num1=204,num2=100,difference=104
num1=104,num2=100,difference=4
num1=100,num2=4,difference=96
num1=96,num2=4,difference=92
num1=92,num2=4,difference=88
num1=88,num2=4,difference=84
num1=84,num2=4,difference=80
num1=80,num2=4,difference=76
num1=76,num2=4,difference=72
num1=72,num2=4,difference=68
num1=68,num2=4,difference=64
num1=64,num2=4,difference=60
num1=60,num2=4,difference=56
num1=56,num2=4,difference=52
num1=52,num2=4,difference=48
num1=48,num2=4,difference=44
num1=44,num2=4,difference=40
num1=40,num2=4,difference=36
num1=36,num2=4,difference=32
num1=32,num2=4,difference=28
num1=28,num2=4,difference=24
num1=24,num2=4,difference=20
num1=20,num2=4,difference=16
num1=16,num2=4,difference=12
num1=12,num2=4,difference=8
num1=8,num2=4,difference=4
4
----------------------------------------------------------------------------------------------------
num1=9876,num2=8756,difference=1120
num1=8756,num2=1120,difference=7636
num1=7636,num2=1120,difference=6516
num1=6516,num2=1120,difference=5396
num1=5396,num2=1120,difference=4276
num1=4276,num2=1120,difference=3156
num1=3156,num2=1120,difference=2036
num1=2036,num2=1120,difference=916
num1=1120,num2=916,difference=204
num1=916,num2=204,difference=712
num1=712,num2=204,difference=508
num1=508,num2=204,difference=304
num1=304,num2=204,difference=100
num1=204,num2=100,difference=104
num1=104,num2=100,difference=4
num1=100,num2=4,difference=96
num1=96,num2=4,difference=92
num1=92,num2=4,difference=88
num1=88,num2=4,difference=84
num1=84,num2=4,difference=80
num1=80,num2=4,difference=76
num1=76,num2=4,difference=72
num1=72,num2=4,difference=68
num1=68,num2=4,difference=64
num1=64,num2=4,difference=60
num1=60,num2=4,difference=56
num1=56,num2=4,difference=52
num1=52,num2=4,difference=48
num1=48,num2=4,difference=44
num1=44,num2=4,difference=40
num1=40,num2=4,difference=36
num1=36,num2=4,difference=32
num1=32,num2=4,difference=28
num1=28,num2=4,difference=24
num1=24,num2=4,difference=20
num1=20,num2=4,difference=16
num1=16,num2=4,difference=12
num1=12,num2=4,difference=8
num1=8,num2=4,difference=4
4

Process finished with exit code 0

 

原理：https://zhidao.baidu.com/question/177881849738799124.html