python - Euclidean algorithm (GCD) with multiple numbers? -


so i'm writing program in python gcd of amount of numbers.

def gcd(numbers):      if numbers[-1] == 0:         return numbers[0]       # i'm stuck here, wrong     in range(len(numbers)-1):         print gcd([numbers[i+1], numbers[i] % numbers[i+1]])   print gcd(30, 40, 36)

the function takes list of numbers. should print 2. however, don't understand how use the algorithm recursively can handle multiple numbers. can explain?

updated, still not working:

def gcd(numbers):      if numbers[-1] == 0:         return numbers[0]      gcd = 0      in range(len(numbers)):         gcd = gcd([numbers[i+1], numbers[i] % numbers[i+1]])         gcdtemp = gcd([gcd, numbers[i+2]])         gcd = gcdtemp      return gcd

ok, solved it

def gcd(a, b):      if b == 0:         return     else:         return gcd(b, % b)

and use reduce, like

reduce(gcd, (30, 40, 36))

since gcd associative, gcd(a,b,c,d) same gcd(gcd(gcd(a,b),c),d). in case, python's reduce function candidate reducing cases len(numbers) > 2 simple 2-number comparison. code this:

if len(numbers) > 2:     return reduce(lambda x,y: gcd([x,y]), numbers)

reduce applies given function each element in list, like

gcd = reduce(lambda x,y:gcd([x,y]),[a,b,c,d])

is same doing

gcd = gcd(a,b) gcd = gcd(gcd,c) gcd = gcd(gcd,d)

now thing left code when len(numbers) <= 2. passing 2 arguments gcd in reduce ensures function recurses @ once (since len(numbers) > 2 in original call), has additional benefit of never overflowing stack.


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