Commit 78ce8cd

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Amogh Singhal

authored

Create karatsuba.py

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	`1`	`+import random`
	`2`	`+from math import ceil`
	`3`	`+from math import log10`
	`4`	`+`
	`5`	`+`
	`6`	`+def get_digits(n):`
	`7`	`+ if n > 0:`
	`8`	`+ digits = int(log10(n)) + 1`
	`9`	`+ elif n == 0:`
	`10`	`+ digits = 1`
	`11`	`+ else:`
	`12`	`+ digits = int(log10(-n)) + 2`
	`13`	`+ return digits`
	`14`	`+`
	`15`	`+`
	`16`	`+def karatsuba(x, y):`
	`17`	`+ # the base case for recursion`
	`18`	`+ if x < 10 and y < 10:`
	`19`	`+ return x * y`
	`20`	`+`
	`21`	`+ # n is the number of digits in the highest input number`
	`22`	`+ n = max(get_digits(x), get_digits(y))`
	`23`	`+`
	`24`	`+ n_2 = int(ceil(n / 2.0))`
	`25`	`+ n = n if n % 2 == 0 else n + 1`
	`26`	`+`
	`27`	`+ # split the input numbers`
	`28`	`+ a, b = divmod(x, 10 ** n_2)`
	`29`	`+ c, d = divmod(y, 10 ** n_2)`
	`30`	`+`
	`31`	`+ # applying the recursive steps`
	`32`	`+ ac = karatsuba(a, c)`
	`33`	`+ bd = karatsuba(b, d)`
	`34`	`+ ad_bc = karatsuba((a + b), (c + d)) - ac - bd`
	`35`	`+`
	`36`	`+ # performs the multiplication`
	`37`	`+ z2 = (10 ** n) * ac`
	`38`	`+ z1 = (10 ** n_2) * ad_bc`
	`39`	`+ z0 = bd`
	`40`	`+ return z2 + z1 + z0`
	`41`	`+`
	`42`	`+`
	`43`	`+def test():`
	`44`	`+ for i in range(1000):`
	`45`	`+ x = random.randint(1, 10**5)`
	`46`	`+ y = random.randint(1, 10**5)`
	`47`	`+ expected = x*y`
	`48`	`+ result = karatsuba(x, y)`
	`49`	`+ if result != expected:`
	`50`	`+ return print("failed")`
	`51`	`+ return print("ok")`
	`52`	`+`
	`53`	`+`
	`54`	`+if __name__ == '__main__':`
	`55`	`+ test()`

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