Merge pull request ephremdeme#209 from STK101/master

Create karatsuba_algorithm.py

Author: ephremdeme

Algorithms/karatsuba_algorithm.py

@@ -0,0 +1,37 @@
+def zero(numberString, zeros, left = True):
+ """Return the string with zeros added to the left or right."""
+ for i in range(zeros):
+ if left:
+ numberString = '0' + numberString
+ else:
+ numberString = numberString + '0'
+ return numberString
+
+
+ def Multiplication(x ,y):
+ 
+ x = str(x)
+ y = str(y)
+ # recursion base case
+ if len(x) == 1 and len(y) == 1:
+ return int(x) * int(y)
+ if len(x) < len(y):
+ x = zero(x, len(y) - len(x))
+ elif len(y) < len(x):
+ y = zero(y, len(x) - len(y))
+ n = len(x)
+ j = n//2
+ if (n % 2) != 0:
+ j += 1 
+ BZeroPadding = n - j
+ AZeroPadding = BZeroPadding * 2
+ a = int(x[:j])
+ b = int(x[j:])
+ c = int(y[:j])
+ d = int(y[j:])
+ ac = Multiplication(a, c)
+ bd = Multiplication(b, d)
+ k = Multiplication(a + b, c + d)
+ A = int(zero(str(ac), AZeroPadding, False))
+ B = int(zero(str(k - ac - bd), BZeroPadding, False))
+ return A + B + bd

Mathematics/LCM/LCM.java

@@ -0,0 +1,18 @@
+public class Main {
+ public static void main(String[] args) {
+
+ int n1 = 72, n2 = 120, lcm;
+
+ // maximum number between n1 and n2 is stored in lcm
+ lcm = (n1 > n2) ? n1 : n2;
+
+ // Always true
+ while(true) {
+ if( lcm % n1 == 0 && lcm % n2 == 0 ) {
+ System.out.printf("The LCM of %d and %d is %d.", n1, n2, lcm);
+ break;
+ }
+ ++lcm;
+ }
+ }
+}