Karatsuba Algorithm In Ruby (jainaman224#3039)

Karatsuba_Algorithm/Karatsuba_Algorithm.rb

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+# Karatsuba Algorithm In Ruby 
+
+= begin
+
+    The Karatsuba Algorithm is a fast multiplication algorithm. 
+    It was discovered by Anatoly Karatsuba in 1960. It reduces 
+    the multiplication of two n-digit numbers to at most single 
+    digit multiplications in general. It is therefore faster 
+    than classical multiplication operation.
+
+= end
+
+def karatsuba(num1, num2) 
+
+    num1, num2 = num1.to_s, num2.to_s
+    num1_mid_point = (num1.length / 2)
+    num2_mid_point = (num2.length / 2)
+
+    a = num1[0...num1_mid_point].to_i
+    b = num1[num1_mid_point..-1].to_i
+    c = num2[0...num2_mid_point].to_i
+    d = num2[num2_mid_point..-1].to_i   
+
+    # Step 1: Computing the products of a * c 
+    a_c = a * c
+
+    # Step 2: Computing the products of a * c 
+    b_d = b * d
+
+    # Step 3: Computing the products of (a+b) and (c+d)
+    sum_product = ((a + b) * (c + d))
+
+    # Step 4: Subtracting first two products from Step 3
+    sub_products = sum_product - (a_c + b_d)
+
+    # Step 5: Padding summation
+    result = (a_c * (10 ** num1.length)) + b_d + (sub_products * (10 ** num1_mid_point))
+
+end
+
+puts "Enter The First Number: "
+x = gets.to_i
+
+puts "Enter The Second Number: "
+y = gets.to_i
+puts
+
+answer = karatsuba(x, y)
+puts "Result: ", answer
+puts
+
+# Sample Input and Output
+
+= begin
+
+Enter The First Number: 121547
+Enter The Second Number: 1855324
+
+Result: 23133311228
+
+--------------------------------------------------
+
+Enter The First Number: -8859460
+Enter The Second Number: 1154486
+
+Result: -10206279662440
+
+= end