Create Karatsuba_algorithm.cpp

C++/Karatsuba_algorithm.cpp

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+#include<iostream>
+#include<stdio.h>
+
+using namespace std;
+
+
+int makeEqualLength(string &str1, string &str2)
+{
+    int len1 = str1.size();
+    int len2 = str2.size();
+    if (len1 < len2)
+    {
+        for (int i = 0 ; i < len2 - len1 ; i++)
+            str1 = '0' + str1;
+        return len2;
+    }
+    else if (len1 > len2)
+    {
+        for (int i = 0 ; i < len1 - len2 ; i++)
+            str2 = '0' + str2;
+    }
+    return len1; // If len1 >= len2
+}
+
+// The main function that adds two bit sequences and returns the addition
+string addBitStrings( string first, string second )
+{
+    string result;  // To store the sum bits
+
+    // make the lengths same before adding
+    int length = makeEqualLength(first, second);
+    int carry = 0;  // Initialize carry
+
+    // Add all bits one by one
+    for (int i = length-1 ; i >= 0 ; i--)
+    {
+        int firstBit = first.at(i) - '0';
+        int secondBit = second.at(i) - '0';
+
+        // boolean expression for sum of 3 bits
+        int sum = (firstBit ^ secondBit ^ carry)+'0';
+
+        result = (char)sum + result;
+
+        // boolean expression for 3-bit addition
+        carry = (firstBit&secondBit) | (secondBit&carry) | (firstBit&carry);
+    }
+
+    // if overflow, then add a leading 1
+    if (carry)  result = '1' + result;
+
+    return result;
+}
+
+// A utility function to multiply single bits of strings a and b
+int multiplyiSingleBit(string a, string b)
+{  return (a[0] - '0')*(b[0] - '0');  }
+
+// The main function that multiplies two bit strings X and Y and returns
+// result as long integer
+long int multiply(string X, string Y)
+{
+    // Find the maximum of lengths of x and Y and make length
+    // of smaller string same as that of larger string
+    int n = makeEqualLength(X, Y);
+
+    // Base cases
+    if (n == 0) return 0;
+    if (n == 1) return multiplyiSingleBit(X, Y);
+
+    int fh = n/2;   // First half of string, floor(n/2)
+    int sh = (n-fh); // Second half of string, ceil(n/2)
+
+    // Find the first half and second half of first string.
+    // Refer http://goo.gl/lLmgn for substr method
+    string Xl = X.substr(0, fh);
+    string Xr = X.substr(fh, sh);
+
+    // Find the first half and second half of second string
+    string Yl = Y.substr(0, fh);
+    string Yr = Y.substr(fh, sh);
+
+    // Recursively calculate the three products of inputs of size n/2
+    long int P1 = multiply(Xl, Yl);
+    long int P2 = multiply(Xr, Yr);
+    long int P3 = multiply(addBitStrings(Xl, Xr), addBitStrings(Yl, Yr));
+
+    // Combine the three products to get the final result.
+    return P1*(1<<(2*sh)) + (P3 - P1 - P2)*(1<<sh) + P2;
+}