From c2f804d6eda6d4a6920d6a48cd37474ab284dd1d Mon Sep 17 00:00:00 2001
From: gunnu13 <gunja131998@gmail.com>
Date: Thu, 31 Oct 2019 12:28:08 +0530
Subject: [PATCH] Create Karatsuba.cpp
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Given two binary strings that represent value of two integers, find the product of two strings. For example, if the first bit string is “1100” and second bit string is “1010”, output should be 120.
---
 Karatsuba.cpp | 105 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 Karatsuba.cpp

diff --git a/Karatsuba.cpp b/Karatsuba.cpp
new file mode 100644
index 0000000..3dd9145
--- /dev/null
+++ b/Karatsuba.cpp
@@ -0,0 +1,105 @@
+#include<iostream> 
+#include<stdio.h> 
+  
+using namespace std; 
+  
+// FOLLOWING TWO FUNCTIONS ARE COPIED FROM http://goo.gl/q0OhZ 
+// Helper method: given two unequal sized bit strings, converts them to 
+// same length by adding leading 0s in the smaller string. Returns the 
+// the new length 
+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; 
+} 
+  
+// Driver program to test above functions 
+int main() 
+{ 
+    printf ("%ld\n", multiply("1100", "1010")); 
+    printf ("%ld\n", multiply("110", "1010")); 
+    printf ("%ld\n", multiply("11", "1010")); 
+    printf ("%ld\n", multiply("1", "1010")); 
+    printf ("%ld\n", multiply("0", "1010")); 
+    printf ("%ld\n", multiply("111", "111")); 
+    printf ("%ld\n", multiply("11", "11")); 
+}