Karatsuba algorithm C++ implementation

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////  main.cpp//  multiply////  Created by Longxiang Lyu on 5/23/16.//  Copyright (c) 2016 Leo Lyu. All rights reserved.//// the karatsuba's algorithm only needs O(n^log3) bit operation to do the// multiplication of two integers, which is better than O(n^2) solutions#include <iostream>#include <string>using namespace std;size_t equalizeLength(string &s1, string &s2){    size_t len1 = s1.size(), len2 = s2.size();    if (len1 < len2)    {        for (int i = 0; i < len2 - len1; ++i)            s1 = '0' + s1;        return len2;    }    else if (len1 > len2)    {        for (int i = 0; i < len1 - len2; ++i)            s2 = '0' + s2;    }    return len1;}string strAddition(string s1, string s2){    string ret;    int carry = 0;    size_t len = equalizeLength(s1, s2);        for (int i = len - 1; i >= 0; --i)    {        int firstBit = s1.at(i) - '0';        int secondBit = s2.at(i) - '0';                int sum = (firstBit ^ secondBit ^ carry) + '0';        ret = static_cast<char>(sum) + ret;                carry = (firstBit & secondBit) | (firstBit & carry) | (secondBit & carry);    }    if (carry)        ret = '1' + ret;    return ret;}long int Karatsuba_multiply(string s1, string s2){    size_t len = equalizeLength(s1, s2);        // base case    if (len == 0) return 0;    if (len == 1) return (s1[0] - '0') * (s2[0] - '0');        size_t floor = len / 2;    size_t ceil = len - floor;    string a = s1.substr(0, floor);    string b = s1.substr(floor, ceil);    string c = s2.substr(0, floor);    string d = s2.substr(floor, ceil);    long int p1 = Karatsuba_multiply(a, c);    long int p2 = Karatsuba_multiply(b, d);    long int p3 = Karatsuba_multiply(strAddition(a, b), strAddition(c, d));        return (1<<(2 * ceil)) * p1 + (1<<(ceil)) * (p3 - p1 - p2) + p2;}int main(int argc, const char * argv[]) {    string s1 = "10101010";    string s2 = "111101";    cout << s1 << " multiplies " << s2 << " is " << Karatsuba_multiply(s1, s2) << endl;    return 0;}

Reference:

https://en.wikipedia.org/wiki/Karatsuba_algorithm

http://www.geeksforgeeks.org/divide-and-conquer-set-2-karatsuba-algorithm-for-fast-multiplication/

http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/05DivideAndConquerII.pdf

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