# Multiply large numbers as strings

This algorithm is very much like factorial. Multiplication of very large numbers represented as strings because they go out of the integer range.

```#include <iostream>
#include <vector>
#include <string>
#include <sstream>

std::string multiply(std::string a, std::string b) {
// take a vector of length 200 and initialize all of its elements to 0.
std::vector<int> multiplication(200, 0);

int place = 0;
for(int i = a.size() - 1 ; i >= 0; i--){
int carry = 0;
std::vector<int>::iterator it = multiplication.begin() + place;
for(int j = b.size() - 1 ; j >= 0; j--){
int a_element = a[i] - '0';
int b_element = b[j] - '0';
int prod = a_element*b_element + carry + *it;
*it = prod % 10;
carry = prod / 10;
it++;
while (carry){
int current_carry = carry + *it;
*it += current_carry % 10;
it++;
carry = current_carry / 10;
}
}
place++;
}

std::stringstream ss;
for(int i = multiplication.size(); i >= 0; i--){
ss << multiplication[i];
}
return ss.str();
}``` ## Author: Saurabh Purnaye

VP - Low Latency Developer @jpmchase... Linux, C++, Python, Ruby. pursuing certificate in #QuantFinance and Passed CFA L1