String Multiplcation.cpp

// C++ program to multiply two numbers represented 
// as strings. 
#include<bits/stdc++.h> 
using namespace std; 

// Multiplies str1 and str2, and prints result. 
string multiply(string num1, string num2) 
{ 
	int n1 = num1.size(); 
	int n2 = num2.size(); 
	if (n1 == 0 || n2 == 0) 
	return "0"; 

	// will keep the result number in vector 
	// in reverse order 
	vector<int> result(n1 + n2, 0); 

	// Below two indexes are used to find positions 
	// in result. 
	int i_n1 = 0; 
	int i_n2 = 0; 
	
	// Go from right to left in num1 
	for (int i=n1-1; i>=0; i--) 
	{ 
		int carry = 0; 
		int n1 = num1[i] - '0'; 

		// To shift position to left after every 
		// multiplication of a digit in num2 
		i_n2 = 0; 
		
		// Go from right to left in num2			 
		for (int j=n2-1; j>=0; j--) 
		{ 
			// Take current digit of second number 
			int n2 = num2[j] - '0'; 

			// Multiply with current digit of first number 
			// and add result to previously stored result 
			// at current position. 
			int sum = n1*n2 + result[i_n1 + i_n2] + carry; 

			// Carry for next iteration 
			carry = sum/10; 

			// Store result 
			result[i_n1 + i_n2] = sum % 10; 

			i_n2++; 
		} 

		// store carry in next cell 
		if (carry > 0) 
			result[i_n1 + i_n2] += carry; 

		// To shift position to left after every 
		// multiplication of a digit in num1. 
		i_n1++; 
	} 

	// ignore '0's from the right 
	int i = result.size() - 1; 
	while (i>=0 && result[i] == 0) 
	i--; 

	// If all were '0's - means either both or 
	// one of num1 or num2 were '0' 
	if (i == -1) 
	return "0"; 

	// generate the result string 
	string s = ""; 
	
	while (i >= 0) 
		s += std::to_string(result[i--]); 

	return s; 
} 

// Driver code 
int main() 
{ 
	string str1 = "3141592653589793238462643383279502884197169399375105820974944592"; 
	string str2 = "2718281828459045235360287471352662497757247093699959574966967627"; 
	
	if((str1.at(0) == '-' || str2.at(0) == '-') && 
		(str1.at(0) != '-' || str2.at(0) != '-' )) 
		cout<<"-"; 


	if(str1.at(0) == '-' && str2.at(0)!='-') 
		{ 
			str1 = str1.substr(1); 
		} 
		else if(str1.at(0) != '-' && str2.at(0) == '-') 
		{ 
			str2 = str2.substr(1); 
		} 
		else if(str1.at(0) == '-' && str2.at(0) == '-') 
		{ 
			str1 = str1.substr(1); 
			str2 = str2.substr(1); 
		} 
	cout << multiply(str1, str2); 
	return 0; 
}