Addition of Large Numbers using strings in C++

The logic behind this is to store the large number as string and operate on each character as string is an array of characters each digit of the number is stored as a character. In order to work with characters there are two ways to do:

1.To write our own arithmetic operators to work with characters (overloading of operators)
2.Convert a character into an integer, work on integers and convert back to a character.  

How to convert a character into an integer?

Method 1:
If we have a character c='10'.We can follow  one of these steps:

int a                                

                                          a=(int)c                      //a has ascii value of 'c' i.e 58

             c=c-48                       //58-48=10

Ascii value of the digit can be obtained by adding 48 to the digit.


Method 2:

            int a                                                            

                    a=c-'0'               // i.e 58-48=10&a contains 10 

The character '0' means 48

Note: To convert from char to integer subtract ‘0’ and to convert from an integer to char add ‘0’

Here is the program to add two large numbers

	#include <iostream>
	#include <cstdlib>
	#include <string>
	using namespace std;
	int main()
	{
	string str1="1234567891011121314151617181920", str2="1234567891011121314151617181920" ;
	string rev_str1, rev_str2;
	string final; //Final product string
	int carry = 0;
	rev_str1 = string(str1.rbegin(), str1.rend());
	rev_str2 = string(str2.rbegin(), str2.rend());
	for (int i = 0; i <rev_str1.length() ; i++)
	{
	int x=rev_str1[i]-'0'; //converting into integer
	int y=rev_str2[i]-'0';
	int z=x+y+carry;
	final+=('0'+z%10); //converting into character
	carry=z/10;
	}
	if(carry>0) //final carry
	final+='0'+carry;
	final = string(final.rbegin(), final.rend());
	cout << "final = " << final << endl;
	}

This numerical example gives better understanding of the program.

  

str1="129" str2="234"

rev_str1="921".rev_str2="432"

carry=0

i=0 to 2

i=0

  

x='9'-'0'=57-48=9

y='4'-'0'=52-48=4

z=9+4+0 //carry=0 for 1st iteration

final +='0'+13%10='3'

carry=13/10=1

i=1

x='2'-'0'=50-48=2

y='3'-'0'=51-48=3

z=2+3+1 //carry=1 

final +='0'+5%10='6'  //final="3"

carry=5/10=0

i=2

x='1'-'0'=59-48=1

y='2'-'0'=50-48=2

z=1+2+0 //carry=0 

final +='0'+3%10='3'  //final="36"

carry=3/10=0

final="363"