# Sum of two large numbers in C++

C++Server Side ProgrammingProgramming

In this problem, we are given two string that defines two large numbers. Our task is to create a program to find the sum of two large numbers.

## Let’s take an example to understand the problem,

Input: number1 = “341299123919”
number2 = “52413424”
Output: 341351537343

To solve this problem, we will traverse both the string. And add digit by digit and propagate the carry. And store the result digit by digit to sum string.

## Algorithm

Initialize sum = 0, carry = 0.
Step 1: loop from n to 0.
Step 1.1: intSum = number1[i] + number2[i]
Step 1.2: carry = intSum/10. Sum += intSum
Step 2: sum += carry.
Step 3: return sum.

## Example

Program to illustrate the working of our solution,

#include<bits/stdc++.h>
using namespace std;
string addBigNumbers(string number1, string number2) {
if (number1.length() > number2.length())
swap(number1, number2);
string sum = "";
int len1 = number1.length();
int len2 = number2.length();
int digitDiff = len2 - len1;
int carry = 0;
int intSum;
for (int i=len1-1; i>=0; i--) {
intSum = ((number1[i]-'0') + (number2[i+digitDiff]- '0') + carry);
sum.push_back(intSum%10 + '0');
carry = intSum/10;
}
for (int i=digitDiff-1; i>=0; i--) {
intSum = ((number2[i]-'0')+carry);
sum.push_back(intSum%10 + '0');
carry = intSum/10;
}
if (carry)
sum.push_back(carry+'0');
reverse(sum.begin(), sum.end());
return sum;
}
int main() {
string number1 = "235235823852";
string number2 = "45230820348";
cout<<"Sum of two large numbers is "<<addBigNumbers(number1,x number2);
return 0;
}

## Output

Sum of two large numbers is 280466644200