Related Articles

# Addition of two numbers without propagating Carry

• Difficulty Level : Easy
• Last Updated : 25 Mar, 2021

Given 2 numbers a and b of same length. The task is to calculate their sum in such a way that when adding two corresponding positions the carry has to be kept with them only instead of propagating to the left.
See the below image for reference: Examples:

```Input: a = 7752 , b = 8834
Output: 151586

Input: a = 123 , b = 456
Output: 579```

Approach: First of all, reverse both of the numbers a and b. Now, to generate the resulting sum:

• Extract digits from both a and b.
• Calculate sum of digits.
• If sum of digits is a single digit number, append it directly to the resultant sum.
• Otherwise, reverse the current calculated digit sum and extract digits from it one by one and append to the resultant sum.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach``#include``using` `namespace` `std;` `// Function to print sum of 2 numbers``// without propagating carry``int` `printSum(``int` `a, ``int` `b)``{``    ``int` `res = 0;``    ` `    ``int` `temp1 = 0, temp2 = 0;``    ` `    ``// Reverse a``    ``while``(a)``    ``{``       ``temp1 = temp1*10 + (a%10);``       ``a /= 10;``    ``}``    ``a = temp1;``    ` `    ``// Reverse b``    ``while``(b)``    ``{``       ``temp2 = temp2*10 + (b%10);``       ``b /= 10;``    ``}``    ``b = temp2;``    ` `    ``// Generate sum``    ``// Since length of both a and b are same,``    ``// take any one of them.``    ``while``(a)``    ``{  ``        ``// Extract digits from a and b and add``        ``int` `sum = (a%10 + b%10);``        ` `        ``// If sum is single digit``        ``if``(sum/10 == 0)   ``            ``res = res*10 + sum;``        ``else``        ``{``            ``// If sum is not single digit``            ``// reverse sum``            ``temp1 = 0;``            ``while``(sum)``            ``{``                ``temp1 = temp1*10 + (sum%10);``                ``sum /= 10;``            ``}``            ``sum = temp1;``            ` `            ``// Extract digits from sum and append``            ``// to result``            ``while``(sum)``            ``{``                ``res = res*10 + (sum%10);``                ``sum /=10;``            ``}``        ``}``        ` `        ``a/=10;``        ``b/=10;``    ``}``    ` `    ``return` `res;``}` `// Driver code``int` `main()``{``    ``int` `a = 7752, b = 8834;``    ``cout<

## Java

 `// Java implementation of the approach``class` `GFG``{` `    ``// Function to print sum of 2 numbers``    ``// without propagating carry``    ``static` `int` `printSum(``int` `a, ``int` `b)``    ``{``        ``int` `res = ``0``;` `        ``int` `temp1 = ``0``, temp2 = ``0``;` `        ``// Reverse a``        ``while` `(a != ``0``)``        ``{``            ``temp1 = temp1 * ``10` `+ (a % ``10``);``            ``a /= ``10``;``        ``}``        ``a = temp1;` `        ``// Reverse b``        ``while` `(b != ``0``)``        ``{``            ``temp2 = temp2 * ``10` `+ (b % ``10``);``            ``b /= ``10``;``        ``}``        ``b = temp2;` `        ``// Generate sum``        ``// Since length of both a and b are same,``        ``// take any one of them.``        ``while` `(a != ``0``)``        ``{``            ``// Extract digits from a and b and add``            ``int` `sum = (a % ``10` `+ b % ``10``);` `            ``// If sum is single digit``            ``if` `(sum / ``10` `== ``0``)``            ``{``                ``res = res * ``10` `+ sum;``            ``}``            ``else``            ``{``                ``// If sum is not single digit``                ``// reverse sum``                ``temp1 = ``0``;``                ``while` `(sum != ``0``)``                ``{``                    ``temp1 = temp1 * ``10` `+ (sum % ``10``);``                    ``sum /= ``10``;``                ``}``                ``sum = temp1;` `                ``// Extract digits from sum and append``                ``// to result``                ``while` `(sum != ``0``)``                ``{``                    ``res = res * ``10` `+ (sum % ``10``);``                    ``sum /= ``10``;``                ``}``            ``}` `            ``a /= ``10``;``            ``b /= ``10``;``        ``}` `        ``return` `res;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``int` `a = ``7752``, b = ``8834``;``        ``System.out.println(printSum(a, b));``    ``}``}` `// This code contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach` `# Function to prsum of 2 numbers``# without propagating carry``def` `printSum(a, b):` `    ``res, temp1, temp2 ``=` `0``, ``0``, ``0``    ` `    ``# Reverse a``    ``while` `a > ``0``:``    ` `        ``temp1 ``=` `temp1 ``*` `10` `+` `(a ``%` `10``)``        ``a ``/``/``=` `10``    ` `    ``a ``=` `temp1``    ` `    ``# Reverse b``    ``while` `b > ``0``:``    ` `        ``temp2 ``=` `temp2 ``*` `10` `+` `(b ``%` `10``)``        ``b ``/``/``=` `10``    ` `    ``b ``=` `temp2``    ` `    ``# Generate sum``    ``# Since length of both a and b are same,``    ``# take any one of them.``    ``while` `a:``        ` `        ``# Extract digits from a and b and add``        ``Sum` `=` `a ``%` `10` `+` `b ``%` `10``        ` `        ``# If sum is single digit``        ``if` `Sum` `/``/` `10` `=``=` `0``:``            ``res ``=` `res ``*` `10` `+` `Sum``        ` `        ``else``:``        ` `            ``# If sum is not single digit``            ``# reverse sum``            ``temp1 ``=` `0``            ``while` `Sum` `> ``0``:``            ` `                ``temp1 ``=` `temp1 ``*` `10` `+` `(``Sum` `%` `10``)``                ``Sum` `/``/``=` `10``            ` `            ``Sum` `=` `temp1``            ` `            ``# Extract digits from sum and``            ``# append to result``            ``while` `Sum` `> ``0``:``            ` `                ``res ``=` `res ``*` `10` `+` `(``Sum` `%` `10``)``                ``Sum` `/``/``=` `10``        ` `        ``a ``/``/``=` `10``        ``b ``/``/``=` `10``    ` `    ``return` `res` `# Driver code``if` `__name__ ``=``=` `"__main__"``:` `    ``a, b ``=` `7752``, ``8834``    ``print``(printSum(a, b))``    ` `# This code is contributed``# by Rituraj Jain`

## C#

 `// C# implementation of the above approach``using` `System;` `class` `GFG``{` `// Function to print sum of 2 numbers``// without propagating carry``static` `int` `printSum(``int` `a, ``int` `b)``{``    ``int` `res = 0;``    ` `    ``int` `temp1 = 0, temp2 = 0;``    ` `    ``// Reverse a``    ``while``(a != 0)``    ``{``        ``temp1 = temp1 * 10 + (a % 10);``        ``a /= 10;``    ``}``    ``a = temp1;``    ` `    ``// Reverse b``    ``while``(b != 0)``    ``{``        ``temp2 = temp2 * 10 + (b % 10);``        ``b /= 10;``    ``}``    ``b = temp2;``    ` `    ``// Generate sum``    ``// Since length of both a and b are same,``    ``// take any one of them.``    ``while``(a != 0)``    ``{``        ``// Extract digits from a and b and add``        ``int` `sum = (a % 10 + b % 10);``        ` `        ``// If sum is single digit``        ``if``(sum / 10 == 0)``            ``res = res * 10 + sum;``        ``else``        ``{``            ``// If sum is not single digit``            ``// reverse sum``            ``temp1 = 0;``            ``while``(sum != 0)``            ``{``                ``temp1 = temp1 * 10 + (sum % 10);``                ``sum /= 10;``            ``}``            ``sum = temp1;``            ` `            ``// Extract digits from sum and append``            ``// to result``            ``while``(sum != 0)``            ``{``                ``res = res * 10 + (sum % 10);``                ``sum /=10;``            ``}``        ``}``        ` `        ``a /= 10;``        ``b /= 10;``    ``}``    ` `    ``return` `res;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `a = 7752, b = 8834;``    ``Console.Write(printSum(a, b));``    ` `}``}` `// This code is contributed``// by Akanksha Rai`

## PHP

 ``

## Javascript

 `  ```
Output:
`151586`

Time Complexity: O(N).

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up