Count the number of carry operations required to add two numbers

Given two numbers, the task is to find the number of carry operations required when two numbers are added as below.

1234 
+ 
5678 
——– 
6912 
——–

Examples:

Input: n = 1234, k = 5678
Output: 2

4+8 = 2 and carry 1
carry+3+7 = carry 1
carry+2+6 = 9, carry 0
carry+1+5 = 6

Input: n = 555, k = 555
Output: 3

Approach: Store the values of n and k in strings. 

1. Initialize the carry variable and count variable to 0.
2. Now, check from the last index of the strings till both the strings come to an end(one string may be smaller than the other).
3. Add both the values(take care of ascii value) with carry in every iteration and check if that sum is greater than 10 or not.
4. If it is greater than 10 then simply increment the value of count by 1 and make carry equal to 1, else make carry equal to 0.
5. At last, print your answer which is count.

Below is the implementation of above approach:

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function to count the number of
// carry operations
int count_carry(string a, string b)
{
    // Initialize the value of carry to 0
    int carry = 0;

    // Counts the number of carry operations
    int count = 0;

    // Initialize len_a and len_b with the sizes of strings
    int len_a = a.length(), len_b = b.length();

    while (len_a != 0 || len_b != 0) {

        // Assigning the ascii value of the character
        int x = 0, y = 0;
        if (len_a > 0) {
            x = a[len_a - 1] - '0';
            len_a--;
        }
        if (len_b > 0) {
            y = b[len_b - 1] - '0';
            len_b--;
        }

        // Add both numbers/digits
        int sum = x + y + carry;

        // If sum > 0, increment count
        // and set carry to 1
        if (sum >= 10) {
            carry = 1;
            count++;
        }

        // Else, set carry to 0
        else
            carry = 0;
    }

    return count;
}

// Driver code
int main()
{

    string a = "9555", b = "555";

    int count = count_carry(a, b);
    if (count == 0)
        cout << "0\n";
    else if (count == 1)
        cout << "1\n";
    else
        cout << count << "\n";

    return 0;
}

Java

// Java implementation of
// above approach
import java.io.*;

class GFG
{

// Function to count the number
// of carry operations
static int count_carry(String a, String b)
{
    // Initialize the value
    // of carry to 0
    int carry = 0;

    // Counts the number of
    // carry operations
    int count = 0;

    // Initialize len_a and len_b
    // with the sizes of strings
    int len_a = a.length(),
        len_b = b.length();

    while (len_a != 0 || len_b != 0)
    {

        // Assigning the ascii value
        // of the character
        int x = 0, y = 0;
        if (len_a > 0)
        {
            x = a.charAt(len_a - 1) - '0';
            len_a--;
        }
        if (len_b > 0)
        {
            y = b.charAt(len_b - 1) - '0';
            len_b--;
        }

        // Add both numbers/digits
        int sum = x + y + carry;

        // If sum > 0, increment count
        // and set carry to 1
        if (sum >= 10)
        {
            carry = 1;
            count++;
        }

        // Else, set carry to 0
        else
            carry = 0;
    }

    return count;
}

// Driver code
public static void main (String[] args)
{
    String a = "9555", b = "555";
    int count = count_carry(a, b);
    if (count == 0)
        System.out.println("0\n");
    else if (count == 1)
        System.out.println("1\n");
    else
        System.out.println(count);
}
}

// This code is contributed by Shashank

Python3

# Python3 implementation of
# above approach

# Function to count the number
# of carry operations
def count_carry(a, b):

    # Initialize the value of
    # carry to 0
    carry = 0;

    # Counts the number of carry
    # operations
    count = 0;

    # Initialize len_a and len_b
    # with the sizes of strings
    len_a = len(a);
    len_b = len(b);

    while (len_a != 0 or len_b != 0):

        # Assigning the ascii value
        # of the character
        x = 0;
        y = 0;
        if (len_a > 0):
            x = int(a[len_a - 1]) + int('0');
            len_a -= 1;

        if (len_b > 0):
            y = int(b[len_b - 1]) + int('0');
            len_b -= 1;

        # Add both numbers/digits
        sum = x + y + carry;

        # If sum > 0, increment count
        # and set carry to 1
        if (sum >= 10):
            carry = 1;
            count += 1;

        # Else, set carry to 0
        else:
            carry = 0;

    return count;

# Driver code
a = "9555";
b = "555";

count = count_carry(a, b);
if (count == 0):
    print("0");
elif (count == 1):
    print("1");
else:
    print(count);

# This code is contributed by mits

C#

// C# implementation of
// above approach
using System;

class GFG
{

// Function to count the number
// of carry operations
static int count_carry(string a, string b)
{
    // Initialize the value
    // of carry to 0
    int carry = 0;

    // Counts the number of
    // carry operations
    int count = 0;

    // Initialize len_a and len_b
    // with the sizes of strings
    int len_a = a.Length,
        len_b = b.Length;

    while (len_a != 0 || len_b != 0)
    {

        // Assigning the ascii value
        // of the character
        int x = 0, y = 0;
        if (len_a > 0)
        {
            x = a[len_a - 1] - '0';
            len_a--;
        }
        if (len_b > 0)
        {
            y = b[len_b - 1] - '0';
            len_b--;
        }

        // Add both numbers/digits
        int sum = x + y + carry;

        // If sum > 0, increment count
        // and set carry to 1
        if (sum >= 10)
        {
            carry = 1;
            count++;
        }

        // Else, set carry to 0
        else
            carry = 0;
    }

    return count;
}

// Driver code
public static void Main ()
{
    string a = "9555", b = "555";
    int count = count_carry(a, b);
    if (count == 0)
        Console.Write("0\n");
    else if (count == 1)
        Console.Write("1\n");
    else
        Console.Write(count);
}
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP implementation of above approach

// Function to count the number
// of carry operations
function count_carry($a, $b)
{
    // Initialize the value of
    // carry to 0
    $carry = 0;

    // Counts the number of carry
    // operations
    $count = 0;

    // Initialize len_a and len_b
    // with the sizes of strings
    $len_a = strlen($a);
    $len_b = strlen($b);

    while ($len_a != 0 || $len_b != 0)
    {

        // Assigning the ascii value
        // of the character
        $x = 0;
        $y = 0;
        if ($len_a > 0)
        {
            $x = $a[$len_a - 1] - '0';
            $len_a--;
        }
        if ($len_b > 0)
        {
            $y = $b[$len_b - 1] - '0';
            $len_b--;
        }

        // Add both numbers/digits
        $sum = $x + $y + $carry;

        // If sum > 0, increment count
        // and set carry to 1
        if ($sum >= 10)
        {
            $carry = 1;
            $count++;
        }

        // Else, set carry to 0
        else
            $carry = 0;
    }

    return $count;
}

// Driver code
$a = "9555";
$b = "555";

$count = count_carry($a, $b);
if ($count == 0)
    echo "0\n";
else if ($count == 1)
    echo "1\n";
else
    echo $count , "\n";

// This code is contributed by jit_t
?>

Javascript

<script>
    // Javascript implementation of above approach

    // Function to count the number
    // of carry operations
    function count_carry(a, b)
    {
        // Initialize the value
        // of carry to 0
        let carry = 0;

        // Counts the number of
        // carry operations
        let count = 0;

        // Initialize len_a and len_b
        // with the sizes of strings
        let len_a = a.length, len_b = b.length;

        while (len_a != 0 || len_b != 0)
        {

            // Assigning the ascii value
            // of the character
            let x = 0, y = 0;
            if (len_a > 0)
            {
                x = a[len_a - 1] - '0';
                len_a--;
            }
            if (len_b > 0)
            {
                y = b[len_b - 1] - '0';
                len_b--;
            }

            // Add both numbers/digits
            let sum = x + y + carry;

            // If sum > 0, increment count
            // and set carry to 1
            if (sum >= 10)
            {
                carry = 1;
                count++;
            }

            // Else, set carry to 0
            else
                carry = 0;
        }

        return count;
    }

    let a = "9555", b = "555";
    let count = count_carry(a, b);
    if (count == 0)
        document.write("0" + "</br>");
    else if (count == 1)
        document.write("1" + "</br>");
    else
        document.write(count);

</script>

Output:

4

Time Complexity: O(|a| + |b|)

Auxiliary Space: O(1)