Program to add two integers of given base

Given three integers X, Y and B, where X and Y are Base-B integers. The task is to find the sum of integers X and Y.

Examples:

Input: X = 123, Y = 234, B = 6
Output: 401
Explanation:
Sum of two integers in base 6 - 
     1 1   
     1 2 3
+    2 3 4
-------------
     4 0 1

Input: X = 546, Y = 248 B = 9
Output: 805
Explanation:
Sum of two integers in base 9 - 
     1 1
     5 4 6
+    2 4 8
-------------
     8 0 5   

Approach: The idea is to use the fact that whenever two digits of the numbers are added, then the place value will be the modulo of the sum of digits by the base whereas carry will be the integer division of the sum of digits by base. i.e.

Let two digits of the number be D1 and D2 -
Place Value = (D1 + D2) % B

Carry = (D1 + D2) / B

Similarly, Add every digit from the last to get the desired result.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation to find the
// sum of two integers of base B
  
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to find the sum of 
// two integers of base B
string sumBaseB(string a, 
      string b, int base)
{
    int len_a, len_b;
  
    len_a = a.size();
    len_b = b.size();
  
    string sum, s;
    s = "";
    sum = "";
  
    int diff;
    diff = abs(len_a - len_b);
      
    // Padding 0 in front of the 
    // number to make both numbers equal
    for (int i = 1; i <= diff; i++)
        s += "0";
      
    // Condition to check if the strings
    // have lengths mis-match
    if (len_a < len_b)
        a = s + a;
    else
        b = s + b;
  
    int curr, carry = 0;
      
    // Loop to find the find the sum 
    // of two integers of base B
    for (int i = max(len_a, len_b) - 1; 
                           i > -1; i--) {
          
        // Current Place value for 
        // the resultant sum
        curr = carry + (a[i] - '0') + 
                       (b[i] - '0');
  
        // Update carry
        carry = curr / base;
  
        // Find current digit
        curr = curr % base;
  
        // Update sum result
        sum = (char)(curr + '0') + sum;
    }
    if (carry > 0)
        sum = (char)(carry + '0') + sum;
    return sum;
}
  
// Driver Code
int main()
{
    string a, b, sum;
    int base;
    a = "123";
    b = "234";
    base = 6;
      
    // Function Call
    sum = sumBaseB(a, b, base);
    cout << sum << endl;
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation to find the 
// sum of two integers of base B 
class GFG {
  
    // Function to find the sum of 
    // two integers of base B 
    static String sumBaseB(String a, String b, int base) 
    
        int len_a, len_b; 
      
        len_a = a.length(); 
        len_b = b.length(); 
      
        String sum, s; 
        s = ""
        sum = ""
      
        int diff; 
        diff = Math.abs(len_a - len_b); 
          
        // Padding 0 in front of the 
        // number to make both numbers equal 
        for (int i = 1; i <= diff; i++) 
            s += "0"
          
        // Condition to check if the strings 
        // have lengths mis-match 
        if (len_a < len_b) 
            a = s + a; 
        else
            b = s + b; 
      
        int curr, carry = 0
          
        // Loop to find the find the sum 
        // of two integers of base B 
        for (int i = Math.max(len_a, len_b) - 1
                            i > -1; i--) { 
              
            // Current Place value for 
            // the resultant sum 
            curr = carry + (a.charAt(i) - '0') + 
                        (b.charAt(i) - '0'); 
      
            // Update carry 
            carry = curr / base; 
      
            // Find current digit 
            curr = curr % base; 
      
            // Update sum result 
            sum = (char)(curr + '0') + sum; 
        
        if (carry > 0
            sum = (char)(carry + '0') + sum; 
        return sum; 
    
      
    // Driver Code 
    public static void main (String[] args) 
    
        String a, b, sum; 
        int base; 
        a = "123"
        b = "234"
        base = 6
          
        // Function Call 
        sum = sumBaseB(a, b, base); 
        System.out.println(sum); 
    
}
  
// This code is contributed by AnkitRai01

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python 3 implementation to find the
# sum of two integers of base B
   
# Function to find the sum of 
# two integers of base B
def sumBaseB(a,b,base):
   
    len_a = len(a)
    len_b = len(b)
  
    s = "";
    sum = "";
   
    diff = abs(len_a - len_b);
       
    # Padding 0 in front of the 
    # number to make both numbers equal
    for i in range(1,diff+1):
        s += "0"
       
    # Condition to check if the strings
    # have lengths mis-match
    if (len_a < len_b):
        a = s + a
    else:
        b = s + b;
   
    carry = 0;
       
    # Loop to find the find the sum 
    # of two integers of base B
    for i in range(max(len_a, len_b) - 1,-1,-1):
           
        # Current Place value for 
        # the resultant sum
        curr = carry + (ord(a[i]) -ord('0')) +( ord(b[i]) - ord('0'));
   
        # Update carry
        carry = curr // base
   
        # Find current digit
        curr = curr % base;
   
        # Update sum result
        sum = chr(curr + ord('0')) + sum
          
    if (carry > 0):
        sum = chr(carry + ord('0')) + sum;
    return sum
   
# Driver Code
  
a = "123"
b = "234"
base = 6
       
# Function Call
sum = sumBaseB(a, b, base);
print(sum)
  
# This code is contributed by atul_kumar_shrivastava

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation to find the 
// sum of two integers of base B 
using System;
  
class GFG {
  
    // Function to find the sum of 
    // two integers of base B 
    static string sumBaseB(string a, string b, int base_var) 
    
        int len_a, len_b; 
      
        len_a = a.Length; 
        len_b = b.Length; 
      
        string sum, s; 
        s = ""
        sum = ""
      
        int diff; 
        diff = Math.Abs(len_a - len_b); 
          
        // Padding 0 in front of the 
        // number to make both numbers equal 
        for (int i = 1; i <= diff; i++) 
            s += "0"
          
        // Condition to check if the strings 
        // have lengths mis-match 
        if (len_a < len_b) 
            a = s + a; 
        else
            b = s + b; 
      
        int curr, carry = 0; 
          
        // Loop to find the find the sum 
        // of two integers of base B 
        for (int i = Math.Max(len_a, len_b) - 1; 
                            i > -1; i--) { 
              
            // Current Place value for 
            // the resultant sum 
            curr = carry + (a[i] - '0') + 
                        (b[i] - '0'); 
      
            // Update carry 
            carry = curr / base_var; 
      
            // Find current digit 
            curr = curr % base_var; 
      
            // Update sum result 
            sum = (char)(curr + '0') + sum; 
        
        if (carry > 0) 
            sum = (char)(carry + '0') + sum; 
        return sum; 
    
      
    // Driver Code 
    public static void Main (string[] args) 
    
        string a, b, sum; 
        int base_var; 
        a = "123"
        b = "234"
        base_var = 6; 
          
        // Function Call 
        sum = sumBaseB(a, b, base_var); 
        Console.WriteLine(sum); 
    
}
  
// This code is contributed by AnkitRai01

chevron_right


Output:

401

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.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Article Tags :
Practice Tags :


2


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.