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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

// 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; 
} 

Java

// 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 

Python 3

# 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 

C#

// 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 

Output:

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

Recommended Posts: