Skip to content
Related Articles
Open in App
Not now

Related Articles

Subtraction of two large numbers using 10’s complement

Improve Article
Save Article
  • Difficulty Level : Medium
  • Last Updated : 10 Nov, 2022
Improve Article
Save Article

Given two strings str1 and str2 of given lengths N and M respectively, each representing a large number, the task is to subtract one from the other using 10’s complement.

Example: 

Input: N = 10, str1 = “3434243434”, M = 14, str2 = “22324365765767” 
Output: 22320931522333

Input: N = 20, str1 = “12345334233242431433”, M = 20, str2 = “12345334233242431432” 
Output:

Approach: The basic idea is similar to Subtraction of two numbers using 2’s complement

Subtraction of given strings can be written as 
Str1 – Str2 = Str1 + (- Str2) = Str1 + (10’s complement of Str2)

Follow the steps below to solve the problem:  

  • Compare the lengths of the two strings and store the smaller of the two in str2.
  • Calculate 10’s complement of str2.
  • Now, add 10’s complement of str2 to str1.
  • If any carry is generated, then drop the carry.
  • If no carry is generated, then the complement of str1 is the final answer.

Below is the implementation of the above approach: 

C++




// C++ Program to calculate the
// subtraction of two large number
// using 10's complement
#include <bits/stdc++.h>
using namespace std;
 
// Function to return sum of two
// large numbers given as strings
string sumBig(string a, string b)
{
 
    // Compare their lengths
    if (a.length() > b.length())
        swap(a, b);
 
    // Stores the result
    string str = "";
 
    // Store the respective lengths
    int n1 = a.length(), n2 = b.length();
 
    int diff = n2 - n1;
 
    // Initialize carry
    int carry = 0;
 
    // Traverse from end of both strings
    for (int i = n1 - 1; i >= 0; i--) {
 
        // Compute sum of
        // current digits and carry
        int sum
            = ((a[i] - '0')
               + (b[i + diff] - '0') + carry);
 
        // Store the result
        str.push_back(sum % 10 + '0');
 
        // Update carry
        carry = sum / 10;
    }
 
    // Add remaining digits of str2[]
    for (int i = n2 - n1 - 1; i >= 0; i--) {
 
        int sum = ((b[i] - '0') + carry);
 
        str.push_back(sum % 10 + '0');
        carry = sum / 10;
    }
 
    // Add remaining carry
    if (carry)
        str.push_back(carry + '0');
 
    // Reverse resultant string
    reverse(str.begin(), str.end());
 
    return str;
}
 
// Function return 10's
// complement of given number
string complement10(string v)
{
    // Stores the complement
    string complement = "";
 
    // Calculate 9's complement
    for (int i = 0; i < v.size(); i++) {
 
        // Subtract every bit from 9
        complement += '9' - v[i] + '0';
    }
 
    // Add 1 to 9's complement
    // to find 10's complement
    complement = sumBig(complement, "1");
    return complement;
}
 
// Function returns subtraction
// of two given numbers as strings
string subtract(string a, string b)
{
 
    // If second string is larger
    if (a.length() < b.length())
        swap(a, b);
 
    // Calculate respective lengths
    int l1 = a.length(), l2 = b.length();
 
    // If lengths aren't equal
    int diffLen = l1 - l2;
 
    for (int i = 0; i < diffLen; i++) {
 
        // Insert 0's to the beginning
        // of b to make both the lengths equal
        b = "0" + b;
    }
 
    // Add (complement of B) and A
    string c = sumBig(a, complement10(b));
 
    // If length of new string is greater
    // than length of first string,
    // than carry is generated
    if (c.length() > a.length()) {
        string::iterator it;
 
        // Erase first bit
        it = c.begin();
 
        c.erase(it);
 
        // Trim zeros at the beginning
        it = c.begin();
 
        while (*it == '0')
            c.erase(it);
 
        return c;
    }
 
    // If both lengths are equal
    else {
        return complement10(c);
    }
}
 
// Driver Code
int main()
{
 
    string str1 = "12345334233242431433";
    string str2 = "12345334233242431432";
 
    cout << subtract(str1, str2) << endl;
 
    return 0;
}

Python3




# Python3 Program to calculate the
# subtraction of two large number
# using 10's complement
 
# Function to return sums of two
# large numbers given as strsings
def sumsBig(a, b):
 
    # Compare their lengths
    if (len(a) > len(b)):
     
        temp = a;
        a = b;
        b = temp;
     
    # Stores the result
    strs = "";
 
    # Store the respective lengths
    n1 = len(a)
    n2 = len(b);
 
    diff = n2 - n1;
 
    # Initialize carry
    carry = 0;
 
    # Traverse from end of both strsings
    for i in range(n1 - 1, -1, -1):
 
        # Compute sums of
        # current digits and carry
        sums = (int(a[i]) + int(b[i + diff]) + carry);
 
        # Store the result
        strs += str(sums % 10);
 
        # Update carry
        carry = int(sums / 10);
     
    # Add remaining digits of strs2[]
    for i in range(n2 - n1 - 1, -1, -1):
 
        sums = ( int(b[i]) + carry);
 
        strs += str(sums % 10);
        carry = int(sums / 10);
     
    # Add remaining carry
    if (carry > 0):
        strs += str(carry);
 
    # Reverse resultant strsing
    strs = strs[::-1]
 
    return strs;
 
# Function return 10's
# complement of given number
def complement10(v):
 
    # Stores the complement
    complement = "";
 
    # Calculate 9's complement
    for i in range(len(v)):
 
        # Subtract every bit from 9
        complement +=   str(9 - int(v[i]));
     
    # Add 1 to 9's complement
    # to find 10's complement
    complement = sumsBig(complement, "1");
    return complement;
 
# Function returns subtraction
# of two given numbers as strsings
def subtract(a, b):
 
    # If second strsing is larger
    if (len(a) < len(b)):   
        temp = b;
        b = a ;
        a = temp;
     
    # Calculate respective lengths
    l1 = len(a)
    l2 = len(b);
 
    # If lengths aren't equal
    diffLen = l1 - l2;
     
    for i in range(diffLen):
 
        # Insert 0's to the beginning
        # of b to make both the lengths equal
        b = "0" + b;
     
    # Add (complement of B) and A
    c = sumsBig(a, complement10(b));
 
    # If length of new strsing is greater
    # than length of first strsing,
    # than carry is generated
    if (len(c) > len(a)):
 
        # Erase first bit
        c = c[1::];
        # Trim zeros at the beginning
        while (c[0] == '0'):
            c = c[1::]
 
        return c;
     
    # If both lengths are equal
    else :
        return complement10(c);
     
# Driver Code
strs1 = "12345334233242431433";
strs2 = "12345334233242431432";
 
print(subtract(strs1, strs2));
 
# This code is contributed by phasing17.

C#




// C# Program to calculate the
// subtraction of two large number
// using 10's complement
using System;
using System.Linq;
using System.Collections.Generic;
 
class GFG
{
   
  // Function to return sum of two
  // large numbers given as strings
  static string sumBig(string a, string b)
  {
 
    // Compare their lengths
    if (a.Length > b.Length)
    {
      string temp = b;
      b = a;
      a = temp;
    }
 
    // Stores the result
    string str = "";
 
    // Store the respective lengths
    int n1 = a.Length, n2 = b.Length;
 
    int diff = n2 - n1;
 
    // Initialize carry
    int carry = 0;
 
    // Traverse from end of both strings
    for (int i = n1 - 1; i >= 0; i--) {
 
      // Compute sum of
      // current digits and carry
      int sum
        = ((a[i] - '0')
           + (b[i + diff] - '0') + carry);
 
      // Store the result
      str += (char)(sum % 10 + '0');
 
      // Update carry
      carry = sum / 10;
    }
 
    // Add remaining digits of str2[]
    for (int i = n2 - n1 - 1; i >= 0; i--) {
 
      int sum = ((b[i] - '0') + carry);
 
      str += (char)(sum % 10 + '0');
      carry = sum / 10;
    }
 
    // Add remaining carry
    if (carry != 0)
      str += (char)(carry + '0');
 
    // Reverse resultant string
    char[] strs = str.ToCharArray();
    Array.Reverse(strs);
 
    return new string(strs);
  }
 
  // Function return 10's
  // complement of given number
  static string complement10(string v)
  {
    // Stores the complement
    string complement = "";
 
    // Calculate 9's complement
    for (int i = 0; i < v.Length; i++) {
 
      // Subtract every bit from 9
      complement += (char)('9' - v[i] + '0');
    }
 
    // Add 1 to 9's complement
    // to find 10's complement
    complement = sumBig(complement, "1");
    return complement;
  }
 
  // Function returns subtraction
  // of two given numbers as strings
  static string subtract(string a, string b)
  {
 
    // If second string is larger
    if (a.Length < b.Length)
    {
      var t = b;
      b = a;
      a = t;
    }
 
    // Calculate respective lengths
    int l1 = a.Length, l2 = b.Length;
 
    // If lengths aren't equal
    int diffLen = l1 - l2;
 
    for (int i = 0; i < diffLen; i++) {
 
      // Insert 0's to the beginning
      // of b to make both the lengths equal
      b = "0" + b;
    }
 
    // Add (complement of B) and A
    string c = sumBig(a, complement10(b));
 
 
 
    // If length of new string is greater
    // than length of first string,
    // than carry is generated
    if (c.Length > a.Length) {
 
      var c1 = c.ToCharArray().ToList();
 
      // Erase first bit
      c1.RemoveAt(0);
 
      // Trim zeros at the beginning
      while(c1[0] == '0')
        c1.RemoveAt(0);
 
      return new string(c1.ToArray());
 
    }
 
    // If both lengths are equal
    else {
      return complement10(c);
    }
  }
 
  // Driver Code
  public static void Main(string[] args)
  {
 
    string str1 = "12345334233242431433";
    string str2 = "12345334233242431432";
 
    Console.WriteLine(subtract(str1, str2));
  }
}
 
// This code is contributed by phasing17.

Javascript




// JS Program to calculate the
// subtraction of two large number
// using 10's complement
 
// Function to return sum of two
// large numbers given as strings
function sumBig(a, b)
{
 
    // Compare their lengths
    if (a.length > b.length)
    {
        let temp = a;
        a = b;
        b = temp;
    }
 
    // Stores the result
    let str = "";
 
    // Store the respective lengths
    let n1 = a.length, n2 = b.length;
 
    let diff = n2 - n1;
 
    // Initialize carry
    let carry = 0;
 
    // Traverse from end of both strings
    for (let i = n1 - 1; i >= 0; i--) {
 
        // Compute sum of
        // current digits and carry
        let sum
            = (parseInt(a[i])
               + parseInt(b[i + diff]) + carry);
 
        // Store the result
        str += (sum % 10).toString();
 
        // Update carry
        carry = Math.floor(sum / 10);
    }
 
    // Add remaining digits of str2[]
    for (let i = n2 - n1 - 1; i >= 0; i--) {
 
        let sum = ( parseInt(b[i]) + carry);
 
        str += (sum % 10).toString();
        carry = Math.floor(sum / 10);
    }
 
    // Add remaining carry
    if (carry > 0)
        str += (carry).toString();
 
    // Reverse resultant string
    str = str.split("").reverse().join("")
 
    return str;
}
 
// Function return 10's
// complement of given number
function complement10(v)
{
    // Stores the complement
    let complement = "";
 
    // Calculate 9's complement
    for (var i = 0; i < v.length; i++) {
 
        // Subtract every bit from 9
        complement +=   (9 - parseInt(v[i])).toString();
    }
 
    // Add 1 to 9's complement
    // to find 10's complement
    complement = sumBig(complement, "1");
    return complement;
}
 
// Function returns subtraction
// of two given numbers as strings
function subtract(a, b)
{
 
    // If second string is larger
    if (a.length < b.length)
    {
        let temp = b;
        b = a ;
        a = temp;
    }
 
    // Calculate respective lengths
    let l1 = a.length, l2 = b.length;
 
    // If lengths aren't equal
    let diffLen = l1 - l2;
 
    for (let i = 0; i < diffLen; i++) {
 
        // Insert 0's to the beginning
        // of b to make both the lengths equal
        b = "0" + b;
    }
 
    // Add (complement of B) and A
    let c = sumBig(a, complement10(b));
 
    // If length of new string is greater
    // than length of first string,
    // than carry is generated
    if (c.length > a.length) {
 
        // Erase first bit
       c = c.substr(1);
 
 
        // Trim zeros at the beginning
         
 
        while (c[0] == '0')
            c = c.substr(1)
 
        return c;
    }
 
    // If both lengths are equal
    else {
        return complement10(c);
    }
}
 
// Driver Code
let str1 = "12345334233242431433";
let str2 = "12345334233242431432";
 
console.log(subtract(str1, str2));
 
// This code is contributed by phasing17.

Output: 

1

 

Time Complexity: O(max(N, M)) 
Auxiliary Space: O(max(N, M))
 


My Personal Notes arrow_drop_up
Related Articles

Start Your Coding Journey Now!