Permutation of a number whose sum with the original number is equal to another given number

Given two integers A and C, the task is to check if there exists a permutation of the number A such that the sum of the number A and its permutation is equal to C.

Examples:

Input: A = 133, C = 446
Output: Yes
Explanation: One of the permutation of A is 313. Therefore, sum = 133 + 313 = 446, which is equal to C.

Input: A = 200, C = 201
Output: No

Naive Approach: The simplest approach to solve the problem is to generate all permutations of the number A and add it with the original value of A. Now, check if their sum is equal to C or not.

Time Complexity: O((log₁₀A)!)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is to subtract the value of A from C and check if there exists a permutation of A which is equal to the difference between C and A or not. Follow the steps below to solve the problem:

• Subtract A from C and check if C is less than 0 or not. If found to be true, then print “No”.
• Otherwise, perform the following steps:
  • Convert A to its equivalent string representation and store it in a variable, say S.
  • Convert C to its equivalent string representation and store it in a variable, say K.
  • Sort the newly generated strings S and K.
  • If S is equal to K, print “Yes” along with the permutation. Otherwise, print “No”.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if there
// exists a permutation of a number
// A whose sum with A results to C
void checkPermutation(int a, int c)
{
    // Subtract a from c
    c -= a;

    // Check if c is less than 0
    if (c <= 0) {

        // If true, print "No"
        cout << "No";
        return;
    }

    // Otherwise, convert a to its
    // equivalent string
    string s = to_string(a);

    // convert c to its
    // equivalent string
    string k = to_string(c);

    // Sort string s
    sort(s.begin(), s.end());

    // Sort string k
    sort(k.begin(), k.end());

    // If both strings are equal,
    // then print "Yes"
    if (k == s) {
        cout << "Yes\n"
             << c;
    }

    // Otherwise, print "No"
    else {
        cout << "No";
    }
}

// Driver Code
int main()
{
    int A = 133, C = 446;
    checkPermutation(A, C);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to check if there
// exists a permutation of a number
// A whose sum with A results to C
static void checkPermutation(int a, int c)
{

    // Subtract a from c
    c -= a;

    // Check if c is less than 0
    if (c <= 0)
    {

        // If true, print "No"
        System.out.println("No");
        return;
    }

    // Otherwise, convert a to its
    // equivalent string
    String s = sortString(Integer.toString(a));

    // Convert c to its
    // equivalent string
    String k = sortString(Integer.toString(c));

    // If both strings are equal,
    // then print "Yes"
    if (k.equals(s))
    {
        System.out.println("Yes");
        System.out.println(c);
    }

    // Otherwise, print "No"
    else
    {
        System.out.println("No");
    }
}

// Method to sort a string alphabetically
public static String sortString(String inputString)
{

    // Convert input string to char array
    char tempArray[] = inputString.toCharArray();

    // sort tempArray
    Arrays.sort(tempArray);

    // Return new sorted string
    return new String(tempArray);
}

// Driver code
public static void main(String[] args)
{
    int A = 133, C = 446;

    checkPermutation(A, C);
}
}

// This code is contributed by offbeat

Python3

# Python3 program for the above approach

# Function to check if there
# exists a permutation of a number
# A whose sum with A results to C
def checkPermutation(a, c):
    # Subtract a from c
    c -= a

    # Check if c is less than 0
    if (c <= 0):
        # If true, print "No"
        print("No")
        return

    # Otherwise, convert a to its
    # equivalent string
    s = str(a)

    # convert c to its
    # equivalent string
    k = str(c)

    res = ''.join(sorted(s))

    # Sort string s
    s = str(res)

    # Sort string k
    res = ''.join(sorted(k))
    k = str(res)

    # If both strings are equal,
    # then print "Yes"
    if (k == s):
        print("Yes")
        print(c)

    # Otherwise, print "No"
    else:
        print("No")

# Driver Code
if __name__ == '__main__':
    A = 133
    C = 446
    checkPermutation(A, C)

    # This code is contributed by ipg2016107.

C#

// C# program for the above approach
using System;
class GFG
{

  // Function to check if there
  // exists a permutation of a number
  // A whose sum with A results to C
  static void checkPermutation(int a, int c)
  {

    // Subtract a from c
    c -= a;

    // Check if c is less than 0
    if (c <= 0) {

      // If true, print "No"
      Console.Write("No");
      return;
    }

    // Otherwise, convert a to its
    // equivalent string
    string s = a.ToString();

    // convert c to its
    // equivalent string
    string k = c.ToString();

    // Sort string s
    char[] arr = s.ToCharArray();
    Array.Sort(arr);

    // Sort string k
    char[] brr = k.ToCharArray();
    Array.Sort(brr);

    // If both strings are equal,
    // then print "Yes"
    if (String.Join("", brr) == String.Join("", arr)) {
      Console.Write("Yes\n" + c);
    }

    // Otherwise, print "No"
    else {
      Console.WriteLine("No");
    }
  }

  // Driver Code
  public static void Main()
  {
    int A = 133, C = 446;
    checkPermutation(A, C);
  }
}

// This code is contributed by ukasp.

Javascript

<script>

// javascript program for the above approach

// Function to check if there
// exists a permutation of a number
// A whose sum with A results to C
function checkPermutation(a, c)
{
    // Subtract a from c
    c -= a;

    // Check if c is less than 0
    if (c <= 0) {

        // If true, print "No"
        print("No");
        return;
    }

    // Otherwise, convert a to its
    // equivalent string
    var s = a.toString();

    // convert c to its
    // equivalent string
    var k = c.toString();

    // Sort string s
    s= s.split('').sort((a, b) => a.localeCompare(b)).join('');
   // sort(s);

    // Sort string k
    k = k.split('').sort((a, b) => a.localeCompare(b)).join('');
    //sort(k);

    // If both strings are equal,
    // then print "Yes"
    if (k == s) {
        document.write("Yes" + "<br>" + c);
    }

    // Otherwise, print "No"
    else {
        document.write("No");
    }
}

// Driver Code
    var A = 133, C = 446;
    checkPermutation(A, C);

</script>

Output:

Yes
313

Time Complexity: O((log₁₀A)*log (log₁₀A))
Auxiliary Space: O(log₁₀A)