Find an anagram of a number A that generates a sum C when added to A

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Given two positive integers A and C, the task is to check if a number B exists such that A + B = C and B is an anagram of A. If found to be true, then print “YES”. Otherwise, print “NO”.

Input: A = 123, C = 354
Output: YES
Explanation:
231 is an anagram of A and 123 + 231 = 354
Therefore, the required output is “YES”.

Input: A = 123, C = 234
Output: NO

Naive Approach: The simplest approach to solve the problem is to generate all possible permutations of digits of A and check if the sum of A and the current permutation of digits of A is equal to C or not. If found to be true, then print “YES”. Otherwise, if no such permutation is found, print “NO”.

Time Complexity: O(log₁₀(N)!)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the following observations:

A + B = C
B = C – A

Follow the steps below to solve the problem:

Check if (C – A) is an anagram of A or not. If found to be true, then print “YES”.
Otherwise, print “NO”.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if an integer B exists
// such that A + B = C and B is an anagram of A
void CheckExistsABCAnagramOfA(int A, int C)
{
 
    int B = C - A;
 
    // Stores A in string format
    string a = to_string(A);
 
    // Stores B in string format
    string b = to_string(B);
 
    // Sort both the strings
    sort(a.begin(), a.end());
    sort(b.begin(), b.end());
 
    // Checks if both strings
    // are equal
    if (a == b) {
        cout << "YES\n";
    }
    else {
        cout << "NO\n";
    }
}
 
// Drivers Code
int main()
{
    int A = 123, C = 354;
    CheckExistsABCAnagramOfA(A, C);
}

Java

// Java program to implement
// the above approach
import java.util.*;
class GFG
{
 
// Function to check if an integer B exists
// such that A + B = C and B is an anagram of A
static void CheckExistsABCAnagramOfA(int A, int C)
{
    int B = C - A;
 
    // Stores A in String format
    String a = String.valueOf(A);
 
    // Stores B in String format
    String b = String.valueOf(B);
 
    // Sort both the Strings
    a = sortString(a);
    b = sortString(b);
 
    // Checks if both Strings
    // are equal
    if (a.equals(b)) 
    {
        System.out.print("YES\n");
    }
    else
    {
        System.out.print("NO\n");
    }
}
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); 
} 
   
// Drivers Code
public static void main(String[] args)
{
    int A = 123, C = 354;
    CheckExistsABCAnagramOfA(A, C);
}
}
 
// This code is contributed by shikhasingrajput

Python3

# Python3 program to implement the above
# approach 
 
# Function to check if an integer B exists
# such that A + B = C and B is an anagram of A
def CheckExistsABCAnagramOfA(A, C):
     
    B = C - A
 
    # To convert number to list of integers 
    a = [int(x) for x in str(A)] 
 
    # To convert number to list of integers 
    b = [int(x) for x in str(B)] 
 
    # Sort both the strings
    a.sort()
    b.sort()
 
    # Checks if both strings
    # are equal
    if (a == b):
        print("YES")
    else:
        print("NO")
     
# Driver Code
A = 123
C = 354
 
CheckExistsABCAnagramOfA(A, C)
 
# This code is contributed by sanjoy_62

C#

// C# program to implement
// the above approach
using System;
 
class GFG{
     
// Function to check if an integer B 
// exists such that A + B = C and B 
// is an anagram of A
static void CheckExistsABCAnagramOfA(int A, int C)
{
    int B = C - A;
     
    // Stores A in String format
    String a = String.Join("", A);
     
    // Stores B in String format
    String b = String.Join("", B);
     
    // Sort both the Strings
    a = sortString(a);
    b = sortString(b);
 
    // Checks if both Strings
    // are equal
    if (a.Equals(b)) 
    {
        Console.Write("YES\n");
    }
    else
    {
        Console.Write("NO\n");
    }
}
 
static String sortString(String inputString) 
{ 
     
    // Convert input string to char array 
    char []tempArray = inputString.ToCharArray(); 
     
    // Sort tempArray 
    Array.Sort(tempArray); 
     
    // Return new sorted string 
    return new String(tempArray); 
} 
 
// Driver Code
public static void Main(String[] args)
{
    int A = 123, C = 354;
     
    CheckExistsABCAnagramOfA(A, C);
}
}
 
// This code is contributed by shikhasingrajput

Javascript

<script>
 
// JavaScript program to implement
// the above approach
 
// Function to check if an integer B exists
// such that A + B = C and B is an anagram of A
function CheckExistsABCAnagramOfA(A, C)
{
 
    var B = C - A;
 
    // Stores A in string format
    var a = (A.toString());
 
    // Stores B in string format
    var b = (B.toString());
 
    // Sort both the strings
    a = a.split('').sort().join('');
    b = b.split('').sort().join('');
 
    // Checks if both strings
    // are equal
    if (a == b) {
        document.write( "YES");
    }
    else {
        document.write( "NO");
    }
}
 
// Drivers Code
var A = 123, C = 354;
CheckExistsABCAnagramOfA(A, C);
 
</script>

Output:

YES

Time Complexity: O(log₁₀(A)*log(log₁₀(A)))
Auxiliary Space: O(log₁₀(A))

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