Maximum value of B less than A such that A ^ B = A + B

Given an integer A, the task is to find the maximum value possible(B) which is less than A, such that xor of these two numbers A and B is equal their sum, that is A ^ B = A + B.

Examples:

Input: A = 4
Output: 3
Explanation:
There are many such integers such that A ^ B = A + B
Some of this integers are –
4 ^ 3 = 4 + 3 = 7
4 ^ 2 = 4 + 2 = 6
4 ^ 1 = 4 + 1 = 5
4 ^ 0 = 4 + 0 = 4
Maximum of these values is 3



Input: 7
Output: 0
There is no integer except 0 such that A + B = A ^ B

Approach: The idea is to use the fact that A + B &= (A \wedge B) + 2*(A \& B) and to get the value of A + B = A \wedge B, the value of (A & B) must be equal to 0.

=> A & B = 0
=> B = ~A

For Example:

A = 4 (1 0 0)  
B = ~ A = (0 1 1) = 3 

Below is the implementation of the above approach:

Java

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// Java implmentation to find
// maximum value of B such that
// A ^ B = A + B
   
// Function to find the maximum
// value of B such that A^B = A+B
class GFG
{
  
static void maxValue(int a)
{
       
    // Binary Representation of A
    String c = Integer.toBinaryString(a);
      
    String b = "";
       
    // Loop to find the negation
    // of the integer A
    for (int i = 0; i < c.length(); i++)
    {
        if((c.charAt(i)-'0')==1)
            b +='0';
        else
            b+='1';
    }
       
    // output
    System.out.print(Integer.parseInt(b, 2));
     
}
   
// Driver Code
public static void main(String []args)
{
    int a = 4;
       
    // Function Call
    maxValue(a);
}
}
  
// This code is contributed by chitranayal

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Python

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# Python implmentation to find
# maximum value of B such that
# A ^ B = A + B
  
# Function to find the maximum
# value of B such that A^B = A+B
def maxValue(a):
      
    # Binary Representation of A
    a = bin(a)[2:]
      
    b = ''
      
    # Loop to find the negation
    # of the integer A
    for i in list(a):
        b += str(int(not int(i)))
          
    # output
    print(int(b, 2))
    return int(b, 2)
  
# Driver Code 
if __name__ == '__main__'
    a = 4
      
    # Function Call
    maxValue(a)

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C#

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// C# implmentation to find
// maximum value of B such that
// A ^ B = A + B
    
// Function to find the maximum
// value of B such that A^B = A+B
using System;
using System.Collections.Generic;
  
class GFG
{
   
static void maxValue(int a)
{
        
    // Binary Representation of A
    String c = Convert.ToString(a, 2);
       
    String b = "";
        
    // Loop to find the negation
    // of the integer A
    for (int i = 0; i < c.Length; i++)
    {
        if((c[i] - '0') == 1)
            b += '0';
        else
            b += '1';
    }
        
    // output
    Console.Write(Convert.ToInt32(b, 2));
      
}
    
// Driver Code
public static void Main(String []args)
{
    int a = 4;
        
    // Function Call
    maxValue(a);
}
}
  
// This code is contributed by 29AjayKumar

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Output:

3

Performance Analysis:

  • Time Complexity: In the above-given approach, there is conversion from decimal to binary which takes O(logN) time in worst case. Therefore, the time complexity for this approach will be O(logN).
  • Auxillary Space Complexity: In the above-given approach, there is no extra space used. Therefore, the auxillary space complexity for the above approach will be O(1)

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Improved By : chitranayal, 29AjayKumar