Count smaller values whose XOR with x is greater than x

Given a integer ‘x’, find the number of values of ‘a’ satisfying the following conditions:

  1. a XOR x > x
  2. 0 < a < x

Examples :

Input : x = 10 
Output : 5
Explanation: For x = 10, following 5 values
             of 'a' satisfy the conditions:
             1 XOR 10 = 11
             4 XOR 10 = 14
             5 XOR 10 = 15
             6 XOR 10 = 12
             7 XOR 10 = 13 

Input : x = 2
Output : 1
Explanation: For x=2, we have just one value
             1 XOR 2 = 3.



Naive Approach
A Simple approach is to check for all values of ‘a’ between 0 and ‘x’ and calculate its XOR with x
and check if the condition 1 satisfies.

C++

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// C++ program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
#include<bits/stdc++.h>
using namespace std;
  
int countValues(int x)
{
    int count = 0;
    for (int i=1; i < x; i++)
        if ((i ^ x) > x)
            count++;
    return count;
}
  
// Driver code
int main()
{
    int x = 10;
    cout << countValues(x);
    return 0;
}

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Java

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// Java program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
  
public class XOR
{
    static int countValues(int x)
    {
        int count = 0;
        for (int i=1; i < x; i++)
            if ((i ^ x) > x)
                count++;
        return count;
    }
      
    public static void main (String[] args)
    {
        int x = 10;
        System.out.println(countValues(x));
    }
}
  
// This code is contributed by Saket Kumar

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Python 3

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# Python3 program to find 
# count of values whose
# XOR with x is greater
# than x and values are 
# smaller than x
  
def countValues(x):
  
    count = 0
    for i in range(1 ,x):
        if ((i ^ x) > x):
            count += 1
    return count
  
# Driver code
x = 10
print(countValues(x))
  
# This code is contributed 
# by Smitha

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C#

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// C# program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
using System;
  
class GFG
{
    static int countValues(int x)
    {
        int count = 0;
        for (int i = 1; i < x; i++)
            if ((i ^ x) > x)
                count++;
        return count;
    }
      
    public static void Main ()
    {
        int x = 10;
        Console.Write(countValues(x));
    }
}
  
// This code is contributed by nitin mittal.

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PHP

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<?php
// PHP program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
  
function countValues($x)
{
    $count = 0;
    for ($i = 1; $i < $x; $i++)
        if (($i ^ $x) > $x)
            $count++;
    return $count;
}
  
    // Driver code
    $x = 10;
    echo countValues($x);
  
// This code is contributed by anuj_67.
?>

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Output :

5

The time complexity of the above approach is O(x).

Efficient Approach
The efficient solution lies in the binary representation of the number. We consider all 0’s in binary representation. For every 0 at the i-th position, we can have 2i numbers smaller than or equal to x with greater XOR.

C++

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// C++ program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
#include<bits/stdc++.h>
using namespace std;
  
int countValues(int x)
{
    // Initialize result
    int count = 0, n = 1;
  
    // Traversing through all bits of x
    while (x != 0)
    {
        // If current last bit of x is set
        // then increment count by n. Here
        // n is a power of 2 corresponding
        // to position of bit
        if (x%2 == 0)
            count += n;
  
        // Simultaneously calculate the 2^n
        n *= 2;
  
        // Replace x with x/2;
        x /= 2;
    }
  
    return count;
}
  
// Driver code
int main()
{
    int x = 10;
    cout << countValues(x);
    return 0;
}

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Java

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// Java program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
  
class GFG
{
    static int countValues(int x)
    {
        // Initialize result
        int count = 0, n = 1;
          
        // Traversing through all bits of x
        while (x != 0)
        {
            // If current last bit of x is set
            // then increment count by n. Here
            // n is a power of 2 corresponding
            // to position of bit
            if (x % 2 == 0)
                count += n;
                  
            // Simultaneously calculate the 2^n
            n *= 2;
              
            // Replace x with x/2;
            x /= 2;
        }
        return count;
    }
      
    // Driver code
    public static void main (String[] args)
    {
        int x = 10;
        System.out.println(countValues(x));
    }
      
}
  
// This code is contributed by Saket Kumar

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Python3

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# Python3 program to find count
# of values whose XOR with
# x is greater than x and 
# values are smaller than x
  
def countValues(x):
      
    # Initialize result
    count = 0;
    n = 1;
  
    # Traversing through 
    # all bits of x
    while (x > 0):
          
        # If current last bit 
        # of x is set then
        # increment count by 
        # n. Here n is a power
        # of 2 corresponding
        # to position of bit
        if (x % 2 == 0):
            count += n;
  
        # Simultaneously 
        # calculate the 2^n
        n *= 2;
  
        # Replace x with x/2;
        x /= 2;
        x = int(x);
  
    return count;
  
# Driver code
x = 10;
print(countValues(x));
  
# This code is contributed
# by mits

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C#

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// C# program to find count of values
// whose XOR with x is greater than x
// and values are smaller than x
using System;
  
class GFG
{
    static int countValues(int x)
    {
        // Initialize result
        int count = 0, n = 1;
          
        // Traversing through all bits of x
        while (x != 0)
        {
            // If current last bit of x is set
            // then increment count by n. Here
            // n is a power of 2 corresponding
            // to position of bit
            if (x % 2 == 0)
                count += n;
                  
            // Simultaneously calculate the 2^n
            n *= 2;
              
            // Replace x with x/2;
            x /= 2;
        }
        return count;
    }
      
    // Driver code
    public static void Main ()
    {
        int x = 10;
        Console.Write(countValues(x));
    }
      
}
  
// This code is contributed by nitin mittal

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PHP

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<?php
// PHP program to find count
// of values whose XOR with
// x is greater than x and 
// values are smaller than x
  
function countValues($x)
{
      
    // Initialize result
    $count = 0;
    $n = 1;
  
    // Traversing through 
    // all bits of x
    while ($x != 0)
    {
        // If current last bit 
        // of x is set then
        // increment count by 
        // n. Here n is a power
        // of 2 corresponding
        // to position of bit
        if ($x % 2 == 0)
            $count += $n;
  
        // Simultaneously 
        // calculate the 2^n
        $n *= 2;
  
        // Replace x with x/2;
        $x /= 2;
        $x = (int)$x;
    
  
    return $count;
}
  
// Driver code
$x = 10;
echo countValues($x);
  
// This code is contributed
// by Smitha
?>

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Output :

5

Time complexity of this solution is O(Log x)

This article is contributed by DANISH KALEEM. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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