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.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 // C++ program to find count of values // whose XOR with x is greater than x // and values are smaller than x #include 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; }

Java

 // 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

Python 3

 # 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

C#

 // 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.

PHP

 \$x)             \$count++;     return \$count; }        // Driver code     \$x = 10;     echo countValues(\$x);    // This code is contributed by anuj_67. ?>

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++

 // C++ program to find count of values // whose XOR with x is greater than x // and values are smaller than x #include 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; }

Java

 // 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

Python3

 # 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

C#

 // 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

PHP



Output :

5

Time complexity of this solution is O(Log x)

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