对按位XOR大于对中两个元素的对进行计数

给定大小为N的数组arr [] ，任务是计算按位XOR大于对中两个元素的对数。

例子：

Input: arr[] = {2, 4, 3}
Output: 2
Explanation: There are only 2 pairs whose Bitwise XOR is greater than both the elements in the pair:
1) (2, 4): Bitwise XOR = 2 ^ 4 = 6, which is greater than both 2 and 4.
2) (4, 3): Bitwise XOR = 4 ^ 3 = 7, which is greater than both 4 and 3.

Input: arr[] = {2, 2, 2}
Output: 0
Explanation:Since all array elements are the same, Bitwise XOR of all possible pairs is 0. Therefore, no such pair exists

方法：最简单的方法是从给定的数组中生成所有可能的对，并对那些按位XOR大于两个元素的对进行计数。仅检查一次所有对之后，打印计数。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function that counts the pairs whose
// Bitwise XOR is greater than both
// the elements of pair
void countPairs(int A[], int N)
{
    // Stores the count of pairs
    int count = 0;
 
    // Generate all possible pairs
    for (int i = 0; i < N; i++) {
 
        for (int j = i + 1; j < N; j++) {
 
            // Find the Bitwise XOR
            int xo = (A[i] ^ A[j]);
 
            // Find the maximum of two
            int mx = max(A[i], A[j]);
 
            // If xo < mx, increment count
            if (xo > mx) {
                count++;
            }
        }
    }
 
    // Print the value of count
    cout << count;
}
 
// Driver Code
int main()
{
    int arr[] = { 2, 4, 3 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    countPairs(arr, N);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.util.*;
 
class GFG{
 
// Function that counts the pairs whose
// Bitwise XOR is greater than both
// the elements of pair
static void countPairs(int[] A, int N)
{
     
    // Stores the count of pairs
    int count = 0;
 
    // Generate all possible pairs
    for(int i = 0; i < N; i++)
    {
        for(int j = i + 1; j < N; j++)
        {
             
            // Find the Bitwise XOR
            int xo = (A[i] ^ A[j]);
 
            // Find the maximum of two
            int mx = Math.max(A[i], A[j]);
 
            // If xo < mx, increment count
            if (xo > mx)
            {
                count++;
            }
        }
    }
 
    // Print the value of count
    System.out.println(count);
}
 
// Driver Code
public static void main(String[] args)
{
    int[] arr = { 2, 4, 3 };
 
    int N = arr.length;
     
    // Function Call
    countPairs(arr, N);
}
}
 
// This code is contributed by akhilsaini

Python3

# Python3 program for the above approach
 
# Function that counts the pairs whose
# Bitwise XOR is greater than both
# the elements of pair
def countPairs(A, N):
     
    # Stores the count of pairs
    count = 0
 
    # Generate all possible pairs
    for i in range(0, N):
        for j in range(i + 1, N):
             
            # Find the Bitwise XOR
            xo = (A[i] ^ A[j])
 
            # Find the maximum of two
            mx = max(A[i], A[j])
 
            # If xo < mx, increment count
            if (xo > mx):
                count += 1
 
    # Print the value of count
    print(count)
 
# Driver Code
if __name__ == '__main__':
 
    arr = [ 2, 4, 3 ]
 
    N = len(arr)
 
    # Function Call
    countPairs(arr, N)
 
# This code is contributed by akhilsaini

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function that counts the pairs whose
// Bitwise XOR is greater than both
// the elements of pair
static void countPairs(int[] A, int N)
{
     
    // Stores the count of pairs
    int count = 0;
 
    // Generate all possible pairs
    for(int i = 0; i < N; i++)
    {
        for(int j = i + 1; j < N; j++)
        {
             
            // Find the Bitwise XOR
            int xo = (A[i] ^ A[j]);
 
            // Find the maximum of two
            int mx = Math.Max(A[i], A[j]);
 
            // If xo < mx, increment count
            if (xo > mx)
            {
                count++;
            }
        }
    }
 
    // Print the value of count
    Console.WriteLine(count);
}
 
// Driver Code
public static void Main()
{
    int[] arr = { 2, 4, 3 };
 
    int N = arr.Length;
 
    // Function Call
    countPairs(arr, N);
}
}
 
// This code is contributed by akhilsaini

输出：

2

时间复杂度： O(N ² )
辅助空间： O(1)

高效方法：为了优化上述方法，我们的想法是使用位操作。考虑X = A ^ B和A 和设K是数A的最高有效位现在，如果X是比元件A和B两者，当且仅当K个B的^第i位是0时。如果K个整数的^第i位是0已经，然后计算，使得^第K位的MSB位的其它整数的数字。步骤如下：

• 初始化变量计数以存储对的计数和一个数组，该数组的大小为32 [bits] ，然后对给定的数组进行排序。
• 遍历数组 并执行以下操作：
  • 如果当前元素为0，则检查下一个元素。
  • 否则，遍历当前元素的所有位，并且如果位置j的任何位被设置，则将计数增加bit [j] 。
  • 完成上述步骤后，将bit [log ₂ (当前元素)]更新为1 。
• 完成上述步骤后，将计数值打印为结果。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to count pairs whose XOR
// is greater than the pair itself
void countPairs(int A[], int N)
{
    // Stores the count of pairs
    int count = 0;
 
    // Sort the array
    sort(A, A + N);
 
    int bits[32] = { 0 };
 
    // Traverse the array
    for (int i = 0; i < N; i++) {
 
        // If current element is 0,
        // then ignore it
        if (A[i] == 0) {
            continue;
        }
 
        // Traverse all the bits of
        // element A[i]
        for (int j = 0; j < 32; j++) {
 
            // If current bit is set
            // then update the count
            if (!((1LL << j) & A[i])) {
                count += bits[j];
            }
        }
 
        // Update bits[] at the most
        // significant bit of A[i]
        ++bits[(int)(log2l(A[i]))];
    }
 
    // Print the count
    cout << count;
}
 
// Driver Code
int main()
{
    int arr[] = { 2, 4, 3 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    countPairs(arr, N);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.util.*;
 
class GFG{
 
// Function to count pairs whose XOR
// is greater than the pair itself
static void countPairs(int[] A, int N)
{
     
    // Stores the count of pairs
    int count = 0;
 
    // Sort the array
    Arrays.sort(A);
 
    int[] bits = new int[32];
 
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // If current element is 0,
        // then ignore it
        if (A[i] == 0)
        {
            continue;
        }
 
        // Traverse all the bits of
        // element A[i]
        for(int j = 0; j < 32; j++)
        {
             
            // If current bit is set
            // then update the count
            if (((1 << j) & A[i]) == 0)
            {
                count += bits[j];
            }
        }
 
        // Update bits[] at the most
        // significant bit of A[i]
        ++bits[(int)((int)(Math.log(A[i]) /
                           Math.log(2)))];
    }
 
    // Print the count
    System.out.println(count);
}
 
// Driver Code
public static void main(String[] args)
{
    int[] arr = { 2, 4, 3 };
 
    int N = arr.length;
 
    // Function Call
    countPairs(arr, N);
}
}
 
// This code is contributed by akhilsaini

Python3

# Python3 program for the above approach
import math
 
# Function to count pairs whose XOR
# is greater than the pair itself
def countPairs(A, N):
     
    # Stores the count of pairs
    count = 0
 
    # Sort the array
    A.sort()
 
    bits = [0] * 32
 
    # Traverse the array
    for i in range(0, N):
 
        # If current element is 0,
        # then ignore it
        if (A[i] == 0):
            continue
 
        # Traverse all the bits of
        # element A[i]
        for j in range(0, 32):
 
            # If current bit is set
            # then update the count
            if (((1 << j) & A[i]) == 0):
                count += bits[j]
 
        # Update bits[] at the most
        # significant bit of A[i]
        bits[(int)(math.log(A[i], 2))] += 1
 
    # Print the count
    print(count)
 
# Driver Code
if __name__ == '__main__':
 
    arr = [ 2, 4, 3 ]
 
    N = len(arr)
 
    # Function Call
    countPairs(arr, N)
 
# This code is contributed by akhilsaini

C＃

// C# program for the above approach
using System;
 
class GFG{
 
// Function to count pairs whose XOR
// is greater than the pair itself
static void countPairs(int[] A, int N)
{
     
    // Stores the count of pairs
    int count = 0;
 
    // Sort the array
    Array.Sort(A);
 
    int[] bits = new int[32];
 
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // If current element is 0,
        // then ignore it
        if (A[i] == 0)
        {
            continue;
        }
 
        // Traverse all the bits of
        // element A[i]
        for(int j = 0; j < 32; j++)
        {
             
            // If current bit is set
            // then update the count
            if (((1 << j) & A[i]) == 0)
            {
                count += bits[j];
            }
        }
 
        // Update bits[] at the most
        // significant bit of A[i]
        ++bits[(int)((int)(Math.Log(A[i]) /
                           Math.Log(2)))];
    }
 
    // Print the count
    Console.WriteLine(count);
}
 
// Driver Code
public static void Main()
{
    int[] arr = { 2, 4, 3 };
 
    int N = arr.Length;
 
    // Function Call
    countPairs(arr, N);
}
}
 
// This code is contributed by akhilsaini

输出：

2

时间复杂度： O(N * log N)
辅助空间： O(1)