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📜  计数具有奇数按位异或的子数组

📅  最后修改于: 2021-04-17 17:48:10             🧑  作者: Mango

给定大小为N的数组arr [] ,任务是计算给定数组中具有奇数按位XOR值的子数组的数量。

例子:

天真的方法:解决此问题的最简单方法是检查每个子数组的按位XOR是否为奇数。如果发现是奇数,则增加计数。最后,将计数打印为结果。

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,该想法基于以下观察结果:仅当子数组中奇数元素的数量为奇数时,子数组的按位XOR才为奇数。要解决该问题,请找到从索引0开始并满足给定条件的子数组的数量。然后,遍历数组并更新从索引i开始的满足给定条件的子数组的数量。请按照以下步骤解决问题:

  • 将变量OddC_odd初始化为0 ,以分别存储直到i索引的奇数个数和从i索引开始的所需子数组的个数。
  • 使用变量i遍历数组arr []并检查以下步骤:
    • 如果arr [i]的值是奇数,则将Odd的值更新为!Odd
    • 如果Odd的值不为零则将C_odd递增1
  • 再次,使用变量i遍历数组arr []并执行以下操作:
    • C_odd的值添加到变量res
    • 如果arr [i]的值是奇数,则将C_odd的值更新为(N – i – C_odd)
  • 完成上述步骤后,打印res的值作为结果。

下面是上述方法的实现:

C++
// C++ program for the above approach
#include 
using namespace std;
 
// Function to count the number of subarrays
// of the given array having odd Bitwise XOR
void oddXorSubarray(int a[], int n)
{
    // Stores number of odd
    // numbers upto i-th index
    int odd = 0;
 
    // Stores number of required
    // subarrays starting from i-th index
    int c_odd = 0;
 
    // Store the required result
    int result = 0;
 
    // Find the number of subarrays having odd
    // Bitwise XOR values starting at 0-th index
    for (int i = 0; i < n; i++) {
 
        // Check if current element is odd
        if (a[i] & 1) {
            odd = !odd;
        }
 
        // If the current value of odd is not
        // zero, increment c_odd by 1
        if (odd) {
            c_odd++;
        }
    }
 
    // Find the number of subarrays having odd
    // bitwise XOR value starting at ith index
    // and add to result
    for (int i = 0; i < n; i++) {
 
        // Add c_odd to result
        result += c_odd;
        if (a[i] & 1) {
            c_odd = (n - i - c_odd);
        }
    }
 
    // Print the result
    cout << result;
}
 
// Driver Code
int main()
{
    // Given array
    int arr[] = { 1, 4, 7, 9, 10 };
 
    // Stores the size of the array
    int N = sizeof(arr) / sizeof(arr[0]);
 
    oddXorSubarray(arr, N);
 
    return 0;
}


Java
// Java program for the above approach
import java.io.*;
class GFG
{
        
// Function to count the number of subarrays
// of the given array having odd Bitwise XOR
static void oddXorSubarray(int a[], int n)
{
   
    // Stores number of odd
    // numbers upto i-th index
    int odd = 0;
 
    // Stores number of required
    // subarrays starting from i-th index
    int c_odd = 0;
 
    // Store the required result
    int result = 0;
 
    // Find the number of subarrays having odd
    // Bitwise XOR values starting at 0-th index
    for (int i = 0; i < n; i++)
    {
 
        // Check if current element is odd
        if (a[i] % 2 != 0)
        {
            odd = (odd == 0) ? 1 : 0;
        }
 
        // If the current value of odd is not
        // zero, increment c_odd by 1
        if (odd != 0)
        {
            c_odd++;
        }
    }
 
    // Find the number of subarrays having odd
    // bitwise XOR value starting at ith index
    // and add to result
    for (int i = 0; i < n; i++)
    {
 
        // Add c_odd to result
        result += c_odd;
        if (a[i] % 2 != 0)
        {
            c_odd = (n - i - c_odd);
        }
    }
 
    // Print the result
    System.out.println(result);
}
 
// Driver Code
public static void main (String[] args)
{
     
      // Given array
    int arr[] = { 1, 4, 7, 9, 10 };
 
    // Stores the size of the array
    int N = arr.length;
    oddXorSubarray(arr, N);
}
}
 
// This code is contributed by Dharanendra L V.


Python3
# Python3 program for the above approach
 
# Function to count the number of subarrays
# of the given array having odd Bitwise XOR
def oddXorSubarray(a, n):
   
    # Stores number of odd
    # numbers upto i-th index
    odd = 0
 
    # Stores number of required
    # subarrays starting from i-th index
    c_odd = 0
 
    # Store the required result
    result = 0
 
    # Find the number of subarrays having odd
    # Bitwise XOR values starting at 0-th index
    for i in range(n):
 
        # Check if current element is odd
        if (a[i] & 1):
            odd = not odd
         
        # If the current value of odd is not
        # zero, increment c_odd by 1
        if (odd):
            c_odd += 1
 
    # Find the number of subarrays having odd
    # bitwise XOR value starting at ith index
    # and add to result
    for i in range(n):
 
        # Add c_odd to result
        result += c_odd
        if (a[i] & 1):
            c_odd = (n - i - c_odd)
 
    # Prthe result
    print (result)
 
# Driver Code
if __name__ == '__main__':
     
    # Given array
    arr = [1, 4, 7, 9, 10]
 
    # Stores the size of the array
    N = len(arr)
    oddXorSubarray(arr, N)
 
    # This code is contributed by mohit kumar 29.


C#
// C# program for the above approach
using System;
 
class GFG{
        
// Function to count the number of subarrays
// of the given array having odd Bitwise XOR
static void oddXorSubarray(int []a, int n)
{
     
    // Stores number of odd
    // numbers upto i-th index
    int odd = 0;
 
    // Stores number of required
    // subarrays starting from i-th index
    int c_odd = 0;
 
    // Store the required result
    int result = 0;
 
    // Find the number of subarrays having
    // odd Bitwise XOR values starting at
    // 0-th index
    for(int i = 0; i < n; i++)
    {
         
        // Check if current element is odd
        if (a[i] % 2 != 0)
        {
            odd = (odd == 0) ? 1 : 0;
        }
 
        // If the current value of odd is not
        // zero, increment c_odd by 1
        if (odd != 0)
        {
            c_odd++;
        }
    }
 
    // Find the number of subarrays having odd
    // bitwise XOR value starting at ith index
    // and add to result
    for(int i = 0; i < n; i++)
    {
         
        // Add c_odd to result
        result += c_odd;
         
        if (a[i] % 2 != 0)
        {
            c_odd = (n - i - c_odd);
        }
    }
 
    // Print the result
    Console.WriteLine(result);
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given array
    int []arr = { 1, 4, 7, 9, 10 };
 
    // Stores the size of the array
    int N = arr.Length;
    oddXorSubarray(arr, N);
}
}
 
// This code is contributed by 29AjayKumar


输出:
8

时间复杂度: O(N)
辅助空间: O(1)