使用大小为4的组中的元素的不同XOR查找数组

给定大小为N (N为4的倍数)的XOR查询的数组q [] ，该数组描述相同大小的数组，如下所示：

q[0 – 3] describe arr[0 – 3], q[4 – 7] describe arr[4 – 7], and so on… 
If arr[0 – 3] = {a1, a2, a3, a4} then 
q[0 – 3] = {a₁ ⊕ a₂ ⊕ a₃, a₁ ⊕ a₂ ⊕ a₄, a₁ ⊕ a₃ ⊕ a₄, a₂ ⊕ a₃ ⊕ a₄} 
 

当仅给出q []时，任务是查找原始数组arr []的值。
例子：

Input: q[] = {4, 1, 7, 0} 
Output: 2 5 3 6 
a₁ ⊕ a₂ ⊕ a₃ = 4 ⊕ 1 ⊕ 7 = 2 
a₁ ⊕ a₂ ⊕ a₄ = 4 ⊕ 1 ⊕ 0 = 5 
a₁ ⊕ a₃ ⊕ a₄ = 4 ⊕ 7 ⊕ 0 = 3 
a₂ ⊕ a₃ ⊕ a₄ = 1 ⊕ 7 ⊕ 0 = 6
Input: q[] = {4, 1, 7, 0, 8, 5, 1, 4} 
Output: 2 5 3 6 12 9 13 0 

方法：从xor的性质来看， a⊕a = 0和a⊕0 = a 。
(a⊕b)c)⊕(b⊕c⊕d)= a⊕d (As(b⊕c)⊕(b⊕c)= 0)
因此，我们将数组分为4个元素的组，对于每个组(a，b，c，d)，我们将
得到以下查询的结果：

1. a⊕b⊕c
2. a⊕b⊕d
3. a⊕c⊕d
4. b⊕c⊕d

As (a ⊕ b ⊕ c) ⊕ (b ⊕ c ⊕ d) = a ⊕ d, 
using this (a ⊕ d) we can get b and c from query 2 and 3 in the following manner: 
(a ⊕ b ⊕ d) ⊕ (a ⊕ d) = b 
(a ⊕ c ⊕ d) ⊕ (a ⊕ d) = c 
Then using b and c we can get a from query 1 and d from query 4 in the following way: 
(a ⊕ b ⊕ c) ⊕ (b) ⊕ (c) = a 
(b ⊕ c ⊕ d) ⊕ (b) ⊕ (c) = d 
This process will be repeated (iteratively) for all groups of 4 elements and we will get elements of all indices(ex.(a$_{1}$, a$_{2}$, a$_{3}$, a$_{4}$) then (a$_{5}$, a$_{6}$, a$_{7}$, a$_{8}$) etc.) 
 

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Utility function to print the contents of the array
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}
 
// Function to find the required array
void findArray(int q[], int n)
{
    int arr[n], ans;
    for (int k = 0, j = 0; j < n / 4; j++) {
        ans = q[k] ^ q[k + 3];
        arr[k + 1] = q[k + 1] ^ ans;
        arr[k + 2] = q[k + 2] ^ ans;
        arr[k] = q[k] ^ ((arr[k + 1]) ^ (arr[k + 2]));
        arr[k + 3] = q[k + 3] ^ (arr[k + 1] ^ arr[k + 2]);
        k += 4;
    }
 
    // Print the array
    printArray(arr, n);
}
 
// Driver code
int main()
{
    int q[] = { 4, 1, 7, 0 };
    int n = sizeof(q) / sizeof(q[0]);
    findArray(q, n);
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
     
    // Utility function to print
    // the contents of the array
    static void printArray(int []arr, int n)
    {
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");
    }
     
    // Function to find the required array
    static void findArray(int []q, int n)
    {
        int ans;
        int []arr = new int[n];
        for (int k = 0, j = 0;
                        j < n / 4; j++)
        {
            ans = q[k] ^ q[k + 3];
            arr[k + 1] = q[k + 1] ^ ans;
            arr[k + 2] = q[k + 2] ^ ans;
            arr[k] = q[k] ^ ((arr[k + 1]) ^
                             (arr[k + 2]));
            arr[k + 3] = q[k + 3] ^ (arr[k + 1] ^
                                     arr[k + 2]);
            k += 4;
        }
     
        // Print the array
        printArray(arr, n);
    }
     
    // Driver code
    public static void main(String args[])
    {
        int []q = { 4, 1, 7, 0 };
        int n = q.length;
        findArray(q, n);
    }
}
 
// This code is contributed
// by Akanksha Rai

Python3

# Python 3 implementation of the approach
 
# Utility function to print the
# contents of the array
def printArray(arr, n):
    for i in range(n):
        print(arr[i], end = " ")
 
# Function to find the required array
def findArray(q, n):
    arr = [None] * n
    k = 0
    for j in range(int(n / 4)):
        ans = q[k] ^ q[k + 3]
        arr[k + 1] = q[k + 1] ^ ans
        arr[k + 2] = q[k + 2] ^ ans
        arr[k] = q[k] ^ ((arr[k + 1]) ^
                         (arr[k + 2]))
        arr[k + 3] = q[k + 3] ^ (arr[k + 1] ^
                                 arr[k + 2])
        k += 4
 
    # Print the array
    printArray(arr, n)
 
# Driver code
if __name__ == '__main__':
    q = [4, 1, 7, 0]
    n = len(q)
    findArray(q, n)
 
# This code is contributed by
# Surendra_Gangwar

C#

// C# implementation of the approach
using System;
 
class GFG
{
     
    // Utility function to print
    // the contents of the array
    static void printArray(int []arr, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }
     
    // Function to find the required array
    static void findArray(int []q, int n)
    {
        int ans;
        int []arr = new int[n] ;
        for (int k = 0, j = 0; j < n / 4; j++)
        {
            ans = q[k] ^ q[k + 3];
            arr[k + 1] = q[k + 1] ^ ans;
            arr[k + 2] = q[k + 2] ^ ans;
            arr[k] = q[k] ^ ((arr[k + 1]) ^ (arr[k + 2]));
            arr[k + 3] = q[k + 3] ^ (arr[k + 1] ^ arr[k + 2]);
            k += 4;
        }
     
        // Print the array
        printArray(arr, n);
    }
     
    // Driver code
    public static void Main()
    {
        int []q = { 4, 1, 7, 0 };
        int n = q.Length ;
        findArray(q, n);
    }
}
 
// This code is contributed by Ryuga

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输出：

2 5 3 6

时间复杂度： O(N)
辅助空间： O(N)