使用XOR和表查找计算数字的奇偶校验

数字奇偶校验是指它是否包含奇数或偶数个1位。如果该数字包含奇数个1位，则具有“奇校验”，如果包含偶数个1位，则具有“偶校验”。

1 --> parity of the set is odd
0 --> parity of the set is even

例子：

Input : 254
Output : Odd Parity
Explanation : Binary of 254 is 11111110. 
There are 7 ones. Thus, parity is odd.

Input : 1742346774
Output : Even

方法1 ：(幼稚的方法)
我们已经在这里讨论了这种方法。

方法2：(有效)
条件：查表，X-OR魔术

如果我们将数字S分为两个部分S ₁和S ₂ ，则S = S ₁ S ₂ 。如果我们知道S ₁和S _2的奇偶性，则可以使用以下事实来计算S的奇偶性：

1. 如果S ₁和S ₂具有相同的奇偶校验，即它们都具有偶数个位数或奇数个位数，则它们的并集S将具有偶数个位数。
2. 因此，S的奇偶性是S ₁和S ₂的奇偶性的异或

这个想法是创建一个查找表来存储所有8位数字的奇偶校验。然后通过将整数除以8位数字并使用上述事实来计算整数的奇偶校验。

脚步：

1. Create a look-up table for 8-bit numbers ( 0 to 255 )
   Parity of 0 is 0.
   Parity of 1 is 1.
   .
   .
   .
   Parity of 255 is 0.
2. Break the number into 8-bit chunks
   while performing XOR operations.
3. Check for the result in the table for
    the 8-bit number.

由于32位或64位数字包含恒定的字节数，因此上述步骤需要O(1)时间。

例子 ：

1. Take 32-bit number : 1742346774

2. Calculate Binary of the number : 
   01100111110110100001101000010110

3. Split the 32-bit binary representation into 
  16-bit chunks :
0110011111011010 | 0001101000010110 

4. Compute X-OR :
  0110011111011010
^ 0001101000010110
___________________
= 0111110111001100

5. Split the 16-bit binary representation 
   into 8-bit chunks : 01111101 | 11001100

6. Again, Compute X-OR :
  01111101
^ 11001100
___________________
= 10110001
10110001 is 177 in decimal. Check
 for its parity in look-up table :
Even number of 1 = Even parity.

Thus, Parity of 1742346774 is even.

以下是适用于32位和64位数字的实现。

C++

// CPP program to illustrate Compute the parity of a
// number using XOR
#include 
  
// Generating the look-up table while pre-processing
#define P2(n) n, n ^ 1, n ^ 1, n
#define P4(n) P2(n), P2(n ^ 1), P2(n ^ 1), P2(n)
#define P6(n) P4(n), P4(n ^ 1), P4(n ^ 1), P4(n)
#define LOOK_UP P6(0), P6(1), P6(1), P6(0)
  
// LOOK_UP is the macro expansion to generate the table
unsigned int table[256] = { LOOK_UP };
  
// Function to find the parity
int Parity(int num)
{
    // Number is considered to be of 32 bits
    int max = 16;
  
    // Dividing the number into 8-bit
    // chunks while performing X-OR
    while (max >= 8) {
        num = num ^ (num >> max);
        max = max / 2;
    }
  
    // Masking the number with 0xff (11111111)
    // to produce valid 8-bit result
    return table[num & 0xff];
}
  
// Driver code
int main()
{
    unsigned int num = 1742346774;
  
    // Result is 1 for odd parity, 0 for even parity
    bool result = Parity(num);
  
    // Printing the desired result
    result ? std::cout << "Odd Parity" :
             std::cout << "Even Parity";
  
    return 0;
}

Python3

# Python3 program to illustrate Compute the 
# parity of a number using XOR 
  
# Generating the look-up table while 
# pre-processing 
def P2(n, table):
    table.extend([n, n ^ 1, n ^ 1, n])
def P4(n, table):
    return (P2(n, table), P2(n ^ 1, table), 
            P2(n ^ 1, table), P2(n, table))
def P6(n, table):
    return (P4(n, table), P4(n ^ 1, table),
            P4(n ^ 1, table), P4(n, table)) 
def LOOK_UP(table):
    return (P6(0, table), P6(1, table),
            P6(1, table), P6(0, table)) 
  
# LOOK_UP is the macro expansion to
# generate the table 
table = [0] * 256
LOOK_UP(table)
  
# Function to find the parity 
def Parity(num) :
  
    # Number is considered to be
    # of 32 bits 
    max = 16
  
    # Dividing the number o 8-bit 
    # chunks while performing X-OR 
    while (max >= 8): 
        num = num ^ (num >> max) 
        max = max // 2
  
    # Masking the number with 0xff (11111111) 
    # to produce valid 8-bit result 
    return table[num & 0xff] 
  
# Driver code 
if __name__ =="__main__":
    num = 1742346774
      
    # Result is 1 for odd parity, 
    # 0 for even parity 
    result = Parity(num)
    print("Odd Parity") if result else print("Even Parity")
  
  
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

PHP

= 8) 
    {
        $num = $num ^ ($num >> $max);
        $max = (int)$max / 2;
    }
  
    // Masking the number with 
    // 0xff (11111111) to produce
    // valid 8-bit result
    return $table[$num & 0xff];
}
  
// Driver code
$num = 1742346774;
  
// Result is 1 for odd 
// parity, 0 for even parity
$result = Parity($num);
  
// Printing the desired result
if($result == true)
        echo "Odd Parity" ;
    else
        echo"Even Parity";
  
// This code is contributed by ajit
?>

输出：

Even Parity

时间复杂度： O(1)。请注意，32位或64位数字具有固定的字节数(如果是32位，则为4，如果是64位，则为8)。