Application of XOR in algorithm

The XOR (Exclusive OR) operation returns true (1) if one or the other (but not both) is 1. Otherwise, it returns false (0).

Properties of XOR

1. Identity ?????????????????????? a ^ 0 = a
2. Self-Inverse ??????????????? a ^ a = 0
3. Associative ??????????????? ( a ^ b ) ^ c = a ^ ( b ^ c )
4. Commutative ???????????? a ^ b = b ^ a
5. Toggled bit value ?????? a ^ (1111)

Application of XOR

1) Swapping without variable

a = a ^ b????????? # XOR the bits and store the result in a????????

b = a ^ b ???????? # XOR the result with b and store it in b

a = a ^ b ???????? # XOR the result with a and store it in a

now a and b are swapped

2) Finding the single missing element in a sequence of number from 1 to n.

a = XOR of numbers from 1 …n

b = XOR of numbers from 1 to n, excluding one number c, where c ranges from 1 to n.

c = a ^ b

3) Finding a number in a sequence of numbers where only one number is repeated an odd number of times.

Example - 1,2,2,1,3,4,5,5,4 XOR of all numbers will return 3 as XORing even times a number return 0 and XORing a number with 0 return the number

4) Self-Inverse property is often utilized in algorithms where you need to cancel out pairs of identical elements.

plain text ^ key = cipher text

cipher text ^ key = plain text

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