Bitwise operators are an essential asset in competitive programming for enabling efficiently fast manipulations of bits in variables.
However, bitwise operations are the go-to solution with milliseconds determining the difference between answers in coding competitions for an optimized performance.
Following are the top 10 uses of bitwise operators:
What Are Bitwise Operators?
Operations that manipulate the bits of integer variables directly are Bitwise Operators.
There is a common bitwise operator including AND (`&`), OR (`|`), XOR (`^`), NOT (`~`), left shift (`<<`), and right shift (`>>`).
Bitwise operations differ from regular arithmetic operations. They handle low-level manipulations of binary data that lead to efficiently faster algorithms.
Fast Arithmetic Using Bitwise Operators
Out of many, one primary use of bitwise operators in competitive programming is to perform faster arithmetic.
The left shift (`<<`) multiplies a number by 2, and the right shift (`>>`) divides it by 2—operations that are faster than arithmetic counterparts.
For instance, multiplying a number `x` by 8 can be done with `x << 3`, which is faster than `x * 8`.
This is well suited for solutions during crucial times like counting every microsecond.
Efficient Power Calculation
Bitwise operations have made calculating powers of two easy for example, `1 << n` gives you `2^n`.
The method is often used in bitmasking problems like dealing with subsets and also to represent a binary state collection.
It is a popular technique in competitive programming due to its capability of determining the power of two.
Swapping Two Numbers Without a Temporary Variable
A clever trick in coding contests is swapping two numbers using bitwise XOR.
Operators can swap `a` and `b` without a third variable by using the below code:
“`cpp
a = a ^ b;
b = a ^ b;
a = a ^ b;
“`
Moreover, it is a fast and memory-saving valuable technique till now.
Detecting Even or Odd Numbers
The bitwise AND operation is employed for determining a number as odd or even.
The number is taken as even, if the result of `n & 1` is `0`, otherwise, it is odd.
It is the most efficient trick instead of modulus operations and more beneficial in tight loops or recursive functions.
Bit masking for Subset Generation
Among all bitmask is the most commonly used bitwise operator in competitive programming.
Bitmasking allows the generalization of all possible subsets. It uses binary number treatment for each subset.
You can loop through all `2^n` subsets by implying a simple bitmask approach for each bit where exclusion and inclusion of an element take place and attain a set of size `n`.
Counting Set Bits
It is a frequent task to count the number of set bits (1s) in many algorithms in a number’s binary representation but performed efficiently with bitwise AND (`&`).
Brian Kernighan’s algorithm is the commonly used method to reduce the number of set bits in a number by one in each iteration:
“`cpp
while (n) {
n = n & (n – 1);
count++;
}
“`
An approach that runs in O(number of set bits) time, for faster than iteration of each bit individually.
Toggle a Specific Bit
A common operation is toggling a specific bit that either changes from 0 to 1 or 1 to 10.
However, it is done through the XOR operator for eg, toggling the `k`th but of a number ‘n’.
It can be employed ‘n = n ^ (1 << k) as an operation.
Finding the Highest Power of Two Less Than or Equal to a Given Number
Bitwise operations can be implied for finding the highest power of two less than or equal to a given number `n`.
Commonly it shifts bits and manipulates the binary representation of `n` which can be faster by multiplying values.
Checking if a Number is a Power of Two
An elegantly faster bitwise operation for checking a number being a power of two is—n `n & (n – 1)` equals zero if `n` is a power of two, as it has one set bit in the binary representation.
Modulo Operation Using Bitwise AND
Modulo operation optimizes by using bitwise AND for numbers that are powers of two. Use `n & (m – 1)` instead of `n % m`.
Conclusion
Bitwise operators have a diverse range making it essential in competitive programming. One can leverage these to compete in coding with efficiency and reliability.
Additionally, if you’re looking to indulge more then doing Full stack Python training is a good-to-go option.
