Explore bitwise operations for problem-solving and algorithm optimization.

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Bitwise Manipulation

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Behavioral

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## Statement
Given an unsigned 32-bit integer `n`, we need to calculate a 32-bit unsigned integer with reversed bits. When we say “reverse” we don’t mean flipping the $0$s to $1$s and vice versa, but simply reversing the order in which they appear, i.e., from left-to-right to right-to-left.

**Constraints:**

* $0 \leq$ `n` $\leq 2^{32}$

## Solution

We start by initializing a variable `result` to $0$, which will hold the 32-bit unsigned integer obtained by reversing the bits of the input integer `n`. We start from the rightmost bit (i.e., the least significant bit) of `n`, iterate through each bit, and reverse it. In each iteration, we left shift the `result` by $1$ position, effectively making room for the next bit to be added, and then extract the rightmost bit from `n` using a bitwise AND (`&`) operation with $1$. This operation sets all bits of `n` to $0$ except for the rightmost bit, which is either $0$ or $1$.

After extracting the rightmost bit, we OR (`|`) it with the `result` to effectively add the extracted bit to the reversed `result`. We now right shift the original number `n` by $1$ position, effectively removing the already processed rightmost bit.

We continue the process until all bits in `n` have been reversed and are saved in the `result`. Now, return the `result` variable.

Now, let’s look at the following illustration to get a better understanding of the solution:

Let's solve the Reverse Bits problem using the Bitwise Manipulation pattern.


Solution: Reverse Bits

Let's solve the Reverse Bits problem using the Bitwise Manipulation pattern.

Solution: Reverse Bits

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Solution: Reverse Bits

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