What is the brute force approach and complexity for Reverse Bits?

Write 32 characters of 0 and 1, reverse the string, read it back as a number with time complexity O(32) and space complexity O(32).

What is the optimal approach and complexity for Reverse Bits?

Read n's bits from the bottom and place each one at the top of res, for exactly 32 steps with optimal time complexity O(32) and space complexity O(1).

How do you identify the pattern for Reverse Bits?

Look for key signals in the prompt: "reverse the bits" indicates Bit `i` must move to position `31 − i`, so the bits are moved one by one.; "32 bits, signed integer" indicates The width is fixed, so exactly 32 steps are right, including the zeros.; "called many times (follow-up)" indicates A lookup table for bytes is the usual speed-up. It is not needed for the main answer..

Reverse Bits

Easy·LeetCode #190 Pro OnlyMedium

LeetCode

Problem Statement

Take the 32 bits of n and put them in the opposite order. Bit 0 moves to position 31, bit 1 moves to position 30, and so on. Return the number that the reversed bits form.

Follow-up: if this function is called many times, how would you speed it up?

Input

An integer n, written in 32 bits (leading zeros count).

Output

The integer formed by the 32 reversed bits.

Example 1

Input: n = 43261596

Output: 964176192

In 32 bits, 43261596 is 00000010100101000001111010011100. Reversed, it is 00111001011110000010100101000000, which is 964176192.

Example 2

Input: n = 2147483644

Output: 1073741822

In 32 bits, it is 01111111111111111111111111111100. Reversed, it is 00111111111111111111111111111110, which is 1073741822.

Constraints

• 0 ≤ n ≤ 2^31 − 2
• n is even

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“reverse the bits”

→ Bit `i` must move to position `31 − i`, so the bits are moved one by one.

“32 bits, signed integer”

→ The width is fixed, so exactly 32 steps are right, including the zeros.

“called many times (follow-up)”

→ A lookup table for bytes is the usual speed-up. It is not needed for the main answer.

Approach Complexity Ladder

Brute Force — reverse the textO(32)O(32)

Write 32 characters of 0 and 1, reverse the string, read it back as a number

Optimal — move each bit to its mirror placeO(32)O(1)

Read n's bits from the bottom and place each one at the top of res, for exactly 32 steps

Brute Force Intuition

Turn n into a 32-character string of 0s and 1s, reverse the string, and parse it back as a binary number. Each step is easy to check by eye.

Recognition rule for this sub-pattern:

n & (n−1) removes the lowest set bit; shifts read bits one at a time.

Remember this · Bit Manipulation

Trigger

"Every element appears twice except…", power of two, counting set bits, subsets as bitmasks, O(1) space tricks.

Think

What happens to this problem if I look at each bit separately?

Key question

Which bit operation (XOR, AND, OR, shift) cancels or isolates what I need?

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