Solution: Minimum One Bit Operations to Make Integers Zero

Let’s solve the Minimum One Bit Operations to Make Integers Zero problem using the Bitwise Manipulation pattern.

Statement

You are given an integer n. Your goal is to reduce it to 00 by repeatedly performing either of the following bit operations:

  • Flip the rightmost bit (bit at position 00) of n.

  • Flip the bit at position ii (for i>0i > 0) only if the bit at position i1i - 1 is 11 and all bits from position i2i - 2 down to 00 are set to 00.

Determine and return the minimum number of these operations required to reduce n to 00.

Constraints:

  • 00 \leqn 109\leq 10^9

Solution

First, we need to analyze how binary numbers can be manipulated using the two allowed operations:

  • Operation 1: Flip the rightmost (0th) bit at any time.

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