Solution: Minimum One Bit Operations to Make Integers Zero

Statement

You are given an integer n. Your goal is to reduce it to $0$ by repeatedly performing either of the following bit operations:

• Flip the rightmost bit (bit at position $0$) of n.

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

Determine and return the minimum number of these operations required to reduce n to $0$.

Constraints:

• $0 \leq$n $\leq 10^9$

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.

• Operation 2: Flip the bit at position $i$ (for $i > 0$) only if the bit at position $i - 1$ ...