Consecutive Ones - The Setup

Convert $n$ to binary. Now each "digit" is $0$ or $1$. At each position, you choose $0$ or $1$ (subject to tight bound). The constraint: no two consecutive $1$s. You need to track the previous bit.

If the previous bit was $1$, you can't place $1$ again. State: $(pos, tight, prevBit)$. The $prevBit$ tells you whether placing $1$ at this position would create $11$. Understanding the problem structure is half the battle.