Problem - Broken Calculator

Given start value $X$ and target $Y$, you can double $X$ or subtract $1$. Find minimum operations to reach $Y$. For $X=2$, $Y=3$: double to $4$, subtract to $3$. Answer is $2$. Going forward is hard because doubling can overshoot.

Think about working backwards from $Y$ to $X$. Tricky: working forward with doubling can overshoot $Y$, making it hard to determine the optimal path. Working backward with halving and adding is deterministic: if $Y$ is even, halving is always better than adding (halving reduces by half, adding by $1$).

This guides the greedy choice.