Broken Calculator - Implementation

Here is the solution:

function brokenCalc(X, Y)
 ops := 0
 while Y > X
 if Y % 2 = 0 then
 Y := Y / 2
 else
 Y := Y + 1
 ops := ops + 1
 return ops + (X - Y)

Time: $O(\log Y)$. Space: $O(1)$.

Once $Y \leq X$, you cannot halve anymore (would go below $X$). Just add the difference.