Solution
Approach 1: Work Backwards
Intuition
Instead of multiplying by 2 or subtracting 1 from X
, we could divide by 2 (when Y
is even) or add 1 to Y
.
The motivation for this is that it turns out we always greedily divide by 2:

If say
Y
is even, then if we perform 2 additions and one division, we could instead perform one division and one addition for less operations [(Y+2) / 2
vsY/2 + 1
]. 
If say
Y
is odd, then if we perform 3 additions and one division, we could instead perform 1 addition, 1 division, and 1 addition for less operations [(Y+3) / 2
vs(Y+1) / 2 + 1
].
Algorithm
While Y
is larger than X
, add 1 if it is odd, else divide by 2. After, we need to do X  Y
additions to reach X
.
Complexity Analysis

Time Complexity: .

Space Complexity: .
Analysis written by: @awice.