How do you find the best set of stack motions that will sort the * known * list?

Question

The problem of sorting unknown lists is known. But what about the problem of finding the optimal sort for a known list in a stacked machine? That is, suppose you have the following stack machine:

[4,1,3,2]
[]
[]

That is, there is a place for 3 stacks, and 1 of them is filled with numbers. Also, suppose your stack machine can do 2 movements: move a b(puts the top element aon b) and join a b(puts the stack aon top of the stack b). In this case, the optimal sorting:

move 0 1
move 0 1
move 0 2
join 1 2
move 0 2

The following sequence will be executed:

[4,1,3,2] → [4,1,3] → [4,1] → [4]   → [4]     → []
[]        → [2]     → [2,3] → [2,3] → []      → []
[]        → []      → []    → [1]   → [1,2,3] → [1,2,3,4]

, , ?

Answer 1

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