• https://fr.wikipedia.org/wiki/Analyse_de_la_complexit%C3%A9_des_algorithmes
• https://en.wikipedia.org/wiki/Best,\_worst_and_average_case
• https://en.wikipedia.org/wiki/Sorting_algorithm#Comparison_of_algorithms
• https://en.wikipedia.org/wiki/Search_data_structure#Asymptotic_amortized_worst-case_analysis
• https://en.wikipedia.org/wiki/Data_structure
• https://en.wikipedia.org/wiki/Random_access
• https://en.wikipedia.org/wiki/Stack_(abstract_data_type)
• https://en.wikipedia.org/wiki/Computational_complexity_theory
• https://www.geeksforgeeks.org/stack-data-structure-introduction-program/
• https://www.geeksforgeeks.org/implement-two-stacks-in-an-array/

After many tests and reasearchs it appeared that the best solution to have best results was to put all the numbers in stack B in the good descending order. So the scale to search the good value in A to put in B is the whole A stack. But as we don't want to run the half of the stack to put the right A value to the top of B, we prefer to see on each A value the perfect spot in B and how many moves it takes to drop it off.

We finally choose the combination of A value/B spot which takes the less moves to be achieved.

While A is not empty, we look for the best move (shortest) to be achieved. We execute this move then search for the next best move. And so on.

B stack is sorted in a descending way but it doesn't necessarily starts from the highest or smallest value. As we need to have the highest value at the bottom of A and the smallest at the top to get the ascending order we want, we just need to move the highest value of B to its top then push them all. End of game.