Write the minimax algorithm. Show all steps of alpha$-$beta pruning on the following game tree shown

in figure $3.$ Also, prove that alpha$-$beta pruning takes time $O(\frac{2^m}{2})$ with optimal move order, where

$m$ is the maximum depth of the game tree.

$(1+3+2=6)$

Figure $3$: Game tree of Question $4.$