Select the CORRECT statements $-$

$1.$With perfect ordering, alpha$-$beta pruning reduces the time complexity from O$($b$^$m$)$ to O$($bm$/2)$

$2.$With perfect ordering, alpha$-$beta pruning increases the depth that can be searched in same time T from d to d$^2.$

$3.$Without alpha$-$beta pruning, the time complexity of search for depth m follows T$($m$)=$ b$.$T$($m$-1)+$ c

$4.$With perfect ordering in alpha$-$beta pruning, the time complexity of search for depth m follows T$($m$)=$ T$($m$-1)+($b$-2)$T$($m$-2)+$ c