$5)$

Def a search$($arr$,$ start, end, key$)$:

If start $>$ end:

Return None

temp $=0$

mid $=$ start $+($end $$ start$)//2$

for i in range $($mid$)$:

$$ temp $+=1$

if arr$[$mid$]<$ key:

$$ return a$\_$search$($arr$,$ mid$+1,$ end, Key$)$

elif arr$[$mid$]>$ key:

$$ return a$\_$search$($arr$,$ start, mid$-1,$ key$)$

else:

$$ return mid

Recursive relation:

T$($N$)=$ Complexity in Big$-$ Theta$=$

$6)$

Def fun$1($n$)$:

If $($n $<1)$:

$$ Return

else:

fun$($n$/2)$

for i in range $($n$*$n$/2)$:

$$ print$(*,$ end$=)$

print$(*)$

fun$($n$/2)$

Recursive relation:

T$($N$)=$

Complexity in Big$-$ Theta$=$

$7)$

Def fun$2($n$)$:

If $($n $<1)$:

$$ Return

else:

fun$($n $-2)$

for i in range $($n$*$n$/2)$:

$$ print$(*,$ end$=)$

print$(*)$

Recursive relation:

T$($N$)=$

Complexity in Big$-$ Theta$=$

Please show me step by step