q$6$: $($true$/$false with justification$)$

$1.$ we can determine how good an algorithm by it is conditions of correctness, time efficiency and space efficiency.

$2.$ for the following pseudocode of insertion sort the basic operation of the code is for loop.

insertiansort$($a$,$ n$)$ for i $=2$ tont

key $=$ a$[$i$]$

j$=$i$-1$;

while $($j $>0)$ and $($a$[$j$]>$ key$)$ a$[$j$+1]=$ a$[$j$]$ j$-$j$-1$ a$[$j$+1]=$ key$\}$

$3.$ the time needs for basic operations in the previous algorithm is o$($n$^3)?$

$4.$ let t$($n$)$ be a function obeying the recurrence t$($n$)=2$t$($n$/2)+$ a with initial condition t $(1)=$ b$,$ where a and b are positive numbers. then t$($n$)=0($n log n$).$