Question $1$

Consider the following algorithm:

function FANCYINSERT array, $($:$m$:$Z^{+}\}$

let $n$ be the size of $N$

let $T$ be an empty B$-$Tree of order $m$

for i from $0$ to $n-1$ do

if $i$ is even then

T$.$INSERT $(N[\frac{i}{2}])$

else

$T.$INSERT$(N[n-(\frac{i-1}{2})-1])$

end if

end for

return $T$

end function

a Give an array $N$ storing the numbers from $1$ to $7$ such that FANCYINSERT$(N,3)$ returns a B$-$Tree consisting only of $2-$nodes $($i$.$e$.,$ all nodes have at most two children$).$

b Give an array $N$ storing the numbers from $1$ to $7$ such that FANCYINSERT$(N,3)$ returns the following B$-$Tree:

Question $1$

Consider the following algorithm:

function FANCYINSERT : array, $($:$m$:$Z^{+}\}$

let $n$ be the size of $N$

let $T$ be an empty B$-$Tree of order $m$

for i from $0$ to $n-1$ do

if $i$ is even then

$T.$INSERT $(N[\frac{i}{2}])$

else

$T.$InSERT$(N[n-(\frac{i-1}{2})-1])$

end if

end for

return $T$

end function

a Give an array $N$ storing the numbers from $1$ to $7$ such that FANCyInSERT$(N,3)$ returns a B$-$Tree consisting only of $2-$nodes $($i$.$e$.,$ all nodes have at most two children$).$

b Give an array $N$ storing the numbers from $1$ to $7$ such that FANCyInSERT$(N,3)$ returns the following B$-$Tree:

c Show the insertions $($one number at a time in the required order$)$ of your array $N($from part b$)$ in $T$ as performed by FANCYInsERT $(N,3).$