Determining the rank of the pivot:

After partitioning, the pivot $3$ is at index $7.$

The number of elements to the left of the pivot $($including the pivot itself$)$ is

$7$

$$

$1$

$+$

$1$

$=$

$7$

$71+1=7.$Please use the given SELECT to select the $4$th smallest element from the array

$6,0,2,4,7,-2,-4,3$

$(50$ points, please show detailed steps for full credits$).$

Select$(A,p,r,i)$

if $p=r$

return $A[p]$

$q=$PARTITION$(A,p,r)$

$k=q-p+1$

if $i==k,//$ the pivot value is the answer

return $A[q]$

elseif SELECT$(A,p,q-1,i)SELECT(A,q+1,r,i-k)(A,p,r)x=A[r]i=p-1j=pr-1A[j]xi=i+1A[i]A[j]A[i+1]A[r]i+1i$

return SELECT$(A,p,q-1,i)$

else return SELECT$(A,q+1,r,i-k)$

PARTITION $(A,p,r)$

$x=A[r]$

$i=p-1$

for $j=ptor-1$

$ifA[j]x$

$i=i+1$

exchange $A[i]$ with $A[j]$

exchange $A[i+1]$ with $A[r]$

return $i+1$