Bubble sort algorithm is given below. Prove the correctness of this algorithm using loop invariant

method. Considering uniform permutation, find the expected number of comparisons, and the

expected number of swap operations. $(10)$

Bubble$-$Sort$($A$)$

$1$ n $=$ A$.$size$()$

$2$ for i $=1$ to n $1$

$3$ for j $=$ n downto i $+1$

$4$ if A$[$j $1]>$ A$[$j$]$

$5$ swap$($A$[$j $1],$ A$[$j$])$