Consider the recursive algorithm given below:
procedure bubblesort (n);
var i,j: index; temp : item;
begin
for i:=1 to n-1 do
if A[i] > A[i+1] then
begin
temp := A[i];
A[i] := A[i+1];
A[i+1] := temp;
end;
bubblesort (n-1)
end
Let $a_n$ be the number of times the ‘if…then…’ statement gets executed when the algorithm is run with value $n$. Set up the recurrence relation by defining $a_n$ in terms of $a_{n-1}$. Solve for $a_n$.