Given the following algorithm:

statement $1$

statement $2$

for i$1$ to n do

for j$1$ to n do

statement $3$

a$)$ Please analysis its complexity $($Hints: Try to count the number of steps and iterations to solve the complexity. Follow the examples from lecture notes. We don$$t need the every$-$case time complexity analysis here. Don$$t need to count the number of primitive operations.$)$ Please list the detailed explanation.

b$)$ Try to point out some operations in the above algorithm that directly enhance the time complexity