Consider the join of $4$ relations $R(a,b),S(b,c),T(c,d),$ and $U(d,a),$ where $R$ and $U$ each have

$1000$ tuples, while $S$ and T each have $100$ tuples. Further, the number of values of each attribute

is shown in the table below. To simplify the analysis, we assume the cost of a plan is the total

cost of writing out intermediate results $($i$.$e$.,$ we ignore the implementation details of physical

operators$).$

a$)(6$ points$)$ What is the best left$-$deep join order and its cost?

b$)(4$ points$)$ Is the above plan you developed the best plan among all possible join orders? If

not, what is the best join order and its cost?