Part $3-(25$ points$)$ Query Optimization

Consider the following schema with three relationships with their keys underlined.

$R(A_{,}B,C),S(B_{,}D,E),T(A_{,}F,G)$

Draw the initial query tree and transform the query into an optimized query tree using the HEURISTIC ALGEBRAIC OPTIMIZATION ALGORITHM. Use the following statistics to estimate the sizes of intermediate tables and join costs.

Assume,

$|R|=2,000,|S|=4,000,$ and $|T|=2,000$

$V(B,R)=100,V(C,R)=200,V(F,T)=20,V(G,T)=100$

Relational Algebr$$ Query: