Given a digraph $G=(V,E),$ its transitive closure $G^{**}$ is a digraph defined as follows: It

has the same vertex set $V$ as $G$ and contains an edge from a vertex $a$ to another vertex

$b$ if and only if there is a directed path from $a$ to $b$ in $G.$ Suppose we want to design

a DP algorithm that outputs $G^{**}$ on input $G.$ Design the subinstances and the Bellman

Equation. $($Note that though this is not an optimization problem, DP is still helpful.$)$