$($a$)$ Give an efficient algorithm that takes as input m constraints over n variables and decides

whether the constraints can be satisfied.

Hint: One possible option is to consider a graph representation of this problem where

each node is a variable $($e$.$g$.$ xi$)$ and an edge represents an $$equality constraint$.$

$($b$)$ Argue $($or do a proof sketch$)$ that your algorithm is correct.

$($c$)$ State the asymptotic cost of your algorithm and justify why it$$s correct.