Please show your work, I will give upvote for your effort.

Suppose you are given a list of m constraints over integer variables Vig..., Vn, with each constraint being either an equality (e.g. Vi = vj) or a disequality (e.g. Vi # v;). Some sets of constraints are consistent, or satisfiable, in that it is possible to make them simultaneously true: for example the constraints vi = V2 and V2 + v3 can be satisfied by assigning vi = v2 = 0) and v3 = 2. Other sets of constraints are inconsistent (or unsatisfiable), being impossible to make simultaneously true: for example vi = V2, V2 = V3, and vi + V3. (a) (30 pts.) Describe an efficient algorithm to determine if a set of constraints in the form described above is satisfiable. Your algorithm should take less than (nm) time. (b) (10 pts.) What is the worst-case asymptotic runtime of your algorithm, in terms of n and m? (e) (40 pts.) Prove your algorithm correct, i.e., prove that it returns true if and only if the given constraints are satisfiable. Suppose you are given a list of m constraints over integer variables Vig..., Vn, with each constraint being either an equality (e.g. Vi = vj) or a disequality (e.g. Vi # v;). Some sets of constraints are consistent, or satisfiable, in that it is possible to make them simultaneously true: for example the constraints vi = V2 and V2 + v3 can be satisfied by assigning vi = v2 = 0) and v3 = 2. Other sets of constraints are inconsistent (or unsatisfiable), being impossible to make simultaneously true: for example vi = V2, V2 = V3, and vi + V3. (a) (30 pts.) Describe an efficient algorithm to determine if a set of constraints in the form described above is satisfiable. Your algorithm should take less than (nm) time. (b) (10 pts.) What is the worst-case asymptotic runtime of your algorithm, in terms of n and m? (e) (40 pts.) Prove your algorithm correct, i.e., prove that it returns true if and only if the given constraints are satisfiable