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Here's a problem that occurs in automatic program analysis. For a set of variables X1, ... , Xn, you are given some equality constraints, of the form X = x; and some disequality constraints, of the form Xi + 2; . Is it possible to satisfy all of them? For instance, the constraints x1 = X2, X2 = x3, x3 = 34,21 + x4 cannot be satisfied. Give an efficient algorithm that takes m constraints over n variables, and outputs whether they can be satisfied or not in time O(m log n). HINT: Construct a graph from these constraints, and try to check whether or not some vertices are connected