Suppose that at some point in the execution of a push-relabel algorithm, there exists an integer 0 < k ≤ |V| − 1 for which no vertex has ν.h = k. Show that all vertices with ν.h > k are on the source side of a minimum cut. If such a k exists, the gap heuristic updates every vertex ν ∈ V – {s} for which ν.h > k, to set ν.h = max(ν.h, |V| + 1). Show that the resulting attribute h is a height function. (The gap heuristic is crucial in making implementations of the push-relabel method perform well in practice.)