Prove that a comparison network with n inputs correctly sorts the input sequence ¬n, n - 1,..., 1¬ if and only if it correctly sorts the n - 1 zero-one sequences ¬1, 0, 0,..., 0, 0¬, ¬1, 1, 0,..., 0, 0¬,..., ¬1, 1, 1,..., 1, 0¬.
Answer to relevant QuestionsHow many comparators are there in SORTER [n]?Show that edge (u, v) isa. a tree edge or forward edge if and only if d[u] < d[v] < f[v] < f[u],b. a back edge if and only if d[v] < d[u] < f[u] < f[v], andc. a cross edge if and only if d[v] < f[v] < d[u] < f[u].Give an O (V + E)-time algorithm to compute the component graph of a directed graph G = (V, E). Make sure that there is at most one edge between two vertices in the component graph your algorithm produces.Given a graph G and a minimum spanning tree T, suppose that we decrease the weight of one of the edges in T. Show that T is still a minimum spanning tree for G. More formally, let T be a minimum spanning tree for G with edge ...Two flows of air both at 200 kPa of equal flow rates mix in an insulated mixing chamber. One flow is at 1500 K and the other is at 300 K. Find the irreversibility in the process per kilogram of air flowing out.
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