By Keller R.
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Extra info for Computer science: abstraction to implementation
Show a list of lists that does not represent a matrix. 2. •• Suppose a binary relation is given as the following list of pairs. Draw the graph. Construct its connection matrix and its reachability matrix. What is the list of pairs corresponding to its transitive closure? [ [1, 2], [2, 3], [2, 4], [5, 3], [6, 5], [4, 6] ] 3. ••• Devise a method, using connection matrices, for determining whether a graph is acyclic. 4. •• Consider the notion of a labeled directed graph as introduced earlier (a graph with labels on its arrows).
The key word above is single, meaning exactly one. A function never associates two or more items with a given member of the domain, nor does it ever fail to associate an item with any member of the domain. We say the function, given a domain value, yields or maps to the value associated with it. The syntax indicating the element associated with a domain element x, if f represents the function, is f(x). However this is only one possible syntax of many; the key idea is the association provided. Examples of functions are: • The add1 function: Associates with any number the number + 1.
How would the representation of this matrix as a list differ from previous representations of graphs as lists? 5. ••• Devise a method for computing the connection matrix of the transitive closure of a graph, given the graph's connection matrix. 9 Undirected graphs An undirected graph is a special case of a directed graph (and not the other way around, as you might first suspect). An undirected graph is usually presented as a set of nodes with lines connecting selected nodes, but with no arrow-heads on the lines.