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Consider the notion of a labeled directed graph as introduced earlier (a graph with labels on its arrows). How could you use a matrix to represent a labeled directed graph? 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).
That is, in the place where the shared structure is to appear is a data item that refers to the apparent item, rather than being the item itself. From the user's viewpoint, it appears that the item itself is where the reference is found. In rex, there is no way to tell the difference. A reference is usually implemented using the lower-level notion of a pointer. Pointers are based on another use of the linear addressing principle: all items in memory are stored in what amounts to a very large array.
Execute the equality testing algorithm on the following two lists: [1, [2, 3], 4], and [1, [2], [3, 4]]. 25 Exploring Abstractions: Information Structures 3. ••• As we saw above, although lists are not the same as sets, lists can be used to represent sets. Present an equality testing algorithm for two sets represented as lists. 4. • What is the length of the list [1, [2, 3], [4, 5, 6]]? What is its leafcount? 7 Binary Relations, Graphs, and Trees A binary relation is a set of ordered pairs. Since both sets and pairs can be represented as lists, a binary relation can be represented as a list of lists.