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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. e. a set of pairs of nodes, a line of an undirected graph connecting a node n to a node m represents two arrows, one from node n to m and another from node m to n.

Identify some fields outside of computer science where directed graphs are used. Give a detailed example in each case. 40 Exploring Abstractions: Information Structures 5. •• The decoding of the Morse code alphabet can be naturally specified using a trie. Each character is a sequence of one of two symbols: dash or dot. For example, an 'a' is dot-dash, 'b' is dash-dot-dot-dot, and so on. Consult a source, such as a dictionary, which contains a listing of the Morse code, then construct a decoding trie for Morse code.

This occurs, for example, in the case of the multiply function: multiply(3, 4) gives the same value as multiply(4, 3). Functions that prohibit f(x) from being the same as f(y) when x and y are bound to different values are called oneto-one functions. Functions such as the zero function, which associates the same value with all elements of the domain are called constant functions. A related definition, where we will tend to blur the distinction with function as defined, is that of partial function: A partial function on a set is an entity that associates, with each member of a set, at most one item.

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