Consider a collection C of subsets of a nite set V . (V; C) is called a hypergraph. A hypergraph (V; C) is 3-regular if every subset in C contains exactly three elements. A subcollection M of C is matching if all subsets in M are disjoint. Show that there exists a polynomial-time 3-approximation for the maximum matching problem in 3-regular hypergraphs as follows: Given a 3-regular hypergraph, find a matching with maximum cardinality.

Write a program which asks you to enter a name in the form of first middle initial last. so you might enter for example samuel p. clemens. use getline to read in the string because it contains spaces. also, apparently the shift key on your keyboard doesn’t work, because you enter it all lower case. pass the string to a function which uses .find to locate the letters which need to be upper case and use toupper to convert those characters to uppercase. the revised string should then be returned to main in the form last, first mi where it will be displayed.

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