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1 show that none of the following greedy algorithms for chained matrix multiplica- tion work at each stepa compute the
1 much of the information used to compute the median-of-median-of-ve is thrown away show how the number of comparisons
1 write a program to implement the closest-pair algorithm2 what is the asymptotic running time of quickselect using a
1 a le contains only colons spaces newlines commas and digits in the following frequency colon 100 space 605 newline
1 show that the greedy algorithm to minimize the mean completion time for multiprocessor job scheduling works2 the
the baseball card collector problem is as follows given packets p1 p2 pm each of which contains a subset of the years
assume that the hamiltonian cycle problem is np-complete for undirected graphsa prove that the hamiltonian cycle
the clique problem can be stated as follows given an undirected graph g v e and an integer k does g contain a complete
the object of thenbspkevin bacon gamenbspis to link a movie actor to kevin bacon via shared movie roles the minimum
a student needs to take a certain number of courses to graduate and these courses have prerequisites that must be
the input is a collection of currencies and their exchange rates is there a sequence of exchanges that makes money
the input is a list of league game scores and there are no ties if all teams have at least one win and a loss we can
1 suppose that walls in the maze can be knocked down with a penalty ofnbsppnbspsquaresnbsppnbspis specied as a
1 when a vertex and its incident edges are removed from a tree a collection of sub- trees remains give a linear-time
1 a graph isnbspk-colorable if each vertex can be given one ofnbspknbspcolors and no edge connects identically colored
1 anbspmultigraphnbspis a graph in which multiple edges are allowed between pairs of vertices which of the algorithms
1 write a program to nd the strongly connected components in a digraph2 give an algorithm that nds the strongly
1 suppose all the edge weights in a graph are integers between 1 and e how fast can dijkstras algorithm be implemented2
1 the disjoint set analysis in section 86 can be rened to provide tight bounds for smallnbspna show thatnbspcmnbspn 0
1 suppose we want to add an extra operation removex which removes x from its current set and places it in its own show
1 suppose we want to add an extra operation deunion which undoes the last union operation that has not been already
1 show the result of the following sequence of instructions union12 union34 union35 union17 union36 union89nbspnbsp
1 propose an algorithm to sort a large le using only two tapes2 a show that a lower bound ofnbspn22nnbspon the number
1 prove that any comparison-based sorting algorithm requiresnbsp0nnbsplognbspn compar- isons on average2 we are given
1 implement an optimized version of quicksort and experiment with combinations of the followinga pivot rst element