final-2005sp-sol - CS312 Final Exam Cornell University...

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CS312 Final Exam Cornell University, Spring 2005 May 17, 2005 Solutions 1. True/False [20 pts] (parts a–j) Each correct answer is 2 pts; each wrong answer is -2 pts; and each blank answer is 0 pts. (a) Software testing proves the presence of bugs, but cannot prove their absence. True (b) The type that SML infers for the expression fn (x,y) => fn x => (y,x) is: ’a * ’b -> ’c -> ’b * ’c . True (c) The function f ( n ) = lg( n lg n ) is O (lg n ). True (d) At each collection, a copying collector must traverse all of the data in the program (including data unreachable from the roots). False (e) The implementation of Dijkstra’s shortest-paths algorithm requires a stack data struc- ture. False (f) The function foldl is tail-recursive. True (g) It is possible that a hash table with n elements and a load factor of 2 has a bucket that contains all of the n elements. True (h) When a program exhibits temporal locality, it will access the same memory location in the near future. True (i) Any lookup operation in a splay tree with n nodes is O (lg n ). False (j) Data races can occur during the execution of message-passing concurrent programs. False 1
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2. Sets [20 pts] (parts a–c) The following is a standard set interface: signature SET = sig (* A ’a set is a set of items of type ’a. *) type ’a set (* empty is the empty set *) val empty : ’a set (* add(s,e) is s union {e} *) val add: ’a set * ’a -> ’a set (* fold over the elements of the set *) val fold: (’a*’b->’b) -> ’b -> ’a set -> ’b end (a) [5 pts] Extend the interface with a function remove that removes an item from a set. Provide a signature and a speciFcation for remove . DeFne an appropriate exception if necessary. Answer: exception NotFound (* remove (s,e) is the set s - {e} *) * Raises: NotFound if e does not belong to s *) val remove: ’a set * ’a -> ’a set (b) [7 pts] Write an implementation for function remove using the other functions in the signature. Assume that an equality funtion for items equal’:’a*’a->bool is also available ( ’a being the type of the items in the set). Your function remove should not visit any of the items more than once.
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final-2005sp-sol - CS312 Final Exam Cornell University...

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