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# ps3 - Problem Set 3 Tries and LZW Compression Due Thursday...

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Problem Set 3: Tries and LZW Compression Due Thursday, February 26 For this problem set, you are to turn in an overview document covering Part 2. The overview document should be composed as described in Overview Requirements . You should read this document carefully. We have provided an example overview document written as if for Problem Set 2 from CS 312, Spring 2008. Submission in PDF is preferred; however, you can also submit your overview document as a .doc or a .txt file. In particular, starting with this problem set, it's your job to convince us that your code works, by describing your implementation and by presenting a testing strategy, test cases, and results. Part 1 : Substitution Model Find an expression that, when substituted for the ??, will cause the following function for the given input to evaluate to 42. Show the evaluation using the substitution model. You may omit minor substitutions, but be sure to show all the main steps. At an absolute minimum, show each step before and after a recursive call. Steps that create new global bindings should also be shown let rec zardoz l = match l with [] -> ?? | h::t -> (h (zardoz t)) in let rec f n = if n=1 then 1 else n*f(n-1)+n+2 in zardoz [( fun n -> 7*n); f];; To do: turn in the solution under Substition Model in CMS. Submission is allowed in .pdf, .doc, or .txt. Please include your name and netid in your solution. Part 2: Tries Several algorithms, including the compression algorithms and string matching algorithms, make use of maps where the keys are strings (or sequences) of values of a certain type. A trie (pronounced "try") or prefix tree is an efficient data structure for implementing the map ADT for this kind of map. The set of possible elements in the key strings is referred to as the alphabet of the trie. A trie is a tree structure whose edges are labeled with the elements of the alphabet. Each node can have up to N children, where N is the size of the alphabet. Nodes correspond to strings of elements of the alphabet. More precisely, each node corresponds to the sequence of elements traversed on the path from the root to that node. The map binds a string s to a value v by storing the value v in the node of s . The advantage of this scheme is that if efficiently represents common string prefixes, and lookups or inserts are achieved using quick searches starting from the root. Suppose we want to build a map from strings of ASCII characters to integer codes. In this case, edges are

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labeled with ASCII characters, and integer codes are stored in (some of) the nodes. Here is an example: The above trie describes the map {"to"->7, "tea"->3, "ten"->12, "in"->5, "inn"->9} . The values (shown in blue) are stored in the nodes. Note that nodes might not have values. For instance the node that corresponds to string "te" doesn't have a value. Hence, "te" is not in the map.
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ps3 - Problem Set 3 Tries and LZW Compression Due Thursday...

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