Programming Assignment 3 Trie Solution

In this assignment you will implement a tree structure called Trie (pronounced "Tree"!!).




You will work on this assignment individually. Read DCS Academic Integrity Policy for Programming Assignments ‐ you are responsible for abiding by the policy. In par cular, note that "All Viola ons of the Academic Integrity Policy will be reported by the instructor to the appropriate Dean".




You get ONE extension pass for the semester, no ques ons asked. There will be a total of 5 assignments this semester, and you may use this one me pass for any assignment except the last one which will NOT permit an extension. A separate Sakai assignment will be opened for extensions AFTER the deadline for the regular submission has passed.




IMPORTANT ‐ READ THE FOLLOWING CAREFULLY!!!







Assignments emailed to the instructor or TAs will be ignored‐‐they will NOT be accepted for grading.

We will only grade submissions in Sakai.




If your program does not compile, you will not get any credit.




Most compila on errors occur for two reasons:




You are programming outside Eclipse, and you delete the "package" statement at the top of the file. If you do this, you are changing the program structure, and it will not compile when we test it.
You make some last minute changes, and submit without compiling.



To avoid these issues, (a) START EARLY, and give yourself plenty of me to work through the assignment, and (b) Submit a version well before the deadline so there is at least something in Sakai for us to grade. And you can keep submi ng later versions (up to 10) ‐ we will accept the LATEST version.







Summary







Trie Structure




Data Structure




Implementa on




Tes ng




Submission




Grading







Summary




You will write an applica on to build a tree structure called Trie for a dic onary of English words, and use the Trie to generate comple on lists for string searches.







Trie Structure




A Trie is a general tree, in that each node can have any number of children. It is used to store a dic onary (list) of words that can be searched on, in a manner that allows for efficient genera on of comple on lists.




The word list is originally stored in an array, and the trie is built off of this array. Here are some word lists, the corresponding tries, followed by an explana on of the structure and its correspondence to the word list.




Trie 1 Trie 2 Trie 3
















Root node is always empty. Child [0,0,3] of root stores "data" in a triplet 0 (for index of word in list), 0 (for position of first character, 'd') and 3 (for position of last character, 'a')






















Child (0,0,0) of root stores common prefix "d" of its children "data" (left child) and "door" (right child), in triplet 0 (index of first word "data" in list), 0 (starting position of prefix "d"), and 0 (ending position of prefix "d"). Internal nodes represent prefixes, leaf nodes represent complete words. The left leaf node stores triplet 0 (first word in list), 1 (first index past the common prefix "d", and 3 (last index in word). The right leaf node is stored similarly.






















Like in trie 2, child of root stores common prefix "d", but this time left child is "door", and right child is "data", because "door" appears before "data" in the array.









Trie 4 Trie 5 Trie 6












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10/24/2016 CS112 Fall 2016: Programming Assignment 3 ­ Trie




























A node stores the longest common prefix among its children. Since "do" is the longest common prefix of all the words in the list, it is stored in the child of the root node as the triplet (0,0,1). The left branch points to a subtree that stores "door" and "doom" since they share a common prefix "doo", while the right branch terminates in the leaf node for "dorm" stored as the triplet 1 (index of word "dorm"), 2 (starting position of substring "rm" following prefix "do"), and 3 (ending position of substring "rm")







Trie 7













There is no common prefix in "door" and "poor", so the root has 2 children, one for each word. (Common suffixes are irrelevant)




There is no common prefix among all the words.




But "door" and "doom" have a common prefix "doo",




while "pore" and "port" have a common prefix




"por".
















































Special Notes




No node, except for the root, can have a single child. In other words, every internal node has at least 2 children. Why? It's because an internal node is a common prefix of several words. Consider these trees, in each of which an internal node has a single child (incorrect), and the equivalent correct tree:










One‐word trie Two‐word trie




Incorrect/Correct Incorrect/Correct








































A single leaf node only
The longest common prefix of the two words is "bar", so there is one internal
node for this, with two branches for the respective trailing substrings








A trie does NOT accept two words where one en re word is a prefix of the other, such as "free" and "freedom".







The process to build the tree (described in the Building a Trie sec on below), will create a single child of the root for the longest common prefix "free", and this node will have a single child, a leaf node for the word "freedom". But this is an incorrect tree because it will (a) violate the constraint that no node apart from the root can have a single child, and (b) violate the requirement that every complete word be a leaf node (the complete word "free" is not a leaf node).







































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10/24/2016 CS112 Fall 2016: Programming Assignment 3 ­ Trie




On the other hand, a tree with two leaf node children off the root node, one for the word "free" and the other for the word "freedom" will be incorrect because the longest common prefix MUST be a separate node. (This is the basis of comple on choices when the user starts typing a word.)







Data Structure




Since the nodes in a trie have varying numbers of children, the structure is built using linked lists in which each node has three fields:




substring (which is a triplet of indexes)







first child, and




sibling, which is a pointer to the next sibling.







Here's a trie and the corresponding data structure:







Trie Data Structure





























































Building a Trie




A trie is built for a given list of words that is stored in array. The word list is input to the trie building algorithm. The trie starts out empty, adding one word at a me.




Example 1




The following sequence shows the building of the above trie, one word at a me, with the complete data structure shown a傶er each word is inserted.




Input and Initial
After Inserting "door"
After Inserting "dorm"
After Inserting "doom"
Empty Tree

































An empty trie has a single root node with nulls for all the fields.




























When "door" is inserted, a leaf node is created and made the first child of the root node. The substring triplet is




(0,0,3), since "door" is at index 0 of the word list array, and the substring is the entire string, from the first position 0 to the last position 3.





































When "dorm" is inserted, its prefix "do" is found to match with prefix "do" in the existing word "door". So the third value in the triplet for the existing node is changed from 3 to 1, corresponding to the prefix "do". (The word index‐‐first value in triplet‐‐is left unchanged.) And two new nodes are made at the next level for the two trailing substrings, "or" of "door" and "rm" of "dorm" ‐ The array indexes of these words are in ascending order, i.e. "door" must come before "dorm" in the node sequence.

















































When "doom" is inserted, its prefix "do" is found to match with the entire substring stored at the child of the root. Descending further, the subsequent "o" is found to match with the prefix "o" of the substring "or" at the (0,2,3) node. This results in a modification of the (0,2,3) triplet to




(0,2,2), and the creation of a new level for the trailing substrings "r" and "m" of "door" and "doom", respectively, in that order ‐ "door" (word index 0 in array) must precede "doom" (word index 3).






Example 2




This shows the sequence of inserts in building Trie 7 shown earlier.



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10/24/2016 CS112 Fall 2016: Programming Assignment 3 ­ Trie



















Empty After inserting "cat" After inserting "muscle" After inserting "pottery" After inserting "possible"

























After inserting "possum" After inserting "musk"


































After inserting "potato" After inserting "muse"































Implementa on




Download the a傶ached trie_project.zip file to your computer. DO NOT unzip it. Instead, follow the instruc ons on the Eclipse page under the sec on "Impor ng a Zipped Project into Eclipse" to get the en re project into your Eclipse workspace.




You will see a project called Trie Assignment with the following classes:




structures.TrieNode







structures.Trie







apps.TrieApp







There are also a number of sample test files of words directly under the project folder (see the Examples sec on that follows.)




You will implement the following methods in the Trie class:




(50 pts) inse Word: Inserts a word into the trie. Input word may be in any combina on of upper and lower case le傶ers (only le傶ers, no other characters), but in the tree, all words are stored in lower case only.







(25 pts) completionList: Gathers and returns the comple on list of words for a given prefix. The order in which the words appear in the list is irrelevant.







Observe the following rules while working on Trie.java:




You may NOT add any impo statements to the file.







You may NOT add any fields to the Trie class.







You may NOT modify the headers of any of the given methods.







You may NOT delete any methods.




You MAY add helper methods if needed, as long as you make them private.







Also, do NOT change TrieNode.java in any way. When we test your program, we will use the original TrieNode.java as supplied with the assignment.







Tes ng




You can test your program using the supplied TrieApp driver. It first asks for words to be stored in the trie (either individually, or from a file), and when done, asks for prefixes for which to compute comple on lists.




Some sample word files are given with the project, directly under the project folder. The first line of an input word file is the number of the words, and the subsequent lines are the words, one per line.




There's a convenient print method implemented in the Trie class that is used by TrieApp to output a tree for debugging purposes. (Note: Our tes ng will NOT look at this output




‐ see the Grading sec on below.)










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10/24/2016
CS112 Fall 2016: Programming Assignment 3 ­ Trie


Submission




Submit your Trie.java file ONLY.














Grading




The inse Word method will be graded by inser ng several words in sequence, and a傶er each insert, comparing the tree structure resulḃng from your implementaḃon, with the correct tree structure produced by our implementaḃon. We will NOT be looking at the printout of the tree, the print method in the Trie class is for your convenience only.




The completionList method will be graded by inpu ng prefix strings to some of the trees created in inse Word. However, these trees will be created by our correct implementaḃon of inse Word. In other words, to test your completionList implementa on, we will NOT use your inse Word implementa on at all. This is fully for your benefit, because if your inse Word implementa on is incorrect, it will not adversely affect the credit you get for your completionList implementa on.


























































































































































































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