Programming Assignment 3 Trie Solution

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 examples of word lists and the tries built to store the words, followed by an explana on of the trie structure and its rela onship to its source 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' in "data") 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




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

Every leaf node represents a complete word, and every complete word is represented by some leaf node. (In other words, internal nodes do not represent complete words, only proper prefixes.)


No node, except for the root, can have a single child. In other words, every internal node has at least 2 children. Why? 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".


(You will not come across this situa on in any of the test cases for your implementa on.)

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 aside 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).
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, inser ng 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
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
















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
these words are in ascending order, i.e.

"door" MUST come before "dorm" in the

node sequence.
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 2).

Example 2

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







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"










Prefix Search

Once the trie is set up for a list of words, you can compute word comple ons efficiently.

For instance, in the trie of Example 2 above (cat, muscle, ...), suppose you wanted to find all words that started with "po" (prefix). The search would start at the root, and touch the nodes [0,0,2],(1,0,2),(2,0,1),(2,2,2),(3,2,3),[2,3,6],[6,3,5],[3,4,7],[4,4,5] . The nodes marked in red are the ones that hold words that begin with the given prefix.

Note that NOT ALL nodes in the tree are examined. In par cular, a er examining (1,0,2), the en re subtree rooted at that node is skipped. This makes the search efficient. (Searching all nodes in the tree would obviously be very inefficient, you might as well have searched the word array in that case, why bother building a trie!)


Implementa on

Download the a 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 with the following classes in the trie package: TrieNode, Trie, and TrieApp.

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

You will implement the following methods in the Trie class:

(50 pts) buildTrie: Star ng with an empty trie, builds it up by inser ng words from an input array, one word at a me. The words in the input array are all lower case, and comprise of le ers ONLY.


(30 pts) completionList: For a given search prefix, scans the trie efficiently, gathers and returns an ArrayList of references to all leaf TrieNodes that hold words


that begin with the search prefix (you should NOT create new nodes.) For instance, in the trie of Example 2 above, for search prefix "po" your implementa on should
return a list of references to these trie leaf nodes: [2,3,6],[6,3,5],[3,4,7],[4,4,5].

NOTE:
The order in which the leaf nodes appear in the returned list does not ma  er.


You may NOT search the words array directly, since that would defeat the purpose of building the trie, which allows for more efficient prefix search. See the Prefix Search sec on above. If you search the array, you will NOT GET ANY credit, even if your result is correct.

If your prefix search examines unnecessary nodes (see Prefix Search sec on above), you will NOT GET ANY credit, even if your result is correct.


Make sure to read the comments in the code that precede classes, fields, and methods for code-specific details that do not appear here. Also, note that the methods are all static, and the Trie has a single private constructor, which means NO Trie instances are to be created - all manipula ons are directly done via TrieNode instances.

You may NOT MAKE ANY CHANGES to the Trie.java file EXCEPT to (a) fill in the body of the required methods, or (b) add private helper methods. Otherwise, your submission will be penalized.

You may NOT MAKE ANY CHANGES to the TrieNode class (you will only be submi ng Trie.java). When we test your submission, we will use the exact same version of TrieNode that we shipped to you.


Tes ng

You can test your program using the supplied TrieApp driver. It first asks for the name of an input file of words, with which it builds a trie by calling the Trie.buuldTree method. A er the trie is built, it asks for search prefixes for which it computes comple on lists, calling the Trie.completionList method.

Several sample word files are given with the project, directly under the project folder. (words0.txt, words1.txt, words2.txt, words3.txt, words4.txt). The first line of a 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 verifica on and debugging ONLY. Our tes ng script will NOT look at this output - see the Grading sec on below.

When we test your program:

Words will ONLY have le  ers in the alphabet.


All words--for building the trie as well as for prefix searches--will be input in lower case.

We will NOT input duplicate words.

We will NOT input two words such that one is a prefix of the other, as in "free" and "freedom", i.e. a complete word will not be a prefix of another word.


Here are a couple of examples of running TrieApp:

The first run is for words3.txt:


Enter words file name => words3.txt

TRIE

---root

|

doo

---(0,0,2)

|

door

---(0,3,3)

|

doom

---(3,3,3)

|

por

---(1,0,2)

|

pore

---(1,3,3)

|

port

---(2,3,3)

completion list for (enter prefix, or 'quit'): do

door,doom

completion list for: quit

The second run is for words4.txt:


Enter words file name => words4.txt

TRIE

---root

|

cat

---(0,0,2)

|

mus

---(1,0,2)

|

muscle
---(1,3,5)


|

musk

---(5,3,3)

|

po

---(2,0,1)

|

pot

---(2,2,2)

|

pottery

---(2,3,6)

|

potato

---(6,3,5)

|

poss

---(3,2,3)

|

possible

---(3,4,7)

|

possum

---(4,4,5)

completion list for (enter prefix, or 'quit'): pos

possible,possum

completion list for: mu

muscle,musk

completion list for: pot

pottery,potato

completion list for: quit

Try these tests with your implementa on - your Trie printout MUST look IDENTICAL to the above. If your tree looks different, either your program logic is incorrect, or there is something different in the sequence of word inserts. In either case, you will not get any credit, so make sure you fix your code.

Also try the other sample word files. AND, try with word files of your own, forma ed exactly like the sample word files - first line is number of words, then one word per subsequent line.

Go over the TrieApp code to understand how the Trie methods are called, and how the returned array list from completionList is processed to actually print the comple on words.


Submission

Submit your Trie.java file.


Grading

The buildTrie method will be graded by comparing the tree structure resulng from your implementaon, with the correct tree structure produced by our implementaon. We will NOT be looking at the printout of the tree, the print method in the Trie class (used by TrieApp as in the above test examples) is for your convenience only.

The completionList method will be graded by inpu ng prefix strings to some of the trees created in buildTrie. However, these trees will be created by our correct implementaon of buildTrie. In other words, to test your completionList implementa on, we will NOT use your buildTrie implementa on at all. This is fully for your benefit, because if your buildTrie implementa on is incorrect, it will not adversely affect the credit you get for your completionList implementa on. We will also make sure that the nodes you return belong to the Trie, and not some independent nodes you created outside of the Trie.