Assignment #3 Trie Solution

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Description

You will write an application to build a tree structure called Trie for a dictionary of English words, and use the Trie to generate completion lists for string searches.

IF YOU SEROUS ABOUT ANSWERING THIS QUESTION I CAN SEND YOU THE FILES NEEDED TO COMPLETE IT. IT IS 3 “.java” files.

A Trie is a general tree, in that each node can have any number of children. It is used to store a dictionary (list) of words that can be searched on, in a manner that allows for efficient generation of completion 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 explanation 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’ 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”)

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”.

Trie 7

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? 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
Incorrect/Correct

Two-word trie
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 entire word is a prefix of the other, such as “free” and “freedom”.
(You will not come across this situation in any of the test cases for your implementation.)

The process to build the tree (described in the Building a Trie section 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 completion 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, inserting one word at a time.

Example 1

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

Input and Initial
Empty Tree

After Inserting “door”

After Inserting “dorm”

After Inserting “doom”

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.

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 completions efficienty.

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 particular, after examining (1,0,2), the entire 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!)

Methods To Write:

buildTrie: Starting with an empty trie, builds it up by inserting words from an input array, one word at a time. The words in the input array are all lower case, and comprise of letters ONLY.

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.

Note: these are references to leaf nodes that exist in the Trie, so you should not create any new nodes. Also, the order in which the leaf nodes appear in the returned list is irrelevant.

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 section above.
For instance, in the trie of Example 2 described in the Prefix Section, for prefix “po” your implementation should return a list of references to these trie nodes: [2,3,6],[6,3,5],[3,4,7],[4,4,5] (in any order).

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 manipulations are directly done via TrieNode instances.

Observe the following rules while working on Trie.java:

You may NOT add any import statements to the file.

You may NOT add any new classes (you will only be submitting Trie.java).

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, you may NOT make any changes to the TrieNode class (you will only be submitting Trie.java). When we test your submission, we will use the exact same version of TrieNode that we shipped to you.

Testing

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. After the trie is built, it asks for search prefixes for which it computes completion 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 verification and debugging ONLY. Our testing script will NOT look at this output – see the Grading section below.

When we test your program:

Words will ONLY have letters in the alphabet.

All words 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.

EXAMPLE OUTPUT:

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: