Description
In this assignment you will implement a tree structure called Trie (pronounced “Tree” or “Try”!).
Summary
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.
Trie Structure
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 efcient 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 examples of word lists and the tries built to store the words, followed by an
explanation of the trie structure and its relationship 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
There is no common prefix in
“door” and “poor”, so the root has
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”)
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 prexes.)
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 prex 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 prex 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 prex “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 prex 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 elds:
substring (which is a triplet of indexes)
rst 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”
found to match with the entire substrin
stored at the child of the root. Descend
further, the subsequent “o” is found to
match with the prefix “o” of the substri
“or” at the (0,2,3) node. This results in
modification of the (0,2,3) triplet to
(0,2,2), and the creation of a new leve
the trailing substrings “r” and “m” of “do
and “doom”, respectively, in that order
“door” (word index 0 in array) MUST pre
“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”
Prex Search
Once the trie is set up for a list of words, you can compute word completions efciently.
For instance, in the trie of Example 2 above (cat, muscle, …), suppose you wanted to nd all words that started with “po”(prex). 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 prex.
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 efcient.
(Searching all nodes in the tree would obviously be very inefcient, you might as well have searched the word array in that case, why bother building a trie!)
Implementation
Download the attached trie_project.zip le to your computer. DO NOT unzip it. Instead, follow the instructions on the Eclipse page under the section “Importing a
Zipped Project into Eclipse”to get the entire 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 les of words directly under the project folder (see the Testing section that follows.)
You will implement the following methods in the Trie class:
(50 pts) 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.
(30 pts) completionList: For a given search prex, scans the trie efciently, gathers and returns an ArrayList of references to all leaf TrieNodes that hold words
that begin with the search prex (you should NOT create new nodes.) For instance, in the trie of Example 2 above, for search prex “po” your implementation 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 matter.
You may NOT search the words array directly, since that would defeat the purpose of building the trie, which allows for more efcient prex search. See the
Prex Search section above. If you search the array, you will NOT GET ANY credit, even if your result is correct.
If your prex search examines unnecessary nodes (see Prex Search section 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, elds, and methods for code-specic 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.
You may NOT MAKE ANY CHANGES to the Trie.java le EXCEPT to (a) ll 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 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 rst asks for the name of an input le of words, with which it builds a trie by calling the Trie.buuldTree
method. After the trie is built, it asks for search prexes for which it computes completion lists, calling the Trie.completionList method.
Several sample word les are given with the project, directly under the project folder. (words0.txt, words1.txt, words2.txt, words3.txt, words4.txt). The rst line of a
word le 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 verication 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–for building the trie as well as for prex searches–will be input in lower case. We will NOT input duplicate words. We will NOT input two words such that one is a prex of the other, as in “free” and “freedom”, i.e. a complete word will not be a prex of another word.
Here are a couple of examples of running TrieApp:
The rst 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 implementation – 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 x your code.
Also try the other sample word les. AND, try with word les of your own, formatted exactly like the sample word les – rst 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
completion words.
Submission
Submit your Trie.java le.
Grading
The buildTrie method will be graded by comparing the tree structure resulting from your implementation, with the correct tree structure produced by our implementation. 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 inputting prex strings to some of the trees created in buildTrie. However, these trees will be created by our correct
implementation of buildTrie. In other words, to test your completionList implementation, we will NOT use your buildTrie implementation at all. This is fully for your
benet, because if your buildTrie implementation is incorrect, it will not adversely affect the credit you get for your completionList implementation. 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.
