2020/3/21 CS112 Spring 2020: Programming Assignment 3 – Trie
Programming Assignment 3
Trie
In this assignment you will implement a tree structure called Trie (pronounced “Tree” or “Try”!).
Worth 80 points (8% of your course grade)
Posted Fri, Mar 13
Due Fri, Apr 3, 11:00 PM
Late submission 1: By Sat, Apr 4, 11:00 PM – 10 point penalty Late submission 2: By Sun, Apr 5, 11:00 PM – 20 point penalty WARNING!! NO GRACE PERIOD FOR ANY SUBMISSION DEADLINE
You will work on this assignment individually. Read the DCS Academic Integrity Policy for Programming Assignments – you are responsible for abiding by the policy. In particular, note that “All Violations of the Academic Integrity Policy will be reported by the instructor to the appropriate Dean”.
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 compilation errors occur for two reasons:
1. You are programming outside Eclipse, and you delete the “package” statement at the top of the le. If you do this, you are changing the program structure, and it will not compile when we test it.
2. You make some last minute changes, and submit without compiling.
To avoid these issues, (a) START EARLY, and give yourself plenty of time to work through the assignment, and (b) Submit a version well before the deadline so there is at least something in Autolab to grade.
Summary
Trie Structure Data Structure Implementation Pre x Search Testing Submission Grading
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 ef cient 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
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’)
Trie 2
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.
Trie 3
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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2020/3/21 CS112 Spring 2020: 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 among all the words. But “door” and “doom” have a common prefix “doo”, while “pore” and “port” have a common prefix “por”.
There is no common prefix in “door” and “poor”, so the root has 2 children, one for each word. (Common suffixes are irrelevant)
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 pre xes.)
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 pre x 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 entire word is a pre x 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 pre x “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).
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2020/3/21 CS112 Spring 2020: 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 pre x 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
An empty trie has a single root node with nulls for all the fields.
After Inserting “door”
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.
After Inserting “dorm”
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
After Inserting “doom”
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
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2020/3/21 CS112 Spring 2020: Programming Assignment 3 – Trie
Example 2
This shows the sequence of inserts in building Trie 7 shown earlier.
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).
After inserting “possible”
Empty After inserting “cat”
After inserting “possum”
After inserting “potato”
Pre x Search
After inserting “muscle”
After inserting “pottery”
After inserting “musk”
After inserting “muse”
Once the trie is set up for a list of words, you can compute word completions ef ciently.
For instance, in the trie of Example 2 above (cat, muscle, …), suppose you wanted to nd all words that started with “po” (pre x). 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] .Thenodesmarkedinredaretheonesthatholdwordsthatbeginwiththegivenpre x. 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 ef cient.
(Searching all nodes in the tree would obviously be very inef cient, 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 pre x, scans the trie ef ciently, gathers and returns an ArrayList of references to all leaf TrieNodes that hold words that begin with the search pre x (you should NOT create new nodes.) For instance, in the trie of Example 2 above, for search pre x “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 ef cient pre x search. See the Pre x Search section above. If you search the array, you will NOT GET ANY credit, even if your result is correct.
If your pre x search examines unnecessary nodes (see Pre x Search section above), you will NOT GET ANY credit, even if your result is correct.
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2020/3/21 CS112 Spring 2020: Programming Assignment 3 – Trie
Make sure to read the comments in the code that precede classes, elds, and methods for code-speci c 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 pre xes 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 veri cation 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 pre x searches–will be input in lower case.
We will NOT input duplicate words.
We will NOT input two words such that one is a pre x of the other, as in “free” and “freedom”, i.e. a complete word will not be a pre x 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)
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) |
(enter prefix, or ‘quit’): do completion list for: quit
completion list for door,doom
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2020/3/21 CS112 Spring 2020: Programming Assignment 3 – Trie
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 pre x 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 bene t, 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.
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