CS201 Discussion 10 DRAWTREE + TRIES

Transcription

1 CS201 Discussion 10 DRAWTREE + TRIES

2 DrwTree

3 First instinct: recursion As very generic structure, we could tckle this problem s follows: drw(): Find the root drw(root) drw(root): Write the line for the root For ech child element of root: drw(child)

4 Recursive rguments First, we should either keep the prents nd nmes rrys s globl vribles, or pss them to our recursive method so it cn ccess them. However, this is not enough. Looking t the Strings in ech subtree wht do ll the Strings in ny subtree hve in common?

5 Recursive rguments All elements (besides the root) in ny subtree hve Strings strting with the sme substring. Thus, we should pss this prefix s one of our rguments. The root will lso strt with prefix, but minus the lst two chrcters.

6 Updted pseudo-code drw(): Find the root drw(root, ) //note the initil vlue drw(root, prefix): Write the line for the root, using prefix minus lst two chrs For ech child element of root: drw(child, updted prefix)

7 Updting the prefix How does the prefix chnge for ech child?

8 Updting the prefix How does the prefix chnge for ech child? For every child but the lst, we ppend to the prefix. For the lst child, we dd

9 Updted pseudocode drw(): Find the root drw(root, ) drw(root, prefix): Write the line for the root, using prefix minus lst two chrs For ech child element of root but the lst: drw(child, prefix + ) For the lst child (if there is one): drw(child, prefix + )

10 Implementtion detils Probbly the esiest wy to hndle writing the line is to keep globl ArryList. Where the pseudocode sys write the line, just dd the String to the ArryList. In ddition, it my be esiest to pss the index of the root vlue, rther thn the vlue itself. Then, to find ll children of the j th vlue, we just find ll indices such tht prents[i]==j.

11 Finl pseudocode drw( ): Find the root s index, i Initilize empty ArryList L globlly. Also keep prents nd nmes globlly. drw(i, ) drw(ind, prefix): Add to L (prefix minus lst two chrcters plus +- plus nmes[ind]) Children = ll indices j such tht prents[j] == ind For ech element of children but the lst, cll drw(child, prefix+ ) For the lst child (if there one), cll drw(child, prefix + )

12 Trie Overview A trie is dt structure used to store words. It s like tree, except insted of ech node hving left nd right child, it cn hve child for ech chrcter of the lphbet. Ech node represents String, which is mde of the chrcters on the pth to it from the root. e.g. the bottom left node represents the word s s t e b

13 Storing words In order to keep trck of which nodes represent Strings tht re ctully words, ech node will hve boolen mrker. If the boolen is true, the String tht node represents is word. e.g if the red nodes re those with the mrker set to true, this trie hs the words, s, t, nd be. Note tht there is node representing the String b, but it is not word. s t e b

14 Prefix property Tries hve the useful property tht if given prefix, ll words which strt with the prefix re in the trie rooted t the node representing tht prefix. e.g. the trie rooted t the node outlined blue contins ll the words in the trie strting with the letter b For this reson, tries re sometimes clled prefix trees In this next ssignment, Autocomplete, this property will prove very useful s t e

15 Checking for words To check if word is in the trie, strt from the root. For ech chrcter in the word, see if there is child corresponding to the chrcter. If there is, move to it. If not, you know the word doesn t exist. After this, you ve rrived t the node representing the word. Then, simply check its boolen mrker. s t e b

16 Checking for words The blue rrows show the result of checking for s. We successfully trverse to the node representing s, nd its mrker is true, so we know s is word in our trie. b s t e

17 Checking for words The blue rrows show the result of checking for best. The node for be hs no child for the letter A, so we know best isn t word since node representing it does not exist. (You cn equivlently think of this s running off of the trie when we move to the A child since it doesn t exist) s t e b

18 Adding words The process for dding words is very similr to the process for seeing if they exist in the trie: We strt t the root, nd then for ech letter of the word, we move on to the child corresponding to tht letter. The difference is, when child we re trying to move to does not exist, we simply crete tht child before moving to it. Then, we set the lst node s boolen mrker to true. s t e b

19 Adding words For exmple, suppose we re dding the word bt to this trie. We set pointer current nd strt it t the root. We ll use the blue outline to represent the node current is pointing to. b s t e

20 Adding words Our first letter is b, so we move our pointer to the child corresponding to b. b s t e

21 Adding words Our next chrcter is. Our current node hs no child for, so we crete new node nd hve the b node point to it. b s t e

22 Adding words Our next chrcter is. Our current node hs no child for, so we crete new node nd hve the b node point to it. Then, we move the pointer down to it. b s t e

23 Adding words We repet this process for the chrcter t since we don t hve t child, we crete new node nd set tht s the t child, nd then move our pointer to tht child. b s t e t

24 Adding words We ve finished moving to the node representing our trget word t this point. Now, ll tht s left to do is set the current node s boolen mrker to true. Then, we ve successfully dded the word bt. b s t e t

25 Add: Pseudocode current = root for ech chrcter in the input word: if current doesn t hve child for tht chrcter: crete node nd set it s current s child current = current s child for tht chrcter set current s mrker to true

26 Actul Jv implementtion To ctully represent the nodes in the Trie, we ll use n implementtion like this: clss TrieNode{ } boolen isword; HshMp<Chrcter, TrieNode> children; //constructors If we hve node current nd we wnt to ccess the child of current corresponding to the chrcter ch we cn do so using current.children.get(ch) Similrly, to dd new child to current, we cn use current.children.put(ch, new TrieNode())

27 Discussion ctivity: TrieExmple Snrf the code for tody, nd complete the clss TrieExmple. The dd method is prtilly written for you. Complete this first before moving on to other methods, s the tester needs it to work. Remember, Mps come with ton of useful built in methods like continskey, keyset, nd vlues. For firstword, think of the most efficient wy to complete the method. You could just find every word, sort them, nd return the first one, but this is inefficient nd will time out the tester.