Boggle TrieProject incorporates a TRIE structure containing a word list. The "Boggle" portion presents a 4x4 matrix of characters. The game is played in 2 phases.WE WILL ONLY FOCUS ON PHASE 2 FOR THIS...

Boggle Trie




Intro to Swift Trie Tree Data structure built to store data Allows for searching Basic structure Root node Each [parent] node can have 0 or more children nodes Each node has only a single parent node Various tree structures exist Different rules regarding the number of nodes or the placement of node (based on values) Selection of the appropriate tree is based on storage or lookup needs Can have a profound efficiency impact Trie Tree structure used for search and retrieval Pronounced “try” or “try-ee” Binary trees used full key comparison Each node contain the key Searching for a value results in finding the entire value or key What if you only have a partial value? Trie Is a ‘prefix’ B-tree Portion of the key required in order to follow the path Each key is a sequence of characters 3 Characteristics Each node has up to n children nodes If we’re storing word strings, then up to 26 nodes in the English alphabet Each node stores a character (‘char’) type Root node is designated as a special character ( we can us ‘^’, the caret) It’s how we know we’re looking at the root node Each word (string) inserted into our Trie can be found by tracing a path from the root node to another node Not necessarily a leaf node End of string is noted with a character value other than A-Z or ^ (a character not part of the alphabet we’re using) We treat this character as ‘sentinel data’ Visually depicting the Trie Adding the words (strings) to the Trie results in the following: ARM ARC ARMED JAZZ JAWS Two strings having the same common prefix ARM, ARMED ARc, ARm, ARmed, ARming, ARmies, ARmy Prefix is only stored once Big O Search, insert, delete for any string s O(m)where m is the length of s Structure is used largely for searching Insertion might be costly, but outweighed by search savings Usage Using our Dictionary as a basis We move the word list to the Trie We can now search to see if a word exists Search character by character Match each character to a child node of the current node A child node is a “$” (or the terminating indicator) character Otherwise it’s not a word in our structure What about a partial word? We know whether or not to keep looking If the current node has more than one child (including the terminating indicator) Another possibility exists Prefix( ) method Finds the ‘prefix’ Match every character in the string to node values in a path of nodes, starting with the root It ends when there is no longer a match Returns the last node that matched Prefix(“JA”)returns “A” (and 2 child nodes) public Node Prefix(string s) { var currentNode = _root; var result = currentNode; foreach (var c in s) { currentNode = currentNode.FindChildNode(c); if (currentNode == null) break; result = currentNode; } return result; } Insert( ) method Relies on Prefix( ) We follow the node path until we hit the last matching node We return that node Insert the appropriate node value and new terminator Delete method Find the complete path to the node Work backward Delete any leaf nodes (no children) Deleting “JAWS” Still leaves us with the “JA” prefix Part of another string Search( ) method Relies on the Prefix( ) method Returns a match (or not) based on the prefix passed to it Only if the “prefix” (what you’re searching for) is a complete word The depth must match the length of the prefix string One of the children must be the sentinel value for a word ending Another child can still be there… it’s a word, but also part of another word! public bool Search(string s) { var prefix = Prefix(s); return prefix.Depth == s.Length && prefix.FindChildNode('$') != null; } Partial( ) method Based on the Prefix() method Looks for the prefix, which returns the last node matched in the prefix Depth must be the length of the prefix string Where Search relied on one of the children being the sentinel (‘$’) character Partial word relies on at least one child value other than the ‘$’ value While it can be a word, there should be at least one other child letter value Returning ‘true’ Partial(“JA”) Partial(“JAZ”) Partial(“JAW”) Returning ‘false’ Partial(“JAWS”) Node Char value is a character in the alphabet The ‘root’ node has a special character “sentinel” value‘^’ The value of the node (a child node) indicating the end of a word also is a special character “sentinel” value‘$’ Boggle How do we get to the “Boggle” game? Add user interaction on the form Clickable object (buttons, labels or textboxes) Each one has a character displayed When selected, we can indicate to the user that it’s selected Change the fore or back color, or disable it, etc… Arrange letters on the form in a 4x4 grid We use the grid to allow users to form a word to check Enforce the rules of the game Minimum of 3 letters Letters selected must be adjacent Cannot select the same position letter more than once Boggle Add internal structure to remember the words found Use this to tell the player it’s already been found, and not to score it again Add internal structure to hold the words which could’ve been found on that grid Use this to display the words to the player Listboxes can be used to display these word listings Create a ‘shadow’ grid Use this version for the backtracking algorithm in finding all possible words Must contain the value of the character Must contain an indicator of whether it’s been used in the construction of the word To avoid using it again Boggle User interaction Added a 4x4 grid of buttons Behind the scenes Create a collection (array) of Control type to hold these buttons Implemented a method to populate the array of Control type with the buttons Create a “Ltr” class Represents a letter on the grid Properties Charthe letter to be displayed Booleanwas the letter previously selected to form the current word Created an array of Ltr as a ‘shadow’ collection to the visible grid This will be used to backtrack Randomly generated characters Based on ASCII values from 65-91 for A-Z Assign these letters to the “letter” objects in the shadow collection Assign these letters to the faces of the buttons on the grid (each button’s “text” property) Boggle Arrays Can be single dimensional or two dimensional You simply keep track of which ‘row’ and ‘column’ User selects a letter Toggle the selection as ‘visited’ or ‘selected’ Don’t let the user select the same letter again in the word Keep track of the letters and “build” the word (prefix) to search Only allow adjacent unused letters to be used to build the word Allow the user to “undo” only the last letter selected Undo the letter in the ‘prefix’ being build as well Backtracking Use the ‘shadow’ structure to try all possible words Array shown has ‘border’ elements which are null or sentinel values Allows to decide if neighbor exists Need to make a ‘FindNeighbors’ method Selects all adjacent letters which are not already selected Consistent search Start with same position (‘North’) and then go clockwise Border can facilitate the algorithm But not necessary Example Start with a limited and known set of letters Take each letter, one at a time Start with the upper left corner (the position and not the letter itself) Add the position to the stack of positions (1,1) Select the letter and mark it as “selected” (C”) Add that letter to the word to seek (“C”) Is it a partial word? Yes Find all neighbors (the positions!) Not already selected? 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