common nonempty prefixthat isexcept for the rootall internal nodes have one child trie for set of strings can be used to implement dictionary whose keys are the strings of namelywe perform search in for string by tracing down from the root the path indicated by the characters in if this path can be traced and terminates at an external nodethen we know is in the dictionary for examplein the trie in figure tracing the path for "bullends up at an external node if the path cannot be traced or the path can be traced but terminates at an internal nodethen is not in the dictionary in the example in figure the path for "betcannot be traced and the path for "beends at an internal node neither such word is in the dictionary note that in this implementation of dictionarysingle characters are compared instead of the entire string (keyit is easy to see that the running time of the search for string of size is (dm)where is the size of the alphabet indeedwe visit at most nodes of and we spend (dtime at each node for some alphabetswe may be able to improve the time spent at node to be ( or (logdby using dictionary of characters implemented in hash table or search table howeversince is constant in most applicationswe can stick with the simple approach that takes (dtime per node visited from the discussion aboveit follows that we can use trie to perform special type of pattern matchingcalled word matchingwhere we want to determine whether given pattern matches one of the words of the text exactly (see figure word matching differs from standard pattern matching since the pattern cannot match an arbitrary substring of the textbut only one of its words using trieword matching for pattern of length takes (dmtimewhere is the size of the alphabetindependent of the size of the text if the alphabet has constant size (as is the case for text in natural languages and dna strings) query takes (mtimeproportional to the size of the pattern simple extension of this scheme supports prefix matching queries howeverarbitrary occurrences of the pattern in the text (for examplethe pattern is proper suffix of word or spans two wordscannot be efficiently performed to construct standard trie for set of stringswe can use an incremental algorithm that inserts the strings one at time recall the assumption that no string of is prefix of another string to insert string into the current trie twe first try to trace the path associated with in since is not already in and no string in is prefix of another stringwe will stop tracing the path at an internal node of before reaching the end of we then create new chain of node descendents of to store the remaining characters of the time to insert is (dm)where is the length of and is the size of the alphabet thusconstructing the entire trie for set takes (dntimewhere is the total length of the strings of figure word matching and prefix matching with standard trie(atext to be searched(bstandard