Problem description:

Implement a trie with insert, search, and startsWith methods.

Example:

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Trie trie = new Trie();

trie.insert("apple");
trie.search("apple");   // returns true
trie.search("app");     // returns false
trie.startsWith("app"); // returns true
trie.insert("app");   
trie.search("app");     // returns true

Note:
You may assume that all inputs are consist of lowercase letters a-z.
All inputs are guaranteed to be non-empty strings.

Solution:

Trie is an important data structure that frequently appeared in interviews. To design a TrieNode, we need a word collection child[26], which is from a-z, and a boolean value isWord that denotes whether this node is a word or not.

Insertion in trie

Searching in trie

Searching prefix in trie

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class TrieNode:
    def __init__(self):
        self.child = defaultdict(TrieNode)
        self.is_word = False
        
class Trie:

    def __init__(self):
        self.root = TrieNode()

    def insert(self, word: str) -> None:
        p = self.root
        for c in word:
            p = p.child[c]
        p.is_word = True

    def search(self, word: str) -> bool:
        p = self.root
        for c in word:
            if c not in p.child:
                return False
            else:
                p = p.child[c]
        return p.is_word

    def startsWith(self, prefix: str) -> bool:
        p = self.root
        for c in prefix:
            if c not in p.child:
                return False
            else:
                p = p.child[c]
        return True
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class TrieNode{
public:
    TrieNode* child[26];
    bool isWord;
        
    TrieNode(): isWord(false){
        for(auto &c: child)
            c= NULL;
    }
};

class Trie {
public:
    /** Initialize your data structure here. */
    TrieNode* root;
    Trie() {
        root= new TrieNode();
    }
    
    /** Inserts a word into the trie. */
    void insert(string word) {
        TrieNode* p= root;
        for(auto a: word){
            int i= a-'a';
            if(!p->child[i]) 
                p->child[i]= new TrieNode();
            
            p= p->child[i];
        }
        p->isWord= true; //!!!!!!!!!!!!!! important!!!!
    }
    
    /** Returns if the word is in the trie. */
    bool search(string key) {
        TrieNode* p= root;
        for(auto c: key){
            int i= c- 'a';
            if(!p->child[i]) return false;
            p= p->child[i];
        }
        return p->isWord;
    }
    
    /** Returns if there is any word in the trie that starts with the given prefix. */
    bool startsWith(string prefix) {
        TrieNode* p= root;
        for(auto c: prefix){
            int i= c- 'a';
            if(!p->child[i]) return false;
            p= p->child[i];
        }
        return true;
    }
};

/**
 * Your Trie object will be instantiated and called as such:
 * Trie obj = new Trie();
 * obj.insert(word);
 * bool param_2 = obj.search(word);
 * bool param_3 = obj.startsWith(prefix);
 */

Insertion:
time complexity: $O(m)$, m is key length
space complexity: $O(m)$, m is key length

Search:
time complexity: $O(m)$, m is key length
space complexity: $O(1)$

Search prefix:
time complexity: $O(m)$, m is key length
space complexity: $O(1)

reference:
https://goo.gl/JjdfdH
https://goo.gl/oYnq3P
https://goo.gl/QvAJQx