# Trie | (Insert and Search)

Trie is an efficient information reTrieval data structure. Using Trie, search complexities can be brought to optimal limit (key length). If we store keys in binary search tree, a well balanced BST will need time proportional to M * log N, where M is maximum string length and N is number of keys in tree. Using Trie, we can search the key in O(M) time. However the penalty is on Trie storage requirements (Please refer Applications of Trie for more details) Every node of Trie consists of multiple branches. Each branch represents a possible character of keys. We need to mark the last node of every key as end of word node. A Trie node field isEndOfWord is used to distinguish the node as end of word node. A simple structure to represent nodes of the English alphabet can be as following,
``` // Trie node struct TrieNode {      struct TrieNode *children[ALPHABET_SIZE];```

``` ```

```     // isEndOfWord is true if the node      // represents end of a word      bool isEndOfWord; }; ```

Inserting a key into Trie is a simple approach. Every character of the input key is inserted as an individual Trie node. Note that the children is an array of pointers (or references) to next level trie nodes. The key character acts as an index into the array children. If the input key is new or an extension of the existing key, we need to construct non-existing nodes of the key, and mark end of the word for the last node. If the input key is a prefix of the existing key in Trie, we simply mark the last node of the key as the end of a word. The key length determines Trie depth.

Searching for a key is similar to insert operation, however, we only compare the characters and move down. The search can terminate due to the end of a string or lack of key in the trie. In the former case, if the isEndofWord field of the last node is true, then the key exists in the trie. In the second case, the search terminates without examining all the characters of the key, since the key is not present in the trie.

The following picture explains construction of trie using keys given in the example below,

```                       root
/
t   a     b
|   |     |
h   n     y
|   |    |
e   s  y  e
/  |   |
i  r   w
|  |   |
r  e   e
|
r```

In the picture, every character is of type trie_node_t. For example, the root is of type trie_node_t, and it’s children a, b and t are filled, all other nodes of root will be NULL. Similarly, “a” at the next level is having only one child (“n”), all other children are NULL. The leaf nodes are in blue.

Insert and search costs O(key_length), however the memory requirements of Trie is O(ALPHABET_SIZE * key_length * N) where N is number of keys in Trie. There are efficient representation of trie nodes (e.g. compressed trie, ternary search tree, etc.) to minimize memory requirements of trie.

## C++

 `// C++ implementation of search and insert ` `// operations on Trie ` `#include ` `using` `namespace` `std; ` ` `  `const` `int` `ALPHABET_SIZE = 26; ` ` `  `// trie node ` `struct` `TrieNode ` `{ ` `    ``struct` `TrieNode *children[ALPHABET_SIZE]; ` ` `  `    ``// isEndOfWord is true if the node represents ` `    ``// end of a word ` `    ``bool` `isEndOfWord; ` `}; ` ` `  `// Returns new trie node (initialized to NULLs) ` `struct` `TrieNode *getNode(``void``) ` `{ ` `    ``struct` `TrieNode *pNode =  ``new` `TrieNode; ` ` `  `    ``pNode->isEndOfWord = ``false``; ` ` `  `    ``for` `(``int` `i = 0; i < ALPHABET_SIZE; i++) ` `        ``pNode->children[i] = NULL; ` ` `  `    ``return` `pNode; ` `} ` ` `  `// If not present, inserts key into trie ` `// If the key is prefix of trie node, just ` `// marks leaf node ` `void` `insert(``struct` `TrieNode *root, string key) ` `{ ` `    ``struct` `TrieNode *pCrawl = root; ` ` `  `    ``for` `(``int` `i = 0; i < key.length(); i++) ` `    ``{ ` `        ``int` `index = key[i] - ``'a'``; ` `        ``if` `(!pCrawl->children[index]) ` `            ``pCrawl->children[index] = getNode(); ` ` `  `        ``pCrawl = pCrawl->children[index]; ` `    ``} ` ` `  `    ``// mark last node as leaf ` `    ``pCrawl->isEndOfWord = ``true``; ` `} ` ` `  `// Returns true if key presents in trie, else ` `// false ` `bool` `search(``struct` `TrieNode *root, string key) ` `{ ` `    ``struct` `TrieNode *pCrawl = root; ` ` `  `    ``for` `(``int` `i = 0; i < key.length(); i++) ` `    ``{ ` `        ``int` `index = key[i] - ``'a'``; ` `        ``if` `(!pCrawl->children[index]) ` `            ``return` `false``; ` ` `  `        ``pCrawl = pCrawl->children[index]; ` `    ``} ` ` `  `    ``return` `(pCrawl != NULL && pCrawl->isEndOfWord); ` `} ` ` `  `// Driver ` `int` `main() ` `{ ` `    ``// Input keys (use only 'a' through 'z' ` `    ``// and lower case) ` `    ``string keys[] = {``"the"``, ``"a"``, ``"there"``, ` `                    ``"answer"``, ``"any"``, ``"by"``, ` `                     ``"bye"``, ``"their"` `}; ` `    ``int` `n = ``sizeof``(keys)/``sizeof``(keys); ` ` `  `    ``struct` `TrieNode *root = getNode(); ` ` `  `    ``// Construct trie ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``insert(root, keys[i]); ` ` `  `    ``// Search for different keys ` `    ``search(root, ``"the"``)? cout << ````"Yes "``` `: ` `                         ``cout << ````"No "````; ` `    ``search(root, ``"these"``)? cout << ````"Yes "``` `: ` `                           ``cout << ````"No "````; ` `    ``return` `0; ` `} `

## C

 `// C implementation of search and insert operations ` `// on Trie ` `#include ` `#include ` `#include ` `#include ` ` `  `#define ARRAY_SIZE(a) sizeof(a)/sizeof(a) ` ` `  `// Alphabet size (# of symbols) ` `#define ALPHABET_SIZE (26) ` ` `  `// Converts key current character into index ` `// use only 'a' through 'z' and lower case ` `#define CHAR_TO_INDEX(c) ((int)c - (int)'a') ` ` `  `// trie node ` `struct` `TrieNode ` `{ ` `    ``struct` `TrieNode *children[ALPHABET_SIZE]; ` ` `  `    ``// isEndOfWord is true if the node represents ` `    ``// end of a word ` `    ``bool` `isEndOfWord; ` `}; ` ` `  `// Returns new trie node (initialized to NULLs) ` `struct` `TrieNode *getNode(``void``) ` `{ ` `    ``struct` `TrieNode *pNode = NULL; ` ` `  `    ``pNode = (``struct` `TrieNode *)``malloc``(``sizeof``(``struct` `TrieNode)); ` ` `  `    ``if` `(pNode) ` `    ``{ ` `        ``int` `i; ` ` `  `        ``pNode->isEndOfWord = ``false``; ` ` `  `        ``for` `(i = 0; i < ALPHABET_SIZE; i++) ` `            ``pNode->children[i] = NULL; ` `    ``} ` ` `  `    ``return` `pNode; ` `} ` ` `  `// If not present, inserts key into trie ` `// If the key is prefix of trie node, just marks leaf node ` `void` `insert(``struct` `TrieNode *root, ``const` `char` `*key) ` `{ ` `    ``int` `level; ` `    ``int` `length = ``strlen``(key); ` `    ``int` `index; ` ` `  `    ``struct` `TrieNode *pCrawl = root; ` ` `  `    ``for` `(level = 0; level < length; level++) ` `    ``{ ` `        ``index = CHAR_TO_INDEX(key[level]); ` `        ``if` `(!pCrawl->children[index]) ` `            ``pCrawl->children[index] = getNode(); ` ` `  `        ``pCrawl = pCrawl->children[index]; ` `    ``} ` ` `  `    ``// mark last node as leaf ` `    ``pCrawl->isEndOfWord = ``true``; ` `} ` ` `  `// Returns true if key presents in trie, else false ` `bool` `search(``struct` `TrieNode *root, ``const` `char` `*key) ` `{ ` `    ``int` `level; ` `    ``int` `length = ``strlen``(key); ` `    ``int` `index; ` `    ``struct` `TrieNode *pCrawl = root; ` ` `  `    ``for` `(level = 0; level < length; level++) ` `    ``{ ` `        ``index = CHAR_TO_INDEX(key[level]); ` ` `  `        ``if` `(!pCrawl->children[index]) ` `            ``return` `false``; ` ` `  `        ``pCrawl = pCrawl->children[index]; ` `    ``} ` ` `  `    ``return` `(pCrawl != NULL && pCrawl->isEndOfWord); ` `} ` ` `  `// Driver ` `int` `main() ` `{ ` `    ``// Input keys (use only 'a' through 'z' and lower case) ` `    ``char` `keys[] = {``"the"``, ``"a"``, ``"there"``, ``"answer"``, ``"any"``, ` `                     ``"by"``, ``"bye"``, ``"their"``}; ` ` `  `    ``char` `output[] = {``"Not present in trie"``, ``"Present in trie"``}; ` ` `  ` `  `    ``struct` `TrieNode *root = getNode(); ` ` `  `    ``// Construct trie ` `    ``int` `i; ` `    ``for` `(i = 0; i < ARRAY_SIZE(keys); i++) ` `        ``insert(root, keys[i]); ` ` `  `    ``// Search for different keys ` `    ``printf``(````"%s --- %s "````, ``"the"``, output[search(root, ``"the"``)] ); ` `    ``printf``(````"%s --- %s "````, ``"these"``, output[search(root, ``"these"``)] ); ` `    ``printf``(````"%s --- %s "````, ``"their"``, output[search(root, ``"their"``)] ); ` `    ``printf``(````"%s --- %s "````, ``"thaw"``, output[search(root, ``"thaw"``)] ); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of search and insert operations ` `// on Trie ` `public` `class` `Trie { ` `     `  `    ``// Alphabet size (# of symbols) ` `    ``static` `final` `int` `ALPHABET_SIZE = ``26``; ` `     `  `    ``// trie node ` `    ``static` `class` `TrieNode ` `    ``{ ` `        ``TrieNode[] children = ``new` `TrieNode[ALPHABET_SIZE]; ` `      `  `        ``// isEndOfWord is true if the node represents ` `        ``// end of a word ` `        ``boolean` `isEndOfWord; ` `         `  `        ``TrieNode(){ ` `            ``isEndOfWord = ``false``; ` `            ``for` `(``int` `i = ``0``; i < ALPHABET_SIZE; i++) ` `                ``children[i] = ``null``; ` `        ``} ` `    ``}; ` `      `  `    ``static` `TrieNode root;  ` `     `  `    ``// If not present, inserts key into trie ` `    ``// If the key is prefix of trie node,  ` `    ``// just marks leaf node ` `    ``static` `void` `insert(String key) ` `    ``{ ` `        ``int` `level; ` `        ``int` `length = key.length(); ` `        ``int` `index; ` `      `  `        ``TrieNode pCrawl = root; ` `      `  `        ``for` `(level = ``0``; level < length; level++) ` `        ``{ ` `            ``index = key.charAt(level) - ``'a'``; ` `            ``if` `(pCrawl.children[index] == ``null``) ` `                ``pCrawl.children[index] = ``new` `TrieNode(); ` `      `  `            ``pCrawl = pCrawl.children[index]; ` `        ``} ` `      `  `        ``// mark last node as leaf ` `        ``pCrawl.isEndOfWord = ``true``; ` `    ``} ` `      `  `    ``// Returns true if key presents in trie, else false ` `    ``static` `boolean` `search(String key) ` `    ``{ ` `        ``int` `level; ` `        ``int` `length = key.length(); ` `        ``int` `index; ` `        ``TrieNode pCrawl = root; ` `      `  `        ``for` `(level = ``0``; level < length; level++) ` `        ``{ ` `            ``index = key.charAt(level) - ``'a'``; ` `      `  `            ``if` `(pCrawl.children[index] == ``null``) ` `                ``return` `false``; ` `      `  `            ``pCrawl = pCrawl.children[index]; ` `        ``} ` `      `  `        ``return` `(pCrawl != ``null` `&& pCrawl.isEndOfWord); ` `    ``} ` `      `  `    ``// Driver ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``// Input keys (use only 'a' through 'z' and lower case) ` `        ``String keys[] = {``"the"``, ``"a"``, ``"there"``, ``"answer"``, ``"any"``, ` `                         ``"by"``, ``"bye"``, ``"their"``}; ` `      `  `        ``String output[] = {``"Not present in trie"``, ``"Present in trie"``}; ` `      `  `      `  `        ``root = ``new` `TrieNode(); ` `      `  `        ``// Construct trie ` `        ``int` `i; ` `        ``for` `(i = ``0``; i < keys.length ; i++) ` `            ``insert(keys[i]); ` `      `  `        ``// Search for different keys ` `        ``if``(search(``"the"``) == ``true``) ` `            ``System.out.println(``"the --- "` `+ output[``1``]); ` `        ``else` `System.out.println(``"the --- "` `+ output[``0``]); ` `         `  `        ``if``(search(``"these"``) == ``true``) ` `            ``System.out.println(``"these --- "` `+ output[``1``]); ` `        ``else` `System.out.println(``"these --- "` `+ output[``0``]); ` `         `  `        ``if``(search(``"their"``) == ``true``) ` `            ``System.out.println(``"their --- "` `+ output[``1``]); ` `        ``else` `System.out.println(``"their --- "` `+ output[``0``]); ` `         `  `        ``if``(search(``"thaw"``) == ``true``) ` `            ``System.out.println(``"thaw --- "` `+ output[``1``]); ` `        ``else` `System.out.println(``"thaw --- "` `+ output[``0``]); ` `        `  `    ``} ` `} ` `// This code is contributed by Sumit Ghosh `

## Python

 `# Python program for insert and search ` `# operation in a Trie ` ` `  `class` `TrieNode: ` `     `  `    ``# Trie node class ` `    ``def` `__init__(``self``): ` `        ``self``.children ``=` `[``None``]``*``26` ` `  `        ``# isEndOfWord is True if node represent the end of the word ` `        ``self``.isEndOfWord ``=` `False` ` `  `class` `Trie: ` `     `  `    ``# Trie data structure class ` `    ``def` `__init__(``self``): ` `        ``self``.root ``=` `self``.getNode() ` ` `  `    ``def` `getNode(``self``): ` `     `  `        ``# Returns new trie node (initialized to NULLs) ` `        ``return` `TrieNode() ` ` `  `    ``def` `_charToIndex(``self``,ch): ` `         `  `        ``# private helper function ` `        ``# Converts key current character into index ` `        ``# use only 'a' through 'z' and lower case ` `         `  `        ``return` `ord``(ch)``-``ord``(``'a'``) ` ` `  ` `  `    ``def` `insert(``self``,key): ` `         `  `        ``# If not present, inserts key into trie ` `        ``# If the key is prefix of trie node,  ` `        ``# just marks leaf node ` `        ``pCrawl ``=` `self``.root ` `        ``length ``=` `len``(key) ` `        ``for` `level ``in` `range``(length): ` `            ``index ``=` `self``._charToIndex(key[level]) ` ` `  `            ``# if current character is not present ` `            ``if` `not` `pCrawl.children[index]: ` `                ``pCrawl.children[index] ``=` `self``.getNode() ` `            ``pCrawl ``=` `pCrawl.children[index] ` ` `  `        ``# mark last node as leaf ` `        ``pCrawl.isEndOfWord ``=` `True` ` `  `    ``def` `search(``self``, key): ` `         `  `        ``# Search key in the trie ` `        ``# Returns true if key presents  ` `        ``# in trie, else false ` `        ``pCrawl ``=` `self``.root ` `        ``length ``=` `len``(key) ` `        ``for` `level ``in` `range``(length): ` `            ``index ``=` `self``._charToIndex(key[level]) ` `            ``if` `not` `pCrawl.children[index]: ` `                ``return` `False` `            ``pCrawl ``=` `pCrawl.children[index] ` ` `  `        ``return` `pCrawl !``=` `None` `and` `pCrawl.isEndOfWord ` ` `  `# driver function ` `def` `main(): ` ` `  `    ``# Input keys (use only 'a' through 'z' and lower case) ` `    ``keys ``=` `[``"the"``,``"a"``,``"there"``,``"anaswe"``,``"any"``, ` `            ``"by"``,``"their"``] ` `    ``output ``=` `[``"Not present in trie"``, ` `              ``"Present in trie"``] ` ` `  `    ``# Trie object ` `    ``t ``=` `Trie() ` ` `  `    ``# Construct trie ` `    ``for` `key ``in` `keys: ` `        ``t.insert(key) ` ` `  `    ``# Search for different keys ` `    ``print``(``"{} ---- {}"``.``format``(``"the"``,output[t.search(``"the"``)])) ` `    ``print``(``"{} ---- {}"``.``format``(``"these"``,output[t.search(``"these"``)])) ` `    ``print``(``"{} ---- {}"``.``format``(``"their"``,output[t.search(``"their"``)])) ` `    ``print``(``"{} ---- {}"``.``format``(``"thaw"``,output[t.search(``"thaw"``)])) ` ` `  `if` `__name__ ``=``=` `'__main__'``: ` `    ``main() ` ` `  `# This code is contributed by Atul Kumar (www.facebook.com/atul.kr.007) `

## C#

 `// C# implementation of search and  ` `// insert operations on Trie ` `using` `System; ` `     `  `public` `class` `Trie  ` `{ ` `     `  `    ``// Alphabet size (# of symbols) ` `    ``static` `readonly` `int` `ALPHABET_SIZE = 26; ` `     `  `    ``// trie node ` `    ``class` `TrieNode ` `    ``{ ` `        ``public` `TrieNode[] children = ``new` `TrieNode[ALPHABET_SIZE]; ` `     `  `        ``// isEndOfWord is true if the node represents ` `        ``// end of a word ` `        ``public` `bool` `isEndOfWord; ` `         `  `        ``public` `TrieNode() ` `        ``{ ` `            ``isEndOfWord = ``false``; ` `            ``for` `(``int` `i = 0; i < ALPHABET_SIZE; i++) ` `                ``children[i] = ``null``; ` `        ``} ` `    ``}; ` `     `  `    ``static` `TrieNode root;  ` `     `  `    ``// If not present, inserts key into trie ` `    ``// If the key is prefix of trie node,  ` `    ``// just marks leaf node ` `    ``static` `void` `insert(String key) ` `    ``{ ` `        ``int` `level; ` `        ``int` `length = key.Length; ` `        ``int` `index; ` `     `  `        ``TrieNode pCrawl = root; ` `     `  `        ``for` `(level = 0; level < length; level++) ` `        ``{ ` `            ``index = key[level] - ``'a'``; ` `            ``if` `(pCrawl.children[index] == ``null``) ` `                ``pCrawl.children[index] = ``new` `TrieNode(); ` `     `  `            ``pCrawl = pCrawl.children[index]; ` `        ``} ` `     `  `        ``// mark last node as leaf ` `        ``pCrawl.isEndOfWord = ``true``; ` `    ``} ` `     `  `    ``// Returns true if key  ` `    ``// presents in trie, else false ` `    ``static` `bool` `search(String key) ` `    ``{ ` `        ``int` `level; ` `        ``int` `length = key.Length; ` `        ``int` `index; ` `        ``TrieNode pCrawl = root; ` `     `  `        ``for` `(level = 0; level < length; level++) ` `        ``{ ` `            ``index = key[level] - ``'a'``; ` `     `  `            ``if` `(pCrawl.children[index] == ``null``) ` `                ``return` `false``; ` `     `  `            ``pCrawl = pCrawl.children[index]; ` `        ``} ` `     `  `        ``return` `(pCrawl != ``null` `&& pCrawl.isEndOfWord); ` `    ``} ` `     `  `    ``// Driver ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``// Input keys (use only 'a'  ` `        ``// through 'z' and lower case) ` `        ``String []keys = {``"the"``, ``"a"``, ``"there"``, ``"answer"``,  ` `                        ``"any"``, ``"by"``, ``"bye"``, ``"their"``}; ` `     `  `        ``String []output = {``"Not present in trie"``, ``"Present in trie"``}; ` `     `  `     `  `        ``root = ``new` `TrieNode(); ` `     `  `        ``// Construct trie ` `        ``int` `i; ` `        ``for` `(i = 0; i < keys.Length ; i++) ` `            ``insert(keys[i]); ` `     `  `        ``// Search for different keys ` `        ``if``(search(``"the"``) == ``true``) ` `            ``Console.WriteLine(``"the --- "` `+ output); ` `        ``else` `Console.WriteLine(``"the --- "` `+ output); ` `         `  `        ``if``(search(``"these"``) == ``true``) ` `            ``Console.WriteLine(``"these --- "` `+ output); ` `        ``else` `Console.WriteLine(``"these --- "` `+ output); ` `         `  `        ``if``(search(``"their"``) == ``true``) ` `            ``Console.WriteLine(``"their --- "` `+ output); ` `        ``else` `Console.WriteLine(``"their --- "` `+ output); ` `         `  `        ``if``(search(``"thaw"``) == ``true``) ` `            ``Console.WriteLine(``"thaw --- "` `+ output); ` `        ``else` `Console.WriteLine(``"thaw --- "` `+ output); ` `         `  `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output :

```the --- Present in trie
these --- Not present in trie
their --- Present in trie
thaw --- Not present in trie```

NOTE : In video, isEndOfWord is referred as isLeaf.

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