Related Articles

# Boggle | Set 2 (Using Trie)

• Difficulty Level : Expert
• Last Updated : 18 Jun, 2021

Given a dictionary, a method to do a lookup in the dictionary and a M x N board where every cell has one character. Find all possible words that can be formed by a sequence of adjacent characters. Note that we can move to any of 8 adjacent characters, but a word should not have multiple instances of the same cell.
Example:

```Input: dictionary[] = {"GEEKS", "FOR", "QUIZ", "GO"};
boggle[][]   = {{'G', 'I', 'Z'},
{'U', 'E', 'K'},
{'Q', 'S', 'E'}};

Output: Following words of the dictionary are present
GEEKS
QUIZ

Explanation:``` ```Input: dictionary[] = {"GEEKS", "ABCFIHGDE"};
boggle[][]   = {{'A', 'B', 'C'},
{'D', 'E', 'F'},
{'G', 'H', 'I'}};
Output: Following words of the dictionary are present
ABCFIHGDE
Explanation:``` ` `

We have discussed a Graph DFS based solution in below post.
Boggle (Find all possible words in a board of characters) | Set 1
Here we discuss a Trie based solution which is better then DFS based solution.
Given Dictionary dictionary[] = {“GEEKS”, “FOR”, “QUIZ”, “GO”}
1. Create an Empty trie and insert all words of given dictionary into trie

```After insertion, Trie looks like(leaf nodes are in RED)
root
/
G   F     Q
/  |   |     |
O   E   O     U
|   |     |
E    R     I
|         |
K         Z
|
S   ```

2. After that we have pick only those character in boggle[][] which are child of root of Trie
Let for above we pick ‘G’ boggle, ‘Q’ boggle (they both are present in boggle matrix)
3. search a word in a trie which start with character that we pick in step 2

```1) Create bool visited boolean matrix (Visited[M][N] = false )
2) Call SearchWord() for every cell (i, j) which has one of the
first characters of dictionary words. In above example,
we have 'G' and 'Q' as first characters.

SearchWord(Trie *root, i, j, visited[][N])
if root->leaf == true
print word

if we have seen this element first time then make it visited.
visited[i][j] = true
do
traverse all child of current root
k goes (0 to 26 ) [there are only 26 Alphabet]
add current char and search for next character

find next character which is adjacent to boggle[i][j]
they are 8 adjacent cells of boggle[i][j] (i+1, j+1),
(i+1, j) (i-1, j) and so on.

make it unvisited visited[i][j] = false ```

Below is the implementation of above idea:

## C++

 `// C++ program for Boggle game``#include ``using` `namespace` `std;` `// Converts key current character into index``// use only 'A' through 'Z'``#define char_int(c) ((int)c - (int)'A')` `// Alphabet size``#define SIZE (26)` `#define M 3``#define N 3` `// trie Node``struct` `TrieNode {``    ``TrieNode* Child[SIZE];` `    ``// isLeaf is true if the node represents``    ``// end of a word``    ``bool` `leaf;``};` `// Returns new trie node (initialized to NULLs)``TrieNode* getNode()``{``    ``TrieNode* newNode = ``new` `TrieNode;``    ``newNode->leaf = ``false``;``    ``for` `(``int` `i = 0; i < SIZE; i++)``        ``newNode->Child[i] = NULL;``    ``return` `newNode;``}` `// If not present, inserts a key into the trie``// If the key is a prefix of trie node, just``// marks leaf node``void` `insert(TrieNode* root, ``char``* Key)``{``    ``int` `n = ``strlen``(Key);``    ``TrieNode* pChild = root;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``int` `index = char_int(Key[i]);` `        ``if` `(pChild->Child[index] == NULL)``            ``pChild->Child[index] = getNode();` `        ``pChild = pChild->Child[index];``    ``}` `    ``// make last node as leaf node``    ``pChild->leaf = ``true``;``}` `// function to check that current location``// (i and j) is in matrix range``bool` `isSafe(``int` `i, ``int` `j, ``bool` `visited[M][N])``{``    ``return` `(i >= 0 && i < M && j >= 0 && j < N && !visited[i][j]);``}` `// A recursive function to print all words present on boggle``void` `searchWord(TrieNode* root, ``char` `boggle[M][N], ``int` `i,``                ``int` `j, ``bool` `visited[][N], string str)``{``    ``// if we found word in trie / dictionary``    ``if` `(root->leaf == ``true``)``        ``cout << str << endl;` `    ``// If both I and j in  range and we visited``    ``// that element of matrix first time``    ``if` `(isSafe(i, j, visited)) {``        ``// make it visited``        ``visited[i][j] = ``true``;` `        ``// traverse all childs of current root``        ``for` `(``int` `K = 0; K < SIZE; K++) {``            ``if` `(root->Child[K] != NULL) {``                ``// current character``                ``char` `ch = (``char``)K + (``char``)``'A'``;` `                ``// Recursively search reaming character of word``                ``// in trie for all 8 adjacent cells of boggle[i][j]``                ``if` `(isSafe(i + 1, j + 1, visited)``                    ``&& boggle[i + 1][j + 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i + 1, j + 1, visited, str + ch);``                ``if` `(isSafe(i, j + 1, visited)``                    ``&& boggle[i][j + 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i, j + 1, visited, str + ch);``                ``if` `(isSafe(i - 1, j + 1, visited)``                    ``&& boggle[i - 1][j + 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i - 1, j + 1, visited, str + ch);``                ``if` `(isSafe(i + 1, j, visited)``                    ``&& boggle[i + 1][j] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i + 1, j, visited, str + ch);``                ``if` `(isSafe(i + 1, j - 1, visited)``                    ``&& boggle[i + 1][j - 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i + 1, j - 1, visited, str + ch);``                ``if` `(isSafe(i, j - 1, visited)``                    ``&& boggle[i][j - 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i, j - 1, visited, str + ch);``                ``if` `(isSafe(i - 1, j - 1, visited)``                    ``&& boggle[i - 1][j - 1] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i - 1, j - 1, visited, str + ch);``                ``if` `(isSafe(i - 1, j, visited)``                    ``&& boggle[i - 1][j] == ch)``                    ``searchWord(root->Child[K], boggle,``                               ``i - 1, j, visited, str + ch);``            ``}``        ``}` `        ``// make current element unvisited``        ``visited[i][j] = ``false``;``    ``}``}` `// Prints all words present in dictionary.``void` `findWords(``char` `boggle[M][N], TrieNode* root)``{``    ``// Mark all characters as not visited``    ``bool` `visited[M][N];``    ``memset``(visited, ``false``, ``sizeof``(visited));` `    ``TrieNode* pChild = root;` `    ``string str = ``""``;` `    ``// traverse all matrix elements``    ``for` `(``int` `i = 0; i < M; i++) {``        ``for` `(``int` `j = 0; j < N; j++) {``            ``// we start searching for word in dictionary``            ``// if we found a character which is child``            ``// of Trie root``            ``if` `(pChild->Child[char_int(boggle[i][j])]) {``                ``str = str + boggle[i][j];``                ``searchWord(pChild->Child[char_int(boggle[i][j])],``                           ``boggle, i, j, visited, str);``                ``str = ``""``;``            ``}``        ``}``    ``}``}` `// Driver program to test above function``int` `main()``{``    ``// Let the given dictionary be following``    ``char``* dictionary[] = { ``"GEEKS"``, ``"FOR"``, ``"QUIZ"``, ``"GEE"` `};` `    ``// root Node of trie``    ``TrieNode* root = getNode();` `    ``// insert all words of dictionary into trie``    ``int` `n = ``sizeof``(dictionary) / ``sizeof``(dictionary);``    ``for` `(``int` `i = 0; i < n; i++)``        ``insert(root, dictionary[i]);` `    ``char` `boggle[M][N] = { { ``'G'``, ``'I'``, ``'Z'` `},``                          ``{ ``'U'``, ``'E'``, ``'K'` `},``                          ``{ ``'Q'``, ``'S'``, ``'E'` `} };` `    ``findWords(boggle, root);` `    ``return` `0;``}`

## Java

 `// Java program for Boggle game``public` `class` `Boggle {` `    ``// Alphabet size``    ``static` `final` `int` `SIZE = ``26``;` `    ``static` `final` `int` `M = ``3``;``    ``static` `final` `int` `N = ``3``;` `    ``// trie Node``    ``static` `class` `TrieNode {``        ``TrieNode[] Child = ``new` `TrieNode[SIZE];` `        ``// isLeaf is true if the node represents``        ``// end of a word``        ``boolean` `leaf;` `        ``// constructor``        ``public` `TrieNode()``        ``{``            ``leaf = ``false``;``            ``for` `(``int` `i = ``0``; i < SIZE; i++)``                ``Child[i] = ``null``;``        ``}``    ``}` `    ``// If not present, inserts a key into the trie``    ``// If the key is a prefix of trie node, just``    ``// marks leaf node``    ``static` `void` `insert(TrieNode root, String Key)``    ``{``        ``int` `n = Key.length();``        ``TrieNode pChild = root;` `        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``int` `index = Key.charAt(i) - ``'A'``;` `            ``if` `(pChild.Child[index] == ``null``)``                ``pChild.Child[index] = ``new` `TrieNode();` `            ``pChild = pChild.Child[index];``        ``}` `        ``// make last node as leaf node``        ``pChild.leaf = ``true``;``    ``}` `    ``// function to check that current location``    ``// (i and j) is in matrix range``    ``static` `boolean` `isSafe(``int` `i, ``int` `j, ``boolean` `visited[][])``    ``{``        ``return` `(i >= ``0` `&& i < M && j >= ``0``                ``&& j < N && !visited[i][j]);``    ``}` `    ``// A recursive function to print``    ``// all words present on boggle``    ``static` `void` `searchWord(TrieNode root, ``char` `boggle[][], ``int` `i,``                           ``int` `j, ``boolean` `visited[][], String str)``    ``{``        ``// if we found word in trie / dictionary``        ``if` `(root.leaf == ``true``)``            ``System.out.println(str);` `        ``// If both I and j in  range and we visited``        ``// that element of matrix first time``        ``if` `(isSafe(i, j, visited)) {``            ``// make it visited``            ``visited[i][j] = ``true``;` `            ``// traverse all child of current root``            ``for` `(``int` `K = ``0``; K < SIZE; K++) {``                ``if` `(root.Child[K] != ``null``) {``                    ``// current character``                    ``char` `ch = (``char``)(K + ``'A'``);` `                    ``// Recursively search reaming character of word``                    ``// in trie for all 8 adjacent cells of``                    ``// boggle[i][j]``                    ``if` `(isSafe(i + ``1``, j + ``1``, visited)``                        ``&& boggle[i + ``1``][j + ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i + ``1``, j + ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i, j + ``1``, visited)``                        ``&& boggle[i][j + ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i, j + ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - ``1``, j + ``1``, visited)``                        ``&& boggle[i - ``1``][j + ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i - ``1``, j + ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i + ``1``, j, visited)``                        ``&& boggle[i + ``1``][j] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i + ``1``, j,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i + ``1``, j - ``1``, visited)``                        ``&& boggle[i + ``1``][j - ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i + ``1``, j - ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i, j - ``1``, visited)``                        ``&& boggle[i][j - ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i, j - ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - ``1``, j - ``1``, visited)``                        ``&& boggle[i - ``1``][j - ``1``] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i - ``1``, j - ``1``,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - ``1``, j, visited)``                        ``&& boggle[i - ``1``][j] == ch)``                        ``searchWord(root.Child[K], boggle,``                                   ``i - ``1``, j,``                                   ``visited, str + ch);``                ``}``            ``}` `            ``// make current element unvisited``            ``visited[i][j] = ``false``;``        ``}``    ``}` `    ``// Prints all words present in dictionary.``    ``static` `void` `findWords(``char` `boggle[][], TrieNode root)``    ``{``        ``// Mark all characters as not visited``        ``boolean``[][] visited = ``new` `boolean``[M][N];``        ``TrieNode pChild = root;` `        ``String str = ``""``;` `        ``// traverse all matrix elements``        ``for` `(``int` `i = ``0``; i < M; i++) {``            ``for` `(``int` `j = ``0``; j < N; j++) {``                ``// we start searching for word in dictionary``                ``// if we found a character which is child``                ``// of Trie root``                ``if` `(pChild.Child[(boggle[i][j]) - ``'A'``] != ``null``) {``                    ``str = str + boggle[i][j];``                    ``searchWord(pChild.Child[(boggle[i][j]) - ``'A'``],``                               ``boggle, i, j, visited, str);``                    ``str = ``""``;``                ``}``            ``}``        ``}``    ``}` `    ``// Driver program to test above function``    ``public` `static` `void` `main(String args[])``    ``{``        ``// Let the given dictionary be following``        ``String dictionary[] = { ``"GEEKS"``, ``"FOR"``, ``"QUIZ"``, ``"GEE"` `};` `        ``// root Node of trie``        ``TrieNode root = ``new` `TrieNode();` `        ``// insert all words of dictionary into trie``        ``int` `n = dictionary.length;``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``insert(root, dictionary[i]);` `        ``char` `boggle[][] = { { ``'G'``, ``'I'``, ``'Z'` `},``                            ``{ ``'U'``, ``'E'``, ``'K'` `},``                            ``{ ``'Q'``, ``'S'``, ``'E'` `} };` `        ``findWords(boggle, root);``    ``}``}``// This code is contributed by Sumit Ghosh`

## C#

 `// C# program for Boggle game``using` `System;` `public` `class` `Boggle {` `    ``// Alphabet size``    ``static` `readonly` `int` `SIZE = 26;` `    ``static` `readonly` `int` `M = 3;``    ``static` `readonly` `int` `N = 3;` `    ``// trie Node``    ``public` `class` `TrieNode {``        ``public` `TrieNode[] Child = ``new` `TrieNode[SIZE];` `        ``// isLeaf is true if the node represents``        ``// end of a word``        ``public` `bool` `leaf;` `        ``// constructor``        ``public` `TrieNode()``        ``{``            ``leaf = ``false``;``            ``for` `(``int` `i = 0; i < SIZE; i++)``                ``Child[i] = ``null``;``        ``}``    ``}` `    ``// If not present, inserts a key into the trie``    ``// If the key is a prefix of trie node, just``    ``// marks leaf node``    ``static` `void` `insert(TrieNode root, String Key)``    ``{``        ``int` `n = Key.Length;``        ``TrieNode pChild = root;` `        ``for` `(``int` `i = 0; i < n; i++) {``            ``int` `index = Key[i] - ``'A'``;` `            ``if` `(pChild.Child[index] == ``null``)``                ``pChild.Child[index] = ``new` `TrieNode();` `            ``pChild = pChild.Child[index];``        ``}` `        ``// make last node as leaf node``        ``pChild.leaf = ``true``;``    ``}` `    ``// function to check that current location``    ``// (i and j) is in matrix range``    ``static` `bool` `isSafe(``int` `i, ``int` `j, ``bool``[, ] visited)``    ``{``        ``return` `(i >= 0 && i < M && j >= 0 && j < N && !visited[i, j]);``    ``}` `    ``// A recursive function to print all words present on boggle``    ``static` `void` `searchWord(TrieNode root, ``char``[, ] boggle, ``int` `i,``                           ``int` `j, ``bool``[, ] visited, String str)``    ``{``        ``// if we found word in trie / dictionary``        ``if` `(root.leaf == ``true``)``            ``Console.WriteLine(str);` `        ``// If both I and j in range and we visited``        ``// that element of matrix first time``        ``if` `(isSafe(i, j, visited)) {``            ``// make it visited``            ``visited[i, j] = ``true``;` `            ``// traverse all child of current root``            ``for` `(``int` `K = 0; K < SIZE; K++) {``                ``if` `(root.Child[K] != ``null``) {``                    ``// current character``                    ``char` `ch = (``char``)(K + ``'A'``);` `                    ``// Recursively search reaming character of word``                    ``// in trie for all 8 adjacent cells of``                    ``// boggle[i, j]``                    ``if` `(isSafe(i + 1, j + 1, visited) && boggle[i + 1, j + 1] == ch)``                        ``searchWord(root.Child[K], boggle, i + 1, j + 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i, j + 1, visited) && boggle[i, j + 1] == ch)``                        ``searchWord(root.Child[K], boggle, i, j + 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - 1, j + 1, visited) && boggle[i - 1, j + 1] == ch)``                        ``searchWord(root.Child[K], boggle, i - 1, j + 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i + 1, j, visited) && boggle[i + 1, j] == ch)``                        ``searchWord(root.Child[K], boggle, i + 1, j,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i + 1, j - 1, visited) && boggle[i + 1, j - 1] == ch)``                        ``searchWord(root.Child[K], boggle, i + 1, j - 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i, j - 1, visited) && boggle[i, j - 1] == ch)``                        ``searchWord(root.Child[K], boggle, i, j - 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - 1, j - 1, visited) && boggle[i - 1, j - 1] == ch)``                        ``searchWord(root.Child[K], boggle, i - 1, j - 1,``                                   ``visited, str + ch);``                    ``if` `(isSafe(i - 1, j, visited) && boggle[i - 1, j] == ch)``                        ``searchWord(root.Child[K], boggle, i - 1, j,``                                   ``visited, str + ch);``                ``}``            ``}` `            ``// make current element unvisited``            ``visited[i, j] = ``false``;``        ``}``    ``}` `    ``// Prints all words present in dictionary.``    ``static` `void` `findWords(``char``[, ] boggle, TrieNode root)``    ``{``        ``// Mark all characters as not visited``        ``bool``[, ] visited = ``new` `bool``[M, N];``        ``TrieNode pChild = root;` `        ``String str = ``""``;` `        ``// traverse all matrix elements``        ``for` `(``int` `i = 0; i < M; i++) {``            ``for` `(``int` `j = 0; j < N; j++) {``                ``// we start searching for word in dictionary``                ``// if we found a character which is child``                ``// of Trie root``                ``if` `(pChild.Child[(boggle[i, j]) - ``'A'``] != ``null``) {``                    ``str = str + boggle[i, j];``                    ``searchWord(pChild.Child[(boggle[i, j]) - ``'A'``],``                               ``boggle, i, j, visited, str);``                    ``str = ``""``;``                ``}``            ``}``        ``}``    ``}` `    ``// Driver program to test above function``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``// Let the given dictionary be following``        ``String[] dictionary = { ``"GEEKS"``, ``"FOR"``, ``"QUIZ"``, ``"GEE"` `};` `        ``// root Node of trie``        ``TrieNode root = ``new` `TrieNode();` `        ``// insert all words of dictionary into trie``        ``int` `n = dictionary.Length;``        ``for` `(``int` `i = 0; i < n; i++)``            ``insert(root, dictionary[i]);` `        ``char``[, ] boggle = { { ``'G'``, ``'I'``, ``'Z'` `},``                            ``{ ``'U'``, ``'E'``, ``'K'` `},``                            ``{ ``'Q'``, ``'S'``, ``'E'` `} };``        ``findWords(boggle, root);``    ``}``}` `// This code has been contributed by 29AjayKumar`

## Javascript

 ``

Output:

`GEE, GEEKS, QUIZ`

Complexity Analysis:

• Time complexity: O(4^(N^2)).
Even after applying trie the time complexity remains same. For every cell there are 4 directions and there are N^2 cells. So the time complexity is O(4^(N^2)).
• Auxiliary Space: O(N^2).
The maximum length of recursion can be N^2, where N is the side of the matrix. So the space Complexity is O(N^2).

This article is contributed by Nishant Singh . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.