Boggle using Trie | DSA in C++ - Software Development PDF Download

Introduction

Boggle is a popular word game that involves finding words in a grid of letters. In this article, we will explore how to solve the Boggle game using a Trie data structure in C++. We will cover the implementation details and provide multiple examples and code explanations to help beginners understand the concept.

What is a Trie?

• Definition: A Trie, also known as a prefix tree, is a tree-like data structure that is commonly used to store and retrieve strings efficiently.
• Trie Structure: Each node in the trie represents a single character. The path from the root to a node forms a string, and the nodes at the same level represent different characters.
• Trie Operations: Trie supports operations like insertion, deletion, and search in O(L) time complexity, where L is the length of the string.

Boggle Game Overview

• Boggle is a word game played on a grid of letters.
• The goal is to find as many words as possible by connecting adjacent letters horizontally, vertically, or diagonally.
• Words must be constructed using contiguous letters and cannot reuse the same letter from a single grid cell.

Implementing Boggle Using Trie

Trie Data Structure

• Each node in the Trie contains an array of pointers to its child nodes, representing the possible characters.
• The Trie node also includes a flag to indicate whether the current node represents the end of a valid word.

Boggle Solver Algorithm

• Generate all possible words by exploring all cells of the Boggle board.
• Use a depth-first search (DFS) algorithm to traverse the board and find words.
• During the DFS traversal, check if the current sequence of characters forms a valid word by searching the Trie data structure.
• To avoid duplicate words, mark visited cells and remove the word from the Trie once it is found.

Code Examples and Explanations

Trie Implementation

'cpp // Code for Trie Node struct TrieNode { TrieNode* children[26]; // 26 possible characters bool isEndOfWord; // flag to mark the end of a word };'

Explanation: The TrieNode structure consists of an array of 26 pointers to child nodes, representing each possible character. The `isEndOfWord` flag indicates whether the current node represents the end of a valid word.

Boggle Solver Implementation

```cpp

// Code for Boggle Solver

void searchWord(TrieNode* root, vector<vector<char>>& board, int i, int j, vector<vector<bool>>& visited, string& currentWord) {

// Base case: Out of bounds or already visited

if (i < 0 || j < 0 || i >= board.size() || j >= board[0].size() || visited[i][j])

return;

    // Mark current cell as visited and append character to the currentWord

    visited[i][j] = true;

    currentWord += board[i][j];

    // Check if the currentWord exists in the Trie

    if (root->children[board[i][j] - 'A'] != nullptr) {

        if (root->children[board[i][j] - 'A']->isEndOfWord)

            cout << currentWord << endl;

        for (int row = -1; row <= 1; row++) {

            for (int col = -1; col <= 1; col++) {

                // Recursive call for all adjacent cells

                searchWord(root->children[board[i][j] - 'A'], board, i + row, j + col, visited, currentWord);

            }

        }

    }

    // Backtrack: Unmark cell as visited and remove the character from the currentWord

    visited[i][j] = false;

    currentWord.pop_back();

}

```

Explanation:

The `searchWord` function performs a depth-first search to find words in the Boggle grid. It starts from a given cell (i, j) and recursively explores all possible adjacent cells while checking if the currentWord exists in the Trie. Once a word is found, it is printed, and the search continues for longer words. The visited cells are marked and unmarked to avoid revisiting the same cell.

Sample Problems and Solutions

Problem 1: Given a Boggle board and a dictionary of words, find all the valid words present on the board.

The solution involves constructing a Trie from the dictionary words and using the Boggle solver algorithm to find all valid words on the board. Iterate over each cell and call the 'searchWord' function to print the valid words.

Conclusion

In this article, we explored the concept of using a Trie data structure to solve the Boggle game in C++. We learned how to implement the Trie data structure and the Boggle solver algorithm. By combining these concepts, we can efficiently find all valid words on a Boggle board. Remember to practice coding and experiment with different scenarios to deepen your understanding of this topic.