LeetCode //C - 212. Word Search II

212. Word Search II

Given an m x n board of characters and a list of strings words, return all words on the board.

Each word must be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word.
 

Example 1:

Input: board = [[“o”,“a”,“a”,“n”],[“e”,“t”,“a”,“e”],[“i”,“h”,“k”,“r”],[“i”,“f”,“l”,“v”]], words = [“oath”,“pea”,“eat”,“rain”]
Output: [“eat”,“oath”]

Example 2:

Input: board = [[“a”,“b”],[“c”,“d”]], words = [“abcb”]
Output: []

Constraints:

• m == board.length
• n == board[i].length
• 1 <= m, n <= 12
• board[i][j] is a lowercase English letter.
• 1 <= words.length <= $3\ast 10^4$
• 1 <= words[i].length <= 10
• words[i] consists of lowercase English letters.
• All the strings of words are unique.

From: LeetCode
Link: 212. Word Search II

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Solution:

Ideas：

Trie (Prefix Tree):
A Trie is a tree-like data structure that is used to store a dynamic set of strings. Tries are particularly useful for searches in dictionaries with a large number of words. Each node of the Trie represents a single character of a word, and the path from the root node to any node in the tree represents the prefix (part of a word) associated with that node.

Benefits of Trie:

1. Provides efficient word insertions and lookups.
2. Allows us to search for a word prefix efficiently.

DFS Backtracking:
Backtracking is a general algorithm used to find all (or some) solutions to computational problems by incrementally building candidates towards solutions and abandoning a candidate as soon as it is determined that it cannot be extended to a valid solution.

In the context of this problem, we use backtracking to traverse the board starting from each cell. For each cell, we explore in all four possible directions (up, down, left, right) to see if we can form a word present in the Trie.

Solution Steps:

1. Building the Trie:

• All the words in the words array are inserted into a Trie.
• Each node in the Trie has 26 pointers (for each lowercase English letter) and a word pointer which points to the word if that node marks the end of a valid word.

2. DFS Search on Board:

• We iterate over each cell of the board.
• Starting from each cell, we perform a DFS search to build words and check if they are in the Trie.
• While traversing, if the current sequence of characters doesn’t match any prefix in the Trie, we backtrack (return from the recursion).
• If we find a valid word (by reaching a Trie node that has a non-null word pointer), we add that word to the results.

3. Optimization:

• Once a word is found, we nullify the word pointer in the Trie node to ensure that the same word is not added multiple times.

Code:

/**
 * Note: The returned array must be malloced, assume caller calls free().
 */

typedef struct TrieNode {
    struct TrieNode *children[26];
    char *word;
} TrieNode;

TrieNode* createNode() {
    TrieNode *node = malloc(sizeof(TrieNode));
    for (int i = 0; i < 26; i++) {
        node->children[i] = NULL;
    }
    node->word = NULL;
    return node;
}

void insert(TrieNode *root, char *word) {
    TrieNode *node = root;
    for (int i = 0; word[i]; i++) {
        int index = word[i] - 'a';
        if (!node->children[index]) {
            node->children[index] = createNode();
        }
        node = node->children[index];
    }
    node->word = word;
}

void backtrack(char **board, int boardSize, int* boardColSize, TrieNode *node, int i, int j, char **result, int *returnSize) {
    if (i < 0 || i >= boardSize || j < 0 || j >= boardColSize[i] || board[i][j] == '#') {
        return;
    }
    
    char c = board[i][j];
    if (!node->children[c - 'a']) {
        return;
    }

    node = node->children[c - 'a'];
    if (node->word) {
        result[*returnSize] = node->word;
        (*returnSize)++;
        node->word = NULL; // To avoid duplication
    }

    board[i][j] = '#';  // Mark as visited
    backtrack(board, boardSize, boardColSize, node, i+1, j, result, returnSize);
    backtrack(board, boardSize, boardColSize, node, i-1, j, result, returnSize);
    backtrack(board, boardSize, boardColSize, node, i, j+1, result, returnSize);
    backtrack(board, boardSize, boardColSize, node, i, j-1, result, returnSize);
    board[i][j] = c;    // Revert back
}

char** findWords(char** board, int boardSize, int* boardColSize, char **words, int wordsSize, int* returnSize) {
    TrieNode *root = createNode();
    for (int i = 0; i < wordsSize; i++) {
        insert(root, words[i]);
    }
    
    char **result = malloc(wordsSize * sizeof(char*));
    *returnSize = 0;

    for (int i = 0; i < boardSize; i++) {
        for (int j = 0; j < boardColSize[i]; j++) {
            backtrack(board, boardSize, boardColSize, root, i, j, result, returnSize);
        }
    }

    return result;
}