JavaAlgorithms/Misc/WordBoggle.java

package Misc;

import java.util.*;

public class WordBoggle {

  /**
   * O(nm * 8^s + ws) time where n = width of boggle board, m = height of boggle board, s = length of
   * longest word in string array, w = length of string array, 8 is due to 8 explorable neighbours
   * O(nm + ws) space.
   */
  public static List<String> boggleBoard(char[][] board, String[] words) {
    Trie trie = new Trie();
    for (String word : words) trie.add(word);
    Set<String> finalWords = new HashSet<>();
    boolean[][] visited = new boolean[board.length][board.length];
    for (int i = 0; i < board.length; i++)
      for (int j = 0; j < board[i].length; j++)
        explore(i, j, board, trie.root, visited, finalWords);
    return new ArrayList<>(finalWords);
  }

  public static void main(String[] args) {
    // Testcase
    List<String> ans =
        new ArrayList<>(
            Arrays.asList("a", "boggle", "this", "NOTRE_PEATED", "is", "simple", "board"));
    assert (boggleBoard(
            new char[][] {
              {'t', 'h', 'i', 's', 'i', 's', 'a'},
              {'s', 'i', 'm', 'p', 'l', 'e', 'x'},
              {'b', 'x', 'x', 'x', 'x', 'e', 'b'},
              {'x', 'o', 'g', 'g', 'l', 'x', 'o'},
              {'x', 'x', 'x', 'D', 'T', 'r', 'a'},
              {'R', 'E', 'P', 'E', 'A', 'd', 'x'},
              {'x', 'x', 'x', 'x', 'x', 'x', 'x'},
              {'N', 'O', 'T', 'R', 'E', '_', 'P'},
              {'x', 'x', 'D', 'E', 'T', 'A', 'E'},
            },
            new String[] {
              "this",
              "is",
              "not",
              "a",
              "simple",
              "test",
              "boggle",
              "board",
              "REPEATED",
              "NOTRE_PEATED",
            })
        .equals(ans));
  }

  public static void explore(
      int i,
      int j,
      char[][] board,
      TrieNode trieNode,
      boolean[][] visited,
      Set<String> finalWords) {
    if (visited[i][j]) return;

    char letter = board[i][j];
    if (!trieNode.children.containsKey(letter)) {
      return;
    }
    visited[i][j] = true;
    trieNode = trieNode.children.get(letter);
    if (trieNode.children.containsKey('*')) finalWords.add(trieNode.word);

    List<Integer[]> neighbors = getNeighbors(i, j, board);
    for (Integer[] neighbor : neighbors)
      explore(neighbor[0], neighbor[1], board, trieNode, visited, finalWords);

    visited[i][j] = false;
  }

  public static List<Integer[]> getNeighbors(int i, int j, char[][] board) {
    List<Integer[]> neighbors = new ArrayList<>();
    if (i > 0 && j > 0) neighbors.add(new Integer[] {i - 1, j - 1});

    if (i > 0 && j < board[0].length - 1) neighbors.add(new Integer[] {i - 1, j + 1});

    if (i < board.length - 1 && j < board[0].length - 1)
      neighbors.add(new Integer[] {i + 1, j + 1});

    if (i < board.length - 1 && j > 0) neighbors.add(new Integer[] {i + 1, j - 1});

    if (i > 0) neighbors.add(new Integer[] {i - 1, j});

    if (i < board.length - 1) neighbors.add(new Integer[] {i + 1, j});

    if (j > 0) neighbors.add(new Integer[] {i, j - 1});

    if (j < board[0].length - 1) neighbors.add(new Integer[] {i, j + 1});

    return neighbors;
  }
}

// Trie used to optimize string search
class TrieNode {

  Map<Character, TrieNode> children = new HashMap<>();
  String word = "";
}

class Trie {

  TrieNode root;
  char endSymbol;

  public Trie() {
    this.root = new TrieNode();
    this.endSymbol = '*';
  }

  public void add(String str) {
    TrieNode node = this.root;
    for (int i = 0; i < str.length(); i++) {
      char letter = str.charAt(i);
      if (!node.children.containsKey(letter)) {
        TrieNode newNode = new TrieNode();
        node.children.put(letter, newNode);
      }
      node = node.children.get(letter);
    }
    node.children.put(this.endSymbol, null);
    node.word = str;
  }
}