Word Search in a 2D Board

Write a JavaScript program to search for a word in a 2D board of characters. Given a 2D board and a word, find if the word exists in the grid. The word can 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 single word.

Example 1

  
Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCCED"
  
Output: true
  
Explanation: 
Start search from each cell that matches first character 'A'. 
Found 'A' at position (0,0), start DFS from here. 
From (0,0), move right to (0,1) for 'B', then (0,2) for 'C'. 
From (0,2), move down to (1,2) for 'C', then (2,2) for 'E'. 
From (2,2), move right to (2,3) for 'D', word "ABCCED" found.

Example 2

  
Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "SEE"
  
Output: true
  
Explanation: 
Start search from each cell that matches first character 'S'. 
Found 'S' at position (1,0), start DFS from here. 
From (1,0), no valid path for "SEE". 
Found 'S' at position (1,3), start DFS from here. 
From (1,3), move down to (2,3) for 'E', then left to (2,2) for 'E', word "SEE" found.

Constraints

  
m == board.length
  
n == board[i].length
  
1 ≤ m, n ≤ 6
  
1 ≤ word.length ≤ 15
  
board and word consists of only lowercase and uppercase English letters
  
Time Complexity: O(m * n * 4^L) where L is word length
  
Space Complexity: O(L) for recursion stack