Problem URL: Word search

We will run dfs on each element of the board, if we find a character match, then we move forward and search for next character in all 4 directions.

class Solution:
    def exist(self, board: List[List[str]], word: str) -> bool:
        ROWS, COLS = len(board), len(board[0])
        path = set()

        def dfs(r: int, c: int, i: int) -> bool:
            if i == len(word):
                return True
            if (
                r < 0
                or c < 0
                or r >= ROWS
                or c >= COLS
                or word[i] != board[r][c]
                or (r, c) in path
            ):
                return False

            path.add((r, c))
            res = (
                dfs(r + 1, c, i + 1)
                or dfs(r - 1, c, i + 1)
                or dfs(r, c + 1, i + 1)
                or dfs(r, c - 1, i + 1)
            )
            path.remove((r, c))

            return res

        for r in range(ROWS):
            for c in range(COLS):
                if dfs(r, c, 0):
                    return True
        return False

Time Complexity: O(n*m*4^n)
Space Complexity: O(n*m)