optimize word-search solution

Author: parkhojeong

word-search/parkhojeong.py

@@ -1,32 +1,51 @@
+from collections import Counter
+from typing import List
+
 class Solution:
     def exist(self, board: List[List[str]], word: str) -> bool:
-        for i in range(len(board)):
-            for j in range(len(board[0])):
-                if self.dfs(board, word, i, j):
-                    return True
+        row_len, col_len = len(board), len(board[0])
 
-        return False
+        board_freq = Counter(ch for row in board for ch in row)
 
-    def dfs(self, board: List[List[str]], word: str, i: int, j: int):
-        if board[i][j] != word[0] or board[i][j] == "-1":
-            return False
-        if len(word) == 1:
-            return True
+        if board_freq.get(word[0], 0) > board_freq.get(word[-1], 0):
+            word = word[::-1]
+
+        DIRECTIONS = ((-1, 0), (1, 0), (0, -1), (0, 1))
+        MARKER = ""
+
+        def in_bounds(r: int, c: int) -> bool:
+            return 0 <= r < row_len and 0 <= c < col_len
 
-        temp_cell = board[i][j]
-        board[i][j] = "-1"
-        word = word[1:]
-        if i >= 1 and self.dfs(board, word, i - 1, j):
-            return True
+        def backtrack(r: int, c: int, idx: int) -> bool:
+            for ch, need in Counter(word[idx:]).items():
+                if board_freq.get(ch, 0) < need:
+                    return False
 
-        if j >= 1 and self.dfs(board, word, i, j - 1):
-            return True
+            if idx == len(word) - 1:
+                return True
 
-        if i < len(board) - 1 and self.dfs(board, word, i + 1, j):
-            return True
+            saved_char = board[r][c]
+            board[r][c] = MARKER
+            board_freq[saved_char] -= 1
 
-        if j < len(board[0]) - 1 and self.dfs(board, word, i, j + 1):
-            return True
+            for dr, dc in DIRECTIONS:
+                nr, nc = r + dr, c + dc
+                next_ch = word[idx + 1]
+
+                if (in_bounds(nr, nc)
+                        and board[nr][nc] != MARKER
+                        and board[nr][nc] == next_ch
+                        and board_freq[next_ch] > 0
+                        and backtrack(nr, nc, idx + 1)):
+                    return True
+
+            board[r][c] = saved_char
+            board_freq[saved_char] += 1
+            return False
+
+        for r in range(row_len):
+            for c in range(col_len):
+                if board[r][c] == word[0] and backtrack(r, c, 0):
+                    return True
 
-        board[i][j] = temp_cell
         return False