Word Search

0079.Word-Search/memo.md

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+# 79. Word Search
+
+## step1
+
+全ての位置から探索する解法が思いつく。最悪だと
+(m * n * 3^L) / 10^7 <= (36*3^15)/ 10^7 = 50
+かかるが大丈夫だろうか。とりあえず実装してみる。
+
+15mぐらいでかけてテストもクリアした。間違えた点：初期開始点のseenをTrueにし忘れた。
+
+> Follow up: Could you use search pruning to make your solution faster with a larger board?
+
+これを考えたいが案は思いつかず答えを見る。
+
+## step2
+
+### 他の人のコード
+
+https://github.com/huyfififi/coding-challenges/pull/61
+
+> というものが提示されていた。これを入れるだけでLeetCode上の実行時間ランキングでの順位が大きく上がった。
+
+> また、wordをひっくり返して word search を行っても同じ結果が得られるので、wordの先頭と末尾の文字のboard上での数を比べて、末尾の文字の個数の方が小さかったら word をひっくり返して search した方がDFSを始める回数が少なく済む。
+
+この通りにやったら確かにBeat 100msとなった
+
+片方しか行わないと遅くなるのでどちらも効果がある。
+
+> なるほど、確かに言われてみれば納得感はあるが、面接中にスラスラと思いつけるかは自信がない。word をひっくり返して探索しても同じ、というのは問題文を読んでいて気づけた方がいいだろうな。
+
+自分はどちらも思いつかないのでまだまだなのだと思う。
+
+
+https://github.com/potrue/leetcode/pull/74
+
+早期リターン
+
+
+https://github.com/thonda28/leetcode/pull/14
+
+再帰 -> ループを自分も書いておく
+
+次に試す方向の index を持たせておくのか。これは人のコードを見ないと書けなかったかもしれない。
+
+再帰をスタックに置き換える場合、フレーウの状態を明示的に持つ必要がある。

0079.Word-Search/step1.py

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+import itertools
+
+
+class Solution:
+    def exist(self, board: list[list[str]], word: str) -> bool:
+        if not board or not board[0]:
+            raise ValueError("invalid board")
+
+        num_row = len(board)
+        num_col = len(board[0])
+
+        def traverse(row: int, col: int, i: int, seen: list[list][bool]) -> bool:
+            if not word[i] == board[row][col]:
+                return False
+            if i == len(word) - 1:
+                return True
+            for row_next, col_next in (
+                (row + 1, col),
+                (row - 1, col),
+                (row, col + 1),
+                (row, col - 1),
+            ):
+                if (
+                    0 <= row_next < num_row
+                    and 0 <= col_next < num_col
+                    and not seen[row_next][col_next]
+                ):
+                    seen[row_next][col_next] = True
+                    if traverse(row_next, col_next, i + 1, seen):
+                        return True
+                    seen[row_next][col_next] = False
+
+            return False
+
+        for row, col in itertools.product(range(num_row), range(num_col)):
+            seen = [[False] * num_col for _ in range(num_row)]
+            seen[row][col] = True
+            if traverse(row, col, 0, seen):
+                return True
+
+        return False

0079.Word-Search/step1_revised.py

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+import itertools
+
+
+class Solution:
+    def exist(self, board: list[list[str]], word: str) -> bool:
+        if not board or not board[0]:
+            raise ValueError("invalid board")
+
+        num_row = len(board)
+        num_col = len(board[0])
+
+        def traverse(row: int, col: int, i: int, seen: list[list][bool]) -> bool:
+            if not word[i] == board[row][col]:
+                return False
+            if i == len(word) - 1:
+                return True
+            for row_next, col_next in (
+                (row + 1, col),
+                (row - 1, col),
+                (row, col + 1),
+                (row, col - 1),
+            ):
+                # fmt: off
+                if (
+                    0 <= row_next < num_row and
+                    0 <= col_next < num_col and
+                    not seen[row_next][col_next]
+                ):
+                # fmt: on
+                    seen[row_next][col_next] = True
+                    if traverse(row_next, col_next, i + 1, seen):
+                        return True
+                    seen[row_next][col_next] = False
+
+            return False
+
+        for row, col in itertools.product(range(num_row), range(num_col)):
+            seen = [[False] * num_col for _ in range(num_row)]
+            seen[row][col] = True
+            if traverse(row, col, 0, seen):
+                return True
+
+        return False

0079.Word-Search/step2_loop.py

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+import itertools
+import collections
+
+
+class Solution:
+    def exist(self, board: list[list[str]], word: str) -> bool:
+        if not board or not board[0]:
+            raise ValueError("invalid board")
+
+        num_row = len(board)
+        num_col = len(board[0])
+
+        board_char_to_count = collections.Counter(itertools.chain.from_iterable(board))
+        word_char_to_count = collections.Counter(word)
+
+        for ch in word_char_to_count:
+            if board_char_to_count[ch] < word_char_to_count[ch]:
+                return False
+
+        if board_char_to_count[word[-1]] < board_char_to_count[word[0]]:
+            word = word[::-1]
+
+        directions = (
+            (1, 0),
+            (-1, 0),
+            (0, 1),
+            (0, -1),
+        )
+
+        def start_from(row_start: int, col_start: int) -> bool:
+            if board[row_start][col_start] != word[0]:
+                return False
+
+            seen = [[False] * num_col for _ in range(num_row)]
+            seen[row_start][col_start] = True
+            stack = [(row_start, col_start, 0, 0)]
+
+            while stack:
+                row, col, letter_index, direction_index = stack[-1]
+                if letter_index == len(word) - 1:
+                    return True
+
+                if direction_index == len(directions):
+                    seen[row][col] = False
+                    stack.pop()
+                    continue
+
+                d_row, d_col = directions[direction_index]
+                stack[-1] = (row, col, letter_index, direction_index + 1)
+                row_next = row + d_row
+                col_next = col + d_col
+                next_letter_index = letter_index + 1
+                if (
+                    0 <= row_next < num_row
+                    and 0 <= col_next < num_col
+                    and not seen[row_next][col_next]
+                    and board[row_next][col_next] == word[next_letter_index]
+                ):
+                    seen[row_next][col_next] = True
+                    stack.append((row_next, col_next, next_letter_index, 0))
+
+            return False
+
+        for row, col in itertools.product(range(num_row), range(num_col)):
+            if start_from(row, col):
+                return True
+
+        return False

0079.Word-Search/step2_optimization.py

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+import itertools
+import collections
+
+
+class Solution:
+    def exist(self, board: list[list[str]], word: str) -> bool:
+        if not board or not board[0]:
+            raise ValueError("invalid board")
+
+        num_row = len(board)
+        num_col = len(board[0])
+
+        board_char_to_count = collections.Counter(itertools.chain.from_iterable(board))
+        word_char_to_count = collections.Counter(word)
+
+        for ch in word_char_to_count:
+            if board_char_to_count[ch] < word_char_to_count[ch]:
+                return False
+
+        if board_char_to_count[word[-1]] < board_char_to_count[word[0]]:
+            word = word[::-1]
+
+        def traverse(
+            row: int, col: int, letter_index: int, seen: list[list][bool]
+        ) -> bool:
+            if not word[letter_index] == board[row][col]:
+                return False
+            if letter_index == len(word) - 1:
+                return True
+            for row_next, col_next in (
+                (row + 1, col),
+                (row - 1, col),
+                (row, col + 1),
+                (row, col - 1),
+            ):
+                if (
+                    0 <= row_next < num_row
+                    and 0 <= col_next < num_col
+                    and not seen[row_next][col_next]
+                ):
+                    seen[row_next][col_next] = True
+                    if traverse(row_next, col_next, letter_index + 1, seen):
+                        return True
+                    seen[row_next][col_next] = False
+
+            return False
+
+        for row, col in itertools.product(range(num_row), range(num_col)):
+            seen = [[False] * num_col for _ in range(num_row)]
+            seen[row][col] = True
+            if traverse(row, col, 0, seen):
+                return True
+
+        return False

0079.Word-Search/step3.py

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+import itertools
+import collections
+
+
+class Solution:
+    def exist(self, board: list[list[str]], word: str) -> bool:
+        if not board or not board[0]:
+            raise ValueError("invalid board")
+
+        num_row = len(board)
+        num_col = len(board[0])
+
+        board_char_to_count = collections.Counter(itertools.chain.from_iterable(board))
+        word_char_to_count = collections.Counter(word)
+
+        for ch in word_char_to_count:
+            if board_char_to_count[ch] < word_char_to_count[ch]:
+                return False
+
+        if board_char_to_count[word[-1]] < board_char_to_count[word[0]]:
+            word = word[::-1]
+
+        directions = (
+            (1, 0),
+            (-1, 0),
+            (0, 1),
+            (0, -1),
+        )
+
+        def start_from(row_start: int, col_start: int) -> bool:
+            if board[row_start][col_start] != word[0]:
+                return False
+
+            seen = [[False] * num_col for _ in range(num_row)]
+            seen[row_start][col_start] = True
+            stack = [(row_start, col_start, 0, 0)]
+
+            while stack:
+                row, col, letter_index, direction_index = stack[-1]
+                if letter_index == len(word) - 1:
+                    return True
+
+                if direction_index == len(directions):
+                    seen[row][col] = False
+                    stack.pop()
+                    continue
+
+                stack[-1] = (row, col, letter_index, direction_index + 1)
+                dr, dc = directions[direction_index]
+                row_next = row + dr
+                col_next = col + dc
+                if (
+                    0 <= row_next < num_row
+                    and 0 <= col_next < num_col
+                    and board[row_next][col_next] == word[letter_index + 1]
+                    and not seen[row_next][col_next]
+                ):
+                    seen[row_next][col_next] = True
+                    stack.append((row_next, col_next, letter_index + 1, 0))
+
+        for row, col in itertools.product(range(num_row), range(num_col)):
+            if start_from(row, col):
+                return True
+
+        return False