Word Break Ii

0140.Word-Break-II/memo.md

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+# 140. Word Break II
+
+## step1
+
+バックトラックで解く。珍しくミスなく一発で通った。
+ただし、str.startwithの引数の順番を調べた。
+
+## step2
+
+https://leetcode.com/problems/word-break-ii/solutions/44311/python-easy-to-understand-solution-by-yi-n05s/?envType=problem-list-v2&envId=7p5x763
+
+トップダウンDFS。確かにバックトラックだと計算が重複している状況が考えられる。
+
+https://leetcode.com/problems/word-break-ii/solutions/763221/python-dp-solution-explained-by-dbabiche-rhhz/?envType=problem-list-v2&envId=7p5x763
+
+ボトムアップの動的計画法
+

0140.Word-Break-II/step1.py

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+class Solution:
+    def wordBreak(self, s: str, wordDict: list[str]) -> list[str]:
+        result = []
+        broken_words = []
+
+        def traverse(start):
+            if start == len(s):
+                result.append(" ".join(broken_words))
+                return
+            for word in wordDict:
+                if s.startswith(word, start):
+                    broken_words.append(word)
+                    traverse(start + len(word))
+                    broken_words.pop()
+
+        traverse(0)
+        return result

0140.Word-Break-II/step2_bottom_up.py

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+class Solution:
+    def wordBreak(self, s: str, wordDict: list[str]) -> list[str]:
+        word_set = set(wordDict)
+        n = len(s)
+
+        # dp[i]: s[i:]で作れる文字列のリスト
+        dp = [[] for _ in range(n + 1)]
+        dp[n] = [""]
+
+        for i in range(n - 1, -1, -1):
+            sentences = []
+            for j in range(i + 1, n + 1):
+                word = s[i:j]
+                if word in word_set:
+                    for sub in dp[j]:
+                        if sub == "":
+                            sentences.append(word)
+                        else:
+                            sentences.append(word + " " + sub)
+            dp[i] = sentences
+
+        return dp[0]

0140.Word-Break-II/step2_top_down_dfs.py

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+import functools
+
+
+class Solution:
+    def wordBreak(self, s: str, wordDict: list[str]) -> list[str]:
+        word_set = set(wordDict)
+
+        @functools.cache
+        def traverse(start):
+            if start == len(s):
+                return [""]
+
+            result = []
+            for end in range(start + 1, len(s) + 1):
+                word = s[start:end]
+                if word in word_set:
+                    sub_sentences = traverse(end)
+                    for sub in sub_sentences:
+                        if sub == "":
+                            result.append(word)
+                        else:
+                            result.append(word + " " + sub)
+            return result
+
+        return traverse(0)