Decode Ways

0091.Decode-Ways/memo.md

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+# 91. Decode Ways
+
+## step1
+DPで書いた。8mほど。配るDP。やや変数名を修正。
+
+## step2
+もらうDPで書いた。この場合は2変数で管理できる。
+
+LeetCodeや他の方のSolutionを見ても新しいものはないので、LLMに聞いてみるとメモ化再帰を提案された。
+
+トップダウンの解法
+
+```python
+from functools import cache
+
+class Solution:
+    def numDecodings(self, s: str) -> int:
+
+        @cache
+        def dfs(i: int) -> int:
+            # 文字列の最後まで到達できたら、1つの有効な分割方法が見つかったということ
+            if i == len(s):
+                return 1
+            # 0から始まるデコードは存在しない
+            if s[i] == "0":
+                return 0
+
+            # パターン1: 1文字としてデコードする
+            ans = dfs(i + 1)
+
+            # パターン2: 2文字としてデコードする
+            if i + 1 < len(s) and (s[i] == "1" or (s[i] == "2" and s[i+1] <= "6")):
+                ans += dfs(i + 2)
+
+            return ans
+
+        return dfs(0)
+```

0091.Decode-Ways/step1_distribute.py

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+class Solution:
+    def numDecodings(self, s: str) -> int:
+        if not s or s[0] == "0":
+            return 0
+
+        dp = [0] * (len(s) + 1)
+        dp[0] = 1
+
+        for i in range(len(s)):
+            if s[i] == "0":
+                continue
+            dp[i+1] += dp[i]
+            if i + 1 < len(s) and int(s[i:i+2]) <= 26:
+                dp[i+2] += dp[i]
+
+        return dp[-1]
+
+
+# solution = Solution()
+# print(solution.numDecodings("12"))
+# print(solution.numDecodings("226"))
+# print(solution.numDecodings("0"))
+# print(solution.numDecodings("1001"))

0091.Decode-Ways/step1_distribute_revised.py

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+class Solution:
+    def numDecodings(self, s: str) -> int:
+        if not s or s[0] == "0":
+            return 0
+
+        num_ways = [0] * (len(s) + 1)
+        num_ways[0] = 1
+
+        for i in range(len(s)):
+            if s[i] == "0":
+                continue
+            num_ways[i+1] += num_ways[i]
+            if i + 1 < len(s) and int(s[i:i+2]) <= 26:
+                num_ways[i+2] += num_ways[i]
+
+        return num_ways[-1]
+
+
+# solution = Solution()
+# print(solution.numDecodings("12"))
+# print(solution.numDecodings("226"))
+# print(solution.numDecodings("0"))
+# print(solution.numDecodings("1001"))

0091.Decode-Ways/step2_receive.py

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+class Solution:
+    def numDecodings(self, s: str) -> int:
+        if not s or s[0] == "0":
+            return 0
+
+        num_end_with_i_minus_2 = 1  # 空文字列
+        num_end_with_i_minus_1 = 1  # 最初の1文字
+
+        for i in range(1, len(s)):
+            num_end_with_i = 0
+
+            if s[i] != "0":
+                num_end_with_i += num_end_with_i_minus_1
+
+            if s[i-1] != "0" and 10 <= int(s[i-1:i+1]) <= 26:
+                num_end_with_i += num_end_with_i_minus_2
+
+            if num_end_with_i == 0:
+                return 0
+
+            num_end_with_i_minus_2 = num_end_with_i_minus_1
+            num_end_with_i_minus_1 = num_end_with_i
+
+        return num_end_with_i_minus_1
+