From 7f722ae570c53e6c6de9d88e8e3de5ff4bab439c Mon Sep 17 00:00:00 2001
From: potrue <126231160+potrue@users.noreply.github.com>
Date: Fri, 22 Aug 2025 00:39:20 +0900
Subject: [PATCH] 22. Generate Parentheses

https://leetcode.com/problems/generate-parentheses/description/
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 22/22.md | 90 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 22/22.md

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+## 何も見ずに解いてみる
+
+```cpp
+class Solution {
+public:
+    vector<string> generateParenthesis(int n) {
+        vector<string> result;
+        string parenthesis;
+        generateParenthesisHelper(n, parenthesis, 0, 0, result);
+        return result;
+    }
+private:
+    void generateParenthesisHelper(
+        const int n,
+        string& parenthesis,
+        int num_open,
+        int num_close,
+        vector<string>& result
+    ) {
+        if (num_close == n) {
+            result.emplace_back(parenthesis);
+            return;
+        }
+        if (num_open < n) {
+            parenthesis.push_back('(');
+            generateParenthesisHelper(n, parenthesis, num_open + 1, num_close, result);
+            parenthesis.pop_back();
+        }
+        if (num_close < num_open) {
+            parenthesis.push_back(')');
+            generateParenthesisHelper(n, parenthesis, num_open, num_close + 1, result);
+            parenthesis.pop_back();
+        }
+    }
+};
+```
+
+## 他の人のコードを見てみる
+
+https://github.com/tokuhirat/LeetCode/pull/53/files  
+https://github.com/ryosuketc/leetcode_arai60/pull/42/files  
+https://github.com/Ryotaro25/leetcode_first60/pull/58/files  
+
+https://ja.wikipedia.org/wiki/%E3%82%AB%E3%82%BF%E3%83%A9%E3%83%B3%E6%95%B0  
+組み合わせの数はカタラン数というので求められるらしい。
+
+<img width="793" height="584" alt="image" src="https://github.com/user-attachments/assets/c42360dc-d14e-44c3-aab4-37737473ba83" />
+
+<img width="808" height="317" alt="image" src="https://github.com/user-attachments/assets/a1f604cc-8d61-4fb8-b685-246e59c4255b" />
+
+ナルホド
+
+## 最終コード
+
+値渡しにしている以上`num_open`や`num_close`についても`const`にしても動くので`n`だけ`const int`なのはどうなのかなーと思いつつ、これだけに`const`をつけていたほうが`n`は最後までトップダウンで動かさずに伝えますよというニュアンスが伝わる気がする。
+
+```cpp
+class Solution {
+public:
+    vector<string> generateParenthesis(int n) {
+        vector<string> result;
+        string parentheses;
+        generateParenthesisHelper(n, parentheses, 0, 0, result);
+        return result;
+    }
+private:
+    void generateParenthesisHelper(
+        const int n,
+        string& parentheses,
+        int num_open,
+        int num_close,
+        vector<string>& result
+    ) {
+        if (parentheses.size() == n * 2) {
+            result.emplace_back(parentheses);
+            return;
+        }
+        if (num_open < n) {
+            parentheses.push_back('(');
+            generateParenthesisHelper(n, parentheses, num_open + 1, num_close, result);
+            parentheses.pop_back();
+        }
+        if (num_close < num_open) {
+            parentheses.push_back(')');
+            generateParenthesisHelper(n, parentheses, num_open, num_close + 1, result);
+            parentheses.pop_back();
+        }
+    }
+};
+```