update: 添加问题“1415.长度为n的开心字符串中字典序第k小的字符串”的代码和题解+docs(swapfile) (#1442)

LetMeFly666 · web-flow · commit 6a1d4b6c2d2b · 2026-03-15T00:04:52.000+08:00
* 1415: WA.cpp (#1441) * 1415: AC.cpp (#1441) - AC,100.00%,91.10% 上个错误反例： last = 'a' can = ['b', 'c'] th = 1 本来应该选can[th] = 'c' 结果can[th] != last就选了'b' * 1415: WA.cpp.dfs (#1441) * 1415: WA.cpp.dfs (#1441) * 1415: AC.cpp.dfs (#1441) - AC,55.51%,54.24% * 1415: AC.cpp.dfs (#1441) - AC,DFS.better,100.00%,55.93% * update: 添加问题“1415.长度为n的开心字符串中字典序第k小的字符串”的代码和题解 (#1442) Signed-off-by: LetMeFly666 <Tisfy@qq.com> --------- Signed-off-by: LetMeFly666 <Tisfy@qq.com>
diff --git a/Codes/1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n_DFS.cpp b/Codes/1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n_DFS.cpp
@@ -0,0 +1,61 @@
+/*
+ * @Author: LetMeFly
+ * @Date: 2026-03-14 22:56:17
+ * @LastEditors: LetMeFly.xyz
+ * @LastEditTime: 2026-03-14 23:33:32
+ */
+#ifdef _DEBUG
+#include "_[1,2]toVector.h"
+#endif
+
+class Solution {
+private:
+    int n, k;
+    string ans;
+    char can[3] = {'a', 'b', 'c'};
+
+    // dfs and return if can stop
+    bool dfs(string now) {
+        if (now.size() == n) {
+            k--;
+            if (!k) {
+                ans = now;
+                return true;
+            }
+            return false;
+        }
+
+        char last = now.empty() ? '0' : now.back();
+        for (int i = 0; i < 3; i++) {
+            if (can[i] == last) {
+                continue;
+            }
+            if (dfs(now + can[i])) {
+                return true;
+            }
+        }
+        return false;   
+    }
+public:
+    string getHappyString(int n, int k) {
+        this->n = n, this->k = k;
+        dfs("");
+        return ans;
+    }
+};
+
+#if defined(_WIN32) || defined(__APPLE__)
+/*
+1 3
+
+c
+*/
+int main() {
+    int a, b;
+    while (cin >> a >> b) {
+        Solution sol;
+        cout << sol.getHappyString(a, b) << endl;
+    }
+    return 0;
+}
+#endif
diff --git a/Codes/1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n_O1.cpp b/Codes/1415-the-k-th-lexicographical-string-of-all-happy-strings-of-length-n_O1.cpp
@@ -0,0 +1,34 @@
+/*
+ * @Author: LetMeFly
+ * @Date: 2026-03-14 22:56:17
+ * @LastEditors: LetMeFly.xyz
+ * @LastEditTime: 2026-03-14 23:21:37
+ */
+#ifdef _DEBUG
+#include "_[1,2]toVector.h"
+#endif
+
+class Solution {
+public:
+    string getHappyString(int n, int k) {
+        int remain = 1 << (n - 1);
+        if (k > 3 * remain) {
+            return "";
+        }
+        
+        k--;
+        char toChoose[3] = {'a', 'b', 'c'};
+        string ans;
+        ans.push_back(toChoose[k / remain]);
+        for (int i = 1; i < n; i++) {
+            k %= remain;
+            remain >>= 1;
+            int th = k / remain;
+            if (toChoose[th] >= ans.back()) {
+                th++;
+            }
+            ans.push_back(toChoose[th]);
+        }
+        return ans;
+    }
+};
diff --git a/README.md b/README.md
@@ -582,6 +582,7 @@
 |1410.HTML实体解析器|中等|<a href="https://leetcode.cn/problems/html-entity-parser/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2023/11/23/LeetCode%201410.HTML%E5%AE%9E%E4%BD%93%E8%A7%A3%E6%9E%90%E5%99%A8/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/134571778" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/html-entity-parser/solutions/2538393/letmefly-1410html-shi-ti-jie-xi-qi-zi-fu-psbk/" target="_blank">LeetCode题解</a>|
 |1411.给Nx3网格图涂色的方案数|困难|<a href="https://leetcode.cn/problems/number-of-ways-to-paint-n-3-grid" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2026/01/03/LeetCode%201411.%E7%BB%99Nx3%E7%BD%91%E6%A0%BC%E5%9B%BE%E6%B6%82%E8%89%B2%E7%9A%84%E6%96%B9%E6%A1%88%E6%95%B0/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/156545186" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/n-repeated-element-in-size-2n-array/solutions/3872035/letmefly-1411gei-n-x-3-wang-ge-tu-tu-se-gbpc3/" target="_blank">LeetCode题解</a>|
 |1413.逐步求和得到正数的最小值|简单|<a href="https://leetcode.cn/problems/minimum-value-to-get-positive-step-by-step-sum/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/08/09/LeetCode%201413.%E9%80%90%E6%AD%A5%E6%B1%82%E5%92%8C%E5%BE%97%E5%88%B0%E6%AD%A3%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/126241399" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/minimum-value-to-get-positive-step-by-step-sum/solution/by-tisfy-txge/" target="_blank">LeetCode题解</a>|
+|1415.长度为n的开心字符串中字典序第k小的字符串|中等|<a href="https://leetcode.cn/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2026/03/14/LeetCode%201415.%E9%95%BF%E5%BA%A6%E4%B8%BAn%E7%9A%84%E5%BC%80%E5%BF%83%E5%AD%97%E7%AC%A6%E4%B8%B2%E4%B8%AD%E5%AD%97%E5%85%B8%E5%BA%8F%E7%AC%ACk%E5%B0%8F%E7%9A%84%E5%AD%97%E7%AC%A6%E4%B8%B2/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/159055459" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/solutions/3925545/letmefly-1415chang-du-wei-n-de-kai-xin-z-ruee/" target="_blank">LeetCode题解</a>|
 |1417.重新格式化字符串|简单|<a href="https://leetcode.cn/problems/reformat-the-string/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/08/11/LeetCode%201417.%E9%87%8D%E6%96%B0%E6%A0%BC%E5%BC%8F%E5%8C%96%E5%AD%97%E7%AC%A6%E4%B8%B2/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/126279589" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/reformat-the-string/solution/letmefly-1417zhong-xin-ge-shi-hua-zi-fu-zhnov/" target="_blank">LeetCode题解</a>|
 |1419.数青蛙|中等|<a href="https://leetcode.cn/problems/minimum-number-of-frogs-croaking/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2023/05/06/LeetCode%201419.%E6%95%B0%E9%9D%92%E8%9B%99/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/130520908" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/minimum-number-of-frogs-croaking/solutions/2258226/letmefly-1419shu-qing-wa-by-tisfy-9w23/" target="_blank">LeetCode题解</a>|
 |1422.分割字符串的最大得分|简单|<a href="https://leetcode.cn/problems/maximum-score-after-splitting-a-string/" target="_blank">题目地址</a>|<a href="https://blog.letmefly.xyz/2022/08/14/LeetCode%201422.%E5%88%86%E5%89%B2%E5%AD%97%E7%AC%A6%E4%B8%B2%E7%9A%84%E6%9C%80%E5%A4%A7%E5%BE%97%E5%88%86/" target="_blank">题解地址</a>|<a href="https://letmefly.blog.csdn.net/article/details/126329351" target="_blank">CSDN题解</a>|<a href="https://leetcode.cn/problems/maximum-score-after-splitting-a-string/solution/letmefly-1422fen-ge-zi-fu-chuan-de-zui-d-8zvi/" target="_blank">LeetCode题解</a>|
diff --git a/Solutions/LeetCode 1415.长度为n的开心字符串中字典序第k小的字符串.md b/Solutions/LeetCode 1415.长度为n的开心字符串中字典序第k小的字符串.md
@@ -0,0 +1,212 @@
+---
+title: 1415.长度为 n 的开心字符串中字典序第 k 小的字符串：DFS构造 / 数学O(1)
+date: 2026-03-14 23:31:04
+tags: [题解, LeetCode, 中等, 字符串, 回溯, 深度优先搜索, DFS, 模拟, 数学, 构造]
+categories: [题解, LeetCode]
+---
+
+# 【LetMeFly】1415.长度为 n 的开心字符串中字典序第 k 小的字符串：DFS构造 / 数学O(n)
+
+力扣题目链接：[https://leetcode.cn/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/](https://leetcode.cn/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/)
+
+<p>一个 「开心字符串」定义为：</p>
+
+<ul>
+	<li>仅包含小写字母&nbsp;<code>[&#39;a&#39;, &#39;b&#39;, &#39;c&#39;]</code>.</li>
+	<li>对所有在&nbsp;<code>1</code>&nbsp;到&nbsp;<code>s.length - 1</code>&nbsp;之间的&nbsp;<code>i</code>&nbsp;，满足&nbsp;<code>s[i] != s[i + 1]</code>&nbsp;（字符串的下标从 1 开始）。</li>
+</ul>
+
+<p>比方说，字符串&nbsp;<strong>&quot;abc&quot;</strong>，<strong>&quot;ac&quot;，&quot;b&quot;</strong> 和&nbsp;<strong>&quot;abcbabcbcb&quot;</strong>&nbsp;都是开心字符串，但是&nbsp;<strong>&quot;aa&quot;</strong>，<strong>&quot;baa&quot;</strong>&nbsp;和&nbsp;<strong>&quot;ababbc&quot;</strong>&nbsp;都不是开心字符串。</p>
+
+<p>给你两个整数 <code>n</code>&nbsp;和 <code>k</code>&nbsp;，你需要将长度为 <code>n</code>&nbsp;的所有开心字符串按字典序排序。</p>
+
+<p>请你返回排序后的第 k 个开心字符串，如果长度为 <code>n</code>&nbsp;的开心字符串少于 <code>k</code>&nbsp;个，那么请你返回 <strong>空字符串</strong>&nbsp;。</p>
+
+<p>&nbsp;</p>
+
+<p><strong>示例 1：</strong></p>
+
+<pre><strong>输入：</strong>n = 1, k = 3
+<strong>输出：</strong>&quot;c&quot;
+<strong>解释：</strong>列表 [&quot;a&quot;, &quot;b&quot;, &quot;c&quot;] 包含了所有长度为 1 的开心字符串。按照字典序排序后第三个字符串为 &quot;c&quot; 。
+</pre>
+
+<p><strong>示例 2：</strong></p>
+
+<pre><strong>输入：</strong>n = 1, k = 4
+<strong>输出：</strong>&quot;&quot;
+<strong>解释：</strong>长度为 1 的开心字符串只有 3 个。
+</pre>
+
+<p><strong>示例 3：</strong></p>
+
+<pre><strong>输入：</strong>n = 3, k = 9
+<strong>输出：</strong>&quot;cab&quot;
+<strong>解释：</strong>长度为 3 的开心字符串总共有 12 个 [&quot;aba&quot;, &quot;abc&quot;, &quot;aca&quot;, &quot;acb&quot;, &quot;bab&quot;, &quot;bac&quot;, &quot;bca&quot;, &quot;bcb&quot;, &quot;cab&quot;, &quot;cac&quot;, &quot;cba&quot;, &quot;cbc&quot;] 。第 9 个字符串为 &quot;cab&quot;
+</pre>
+
+<p><strong>示例 4：</strong></p>
+
+<pre><strong>输入：</strong>n = 2, k = 7
+<strong>输出：</strong>&quot;&quot;
+</pre>
+
+<p><strong>示例 5：</strong></p>
+
+<pre><strong>输入：</strong>n = 10, k = 100
+<strong>输出：</strong>&quot;abacbabacb&quot;
+</pre>
+
+<p>&nbsp;</p>
+
+<p><strong>提示：</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 10</code></li>
+	<li><code>1 &lt;= k &lt;= 100</code></li>
+</ul>
+
+<p>&nbsp;</p>
+
+
+    
+## 解题方法一：DFS构造
+
+写一个`dfs`函数接收已经构造的字符串并继续构造字符串：
+
++ 如果之前字符串已经长度为`n`了，就看看这是不是第`k`次长度为`n`。如果是，则说明找到了答案；否则，不继续向后追加字符串，结束这层递归在其他层递归继续寻找答案。
++ 否则，尝试把`abc`中每个和上一个字符(如有)不同的字符拼接到字符串上并递归。
+
+特别的，我们可以控制这个函数的返回值，返回`true`代表已经找到了最终答案，可以不再进行后续递归。
+
++ 时间复杂度$O(nk)$
++ 空间复杂度$O(n)$
+
+### AC代码
+
+#### C++
+
+```cpp
+/*
+ * @LastEditTime: 2026-03-14 23:29:38
+ */
+class Solution {
+private:
+    int n, k;
+    string ans;
+    char can[3] = {'a', 'b', 'c'};
+
+    // dfs and return if can stop
+    bool dfs(string now) {
+        if (now.size() == n) {
+            k--;
+            if (!k) {
+                ans = now;
+                return true;
+            }
+            return false;
+        }
+
+        char last = now.empty() ? '0' : now.back();
+        for (int i = 0; i < 3; i++) {
+            if (can[i] == last) {
+                continue;
+            }
+            if (dfs(now + can[i])) {
+                return true;
+            }
+        }
+        return false;   
+    }
+public:
+    string getHappyString(int n, int k) {
+        this->n = n, this->k = k;
+        dfs("");
+        return ans;
+    }
+};
+
+#if defined(_WIN32) || defined(__APPLE__)
+/*
+1 3
+
+c
+*/
+int main() {
+    int a, b;
+    while (cin >> a >> b) {
+        Solution sol;
+        cout << sol.getHappyString(a, b) << endl;
+    }
+    return 0;
+}
+#endif
+```
+
+## 解题方法二：数学直接找
+
+长度为$n$的字符串一共有多少种开心字符串呢？
+
+> 第一个字符有$3$种选择，后续每个字符有$2$种选择，共计$3\times2^{n-1}$种。
+>
+> 如果$k\gt 3\times2^{n-1}$则答案不存在，返回空串。
+
+第$k$个开心字符串的每一位分别应该对应哪个字符呢？很简单，我们只需要计算下这个字符后面字符串有多少种。
+
+举个例子：
+
++ 假设后面字符串有$2^2$共4种，而当前$k=3\leq 4$，那么当前字符选哪个？当然选能选的字符中第一个就够了；
++ 假设后面字符串有$2^2$共4种，而当前$k=5\lt 4$，那么当前字符选哪个？当然选能选的字符中第二个，因为选第一个的话后面最多$4$种情况，到不了$k=5$。
+
+> PS: 上面的“能选的字符”指的是属于`abc`且和前一个字符不同的字符。
+
+选完这个字符后，令$k$对剩余种类数取模，并更新剩余字符的种类数。
+
+为什么取模呢？
+
++ 仍然假设后面字符串有$2^2$共4种，而当前$k=5\lt 4$，假设当前可选字符为`ab`，那么相当于当前选`a`时候后面共有$4$个开心字符串，后面选完了当前字符**确定**选`b`了，后面还需要$5\%4=1$个开心字符串，使得总开心字符串数是当前$k=5$个。
+
+我们也可以将$k-1$以便后面的取模整除运算。
+
++ 时间复杂度$O(n)$
++ 空间复杂度$O(n)$
+
+### AC代码
+
+#### C++
+
+```cpp
+/*
+ * @LastEditTime: 2026-03-14 23:21:37
+ */
+class Solution {
+public:
+    string getHappyString(int n, int k) {
+        int remain = 1 << (n - 1);
+        if (k > 3 * remain) {
+            return "";
+        }
+        
+        k--;
+        char toChoose[3] = {'a', 'b', 'c'};
+        string ans;
+        ans.push_back(toChoose[k / remain]);
+        for (int i = 1; i < n; i++) {
+            k %= remain;
+            remain >>= 1;
+            int th = k / remain;
+            if (toChoose[th] >= ans.back()) {
+                th++;
+            }
+            ans.push_back(toChoose[th]);
+        }
+        return ans;
+    }
+};
+```
+
+感觉描述得还不错哈哈。
+
+> 同步发文于[CSDN](https://letmefly.blog.csdn.net/article/details/159055459)和我的[个人博客](https://blog.letmefly.xyz/)，原创不易，转载经作者同意后请附上[原文链接](https://blog.letmefly.xyz/2026/03/14/LeetCode%201415.%E9%95%BF%E5%BA%A6%E4%B8%BAn%E7%9A%84%E5%BC%80%E5%BF%83%E5%AD%97%E7%AC%A6%E4%B8%B2%E4%B8%AD%E5%AD%97%E5%85%B8%E5%BA%8F%E7%AC%ACk%E5%B0%8F%E7%9A%84%E5%AD%97%E7%AC%A6%E4%B8%B2/)哦~
+>
+> 千篇源码题解[已开源](https://github.com/LetMeFly666/LeetCode)
diff --git a/Solutions/Other-English-LearningNotes-SomeWords.md b/Solutions/Other-English-LearningNotes-SomeWords.md
@@ -1872,6 +1872,9 @@ categories: [自用]
 |wreath|n. (祭奠)花圈，(圣诞节)花环|
 |||
 |prohibitive|adj. (法令)禁止的，贵得买不起的|
+|||
+|deduct|v. 减去，扣除，演绎|
+|henceforth|adv. 从此之后|
 
 + 这个web要是能设计得可以闭眼(完全不睁眼)键盘控制背单词就好了。
 + 也许可以加个AI用最近词编故事功能(返回接口中支持标注所使用单词高亮?)
diff --git a/swap.md b/swap.md
