deploy: 110e86a

Author: yanglbme

en/lc/753/index.html

@@ -23171,9 +23171,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-eulerian-circuit" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Eulerian Circuit
     </span>
   </a>
 
@@ -81817,8 +81817,11 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
-<div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label></div>
+<h3 id="solution-1-eulerian-circuit">Solution 1: Eulerian Circuit</h3>
+<p>We can construct a directed graph based on the description in the problem: each point is considered as a length $n-1$ $k$-string, and each edge carries a character from $0$ to $k-1$. If there is a directed edge $e$ from point $u$ to point $v$, and the character carried by $e$ is $c$, then the last $k-1$ characters of $u+c$ form the string $v$. At this point, the edge $u+c$ represents a password of length $n$.</p>
+<p>In this directed graph, there are $k^{n-1}$ points, each point has $k$ outgoing edges and $k$ incoming edges. Therefore, this directed graph has an Eulerian circuit, and the path traversed by the Eulerian circuit is the answer to the problem.</p>
+<p>The time complexity is $O(k^n)$, and the space complexity is $O(k^n)$.</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">TypeScript</label></div>
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 <div class="tabbed-block">
 <div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 1</span>
@@ -81990,6 +81993,50 @@ <h3 id="solution-1">Solution 1</h3>
 <span class="p">}</span>
 </code></pre></div></td></tr></table></div>
 </div>
+<div class="tabbed-block">
+<div class="highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"> 1</span>
+<span class="normal"> 2</span>
+<span class="normal"> 3</span>
+<span class="normal"> 4</span>
+<span class="normal"> 5</span>
+<span class="normal"> 6</span>
+<span class="normal"> 7</span>
+<span class="normal"> 8</span>
+<span class="normal"> 9</span>
+<span class="normal">10</span>
+<span class="normal">11</span>
+<span class="normal">12</span>
+<span class="normal">13</span>
+<span class="normal">14</span>
+<span class="normal">15</span>
+<span class="normal">16</span>
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+<span class="normal">18</span>
+<span class="normal">19</span>
+<span class="normal">20</span>
+<span class="normal">21</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">crackSafe</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">k</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="p">{</span>
+<span class="w">    </span><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">u</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">k</span><span class="p">;</span><span class="w"> </span><span class="nx">x</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">            </span><span class="kd">const</span><span class="w"> </span><span class="nx">e</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">u</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span>
+<span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">vis</span><span class="p">.</span><span class="nx">has</span><span class="p">(</span><span class="nx">e</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<span class="w">                </span><span class="nx">vis</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">e</span><span class="p">);</span>
+<span class="w">                </span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">e</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="nx">mod</span><span class="p">;</span>
+<span class="w">                </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
+<span class="w">                </span><span class="nx">ans</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">x</span><span class="p">.</span><span class="nx">toString</span><span class="p">());</span>
+<span class="w">            </span><span class="p">}</span>
+<span class="w">        </span><span class="p">}</span>
+<span class="w">    </span><span class="p">}</span>
+
+<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">mod</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">vis</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Set</span><span class="o">&lt;</span><span class="kt">number</span><span class="o">&gt;</span><span class="p">();</span>
+<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">ans</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+
+<span class="w">    </span><span class="nx">dfs</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<span class="w">    </span><span class="nx">ans</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="s1">&#39;0&#39;</span><span class="p">.</span><span class="nx">repeat</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
+<span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">ans</span><span class="p">.</span><span class="nx">join</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">);</span>
+<span class="p">}</span>
+</code></pre></div></td></tr></table></div>
+</div>
 </div>
 </div>
 <!-- solution:end -->

en/lc/754/index.html

@@ -23192,9 +23192,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-mathematical-analysis" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Mathematical Analysis
     </span>
   </a>
 
@@ -81800,7 +81800,12 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-mathematical-analysis">Solution 1: Mathematical Analysis</h3>
+<p>Due to symmetry, each time we can choose to move left or right, so we can take the absolute value of $\textit{target}$.</p>
+<p>Define $s$ as the current position, and use the variable $k$ to record the number of moves. Initially, both $s$ and $k$ are $0$.</p>
+<p>We keep adding to $s$ in a loop until $s \ge \textit{target}$ and $(s - \textit{target}) \bmod 2 = 0$. At this point, the number of moves $k$ is the answer, and we return it directly.</p>
+<p>Why? Because if $s \ge \textit{target}$ and $(s - \textit{target}) \bmod 2 = 0$, we only need to change the sign of the positive integer $\frac{s - \textit{target}}{2}$ to negative, so that $s$ equals $\textit{target}$. Changing the sign of a positive integer essentially means changing the direction of the move, but the actual number of moves remains the same.</p>
+<p>The time complexity is $O(\sqrt{\left | \textit{target} \right | })$, and the space complexity is $O(1)$.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label></div>
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en/lc/755/index.html

@@ -23213,9 +23213,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-simulation" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Simulation
     </span>
   </a>
 
@@ -81816,7 +81816,9 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-simulation">Solution 1: Simulation</h3>
+<p>We can simulate the process of each unit of water dropping. Each time a drop falls, we first try to move left. If it can move to a lower height, it moves to the lowest height; if it cannot move to a lower height, we try to move right. If it can move to a lower height, it moves to the lowest height; if it cannot move to a lower height, it rises at the current position.</p>
+<p>The time complexity is $O(v \times n)$, and the space complexity is $O(1)$, where $v$ and $n$ are the number of water drops and the length of the height array, respectively.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python3</label><label for="__tabbed_1_2">Java</label><label for="__tabbed_1_3">C++</label><label for="__tabbed_1_4">Go</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">