deploy: 497b411

Author: acbin

en/lc/1614/index.html

@@ -41048,9 +41048,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-traversal" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Traversal
     </span>
   </a>
 
@@ -79457,7 +79457,11 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-traversal">Solution 1: Traversal</h3>
+<p>We use a variable $d$ to record the current depth, initially $d = 0$.</p>
+<p>Traverse the string $s$. When encountering a left parenthesis, increment the depth $d$ by one and update the answer to be the maximum of the current depth $d$ and the answer. When encountering a right parenthesis, decrement the depth $d$ by one.</p>
+<p>Finally, return the answer.</p>
+<p>The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(1)$.</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:7"><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" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" 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><label for="__tabbed_1_6">JavaScript</label><label for="__tabbed_1_7">C#</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">

en/lc/1615/index.html

@@ -41069,18 +41069,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-counting" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
-    </span>
-  </a>
-  
-</li>
-        
-          <li class="md-nav__item">
-  <a href="#solution-2" class="md-nav__link">
-    <span class="md-ellipsis">
-      Solution 2
+      Solution 1: Counting
     </span>
   </a>
 
@@ -79465,33 +79456,30 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-counting">Solution 1: Counting</h3>
+<p>We can use a one-dimensional array $\textit{cnt}$ to record the degree of each city and a two-dimensional array $\textit{g}$ to record whether there is a road between each pair of cities. If there is a road between city $a$ and city $b$, then $\textit{g}[a][b] = \textit{g}[b][a] = 1$; otherwise, $\textit{g}[a][b] = \textit{g}[b][a] = 0$.</p>
+<p>Next, we enumerate each pair of cities $(a, b)$, where $a \lt b$, and calculate their network rank, which is $\textit{cnt}[a] + \textit{cnt}[b] - \textit{g}[a][b]$. The maximum value among these is the answer.</p>
+<p>The time complexity is $O(n^2)$, and the space complexity is $O(n^2)$. Here, $n$ is the number of cities.</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>
 <div class="tabbed-content">
 <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></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">Solution</span><span class="p">:</span>
+<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></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">Solution</span><span class="p">:</span>
     <span class="k">def</span> <span class="nf">maximalNetworkRank</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">roads</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-        <span class="n">g</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">set</span><span class="p">)</span>
+        <span class="n">g</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
+        <span class="n">cnt</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
         <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">roads</span><span class="p">:</span>
-            <span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
-            <span class="n">g</span><span class="p">[</span><span class="n">b</span><span class="p">]</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
-        <span class="n">ans</span> <span class="o">=</span> <span class="mi">0</span>
-        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-            <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">a</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
-                <span class="k">if</span> <span class="p">(</span><span class="n">t</span> <span class="o">:=</span> <span class="nb">len</span><span class="p">(</span><span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">])</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">g</span><span class="p">[</span><span class="n">b</span><span class="p">])</span> <span class="o">-</span> <span class="p">(</span><span class="n">a</span> <span class="ow">in</span> <span class="n">g</span><span class="p">[</span><span class="n">b</span><span class="p">]))</span> <span class="o">&gt;</span> <span class="n">ans</span><span class="p">:</span>
-                    <span class="n">ans</span> <span class="o">=</span> <span class="n">t</span>
-        <span class="k">return</span> <span class="n">ans</span>
+            <span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">][</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">g</span><span class="p">[</span><span class="n">b</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+            <span class="n">cnt</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+            <span class="n">cnt</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+        <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="n">cnt</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">cnt</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">-</span> <span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">][</span><span class="n">b</span><span class="p">]</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">a</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>
 </code></pre></div></td></tr></table></div>
 </div>
 <div class="tabbed-block">
@@ -79640,8 +79628,8 @@ <h3 id="solution-1">Solution 1</h3>
 <span class="normal">15</span>
 <span class="normal">16</span>
 <span class="normal">17</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">maximalNetworkRank</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">roads</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">number</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">g</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">(</span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">),</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">));</span>
-<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">cnt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</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">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">g</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[][]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="kt">n</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">));</span>
+<span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">cnt</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</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">const</span><span class="w"> </span><span class="p">[</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">roads</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <span class="w">        </span><span class="nx">g</span><span class="p">[</span><span class="nx">a</span><span class="p">][</span><span class="nx">b</span><span class="p">]</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="nx">g</span><span class="p">[</span><span class="nx">b</span><span class="p">][</span><span class="nx">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
@@ -79662,35 +79650,6 @@ <h3 id="solution-1">Solution 1</h3>
 </div>
 <!-- solution:end -->
 
-<!-- solution:start -->
-
-<h3 id="solution-2">Solution 2</h3>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:1"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python3</label></div>
-<div class="tabbed-content">
-<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></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span> <span class="nc">Solution</span><span class="p">:</span>
-    <span class="k">def</span> <span class="nf">maximalNetworkRank</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">roads</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-        <span class="n">g</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
-        <span class="n">cnt</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
-        <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">roads</span><span class="p">:</span>
-            <span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">][</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">g</span><span class="p">[</span><span class="n">b</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
-            <span class="n">cnt</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-            <span class="n">cnt</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
-        <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="n">cnt</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">cnt</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">-</span> <span class="n">g</span><span class="p">[</span><span class="n">a</span><span class="p">][</span><span class="n">b</span><span class="p">]</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">a</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>
-</code></pre></div></td></tr></table></div>
-</div>
-</div>
-</div>
-<!-- solution:end -->
-
 <!-- problem:end -->