deploy: b5605cd

Author: yanglbme

en/lc/769/index.html

@@ -81430,7 +81430,7 @@ <h3 id="solution-1">Solution 1</h3>
 <!-- solution:start -->
 
 <h3 id="solution-2">Solution 2</h3>
-<div class="tabbed-set tabbed-alternate" data-tabs="2:4"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python3</label><label for="__tabbed_2_2">Java</label><label for="__tabbed_2_3">C++</label><label for="__tabbed_2_4">Go</label></div>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:6"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python3</label><label for="__tabbed_2_2">Java</label><label for="__tabbed_2_3">C++</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">TypeScript</label><label for="__tabbed_2_6">JavaScript</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>
@@ -81568,6 +81568,62 @@ <h3 id="solution-2">Solution 2</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></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">maxChunksToSorted</span><span class="p">(</span><span class="nx">arr</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">stk</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="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="nx">x</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">stk</span><span class="p">.</span><span class="nx">at</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="o">!</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">x</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">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="o">!</span><span class="p">;</span>
+<span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">stk</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">at</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="o">!</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<span class="w">            </span><span class="nx">stk</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">top</span><span class="p">);</span>
+<span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">stk</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="w">    </span><span class="p">}</span>
+
+<span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<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></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">maxChunksToSorted</span><span class="p">(</span><span class="nx">arr</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">stk</span><span class="w"> </span><span class="o">=</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">const</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">stk</span><span class="p">.</span><span class="nx">at</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">x</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">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">stk</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">at</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">x</span><span class="p">)</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<span class="w">            </span><span class="nx">stk</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">top</span><span class="p">);</span>
+<span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">stk</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="w">    </span><span class="p">}</span>
+
+<span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">stk</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<span class="p">}</span>
+</code></pre></div></td></tr></table></div>
+</div>
 </div>
 </div>
 <!-- solution:end -->
@@ -81601,6 +81657,11 @@ <h3 id="solution-2">Solution 2</h3>
 
     <nav>
 
+        <a href="https://github.com/rain84" class="md-author" title="@rain84">
+          
+          <img src="https://avatars.githubusercontent.com/u/1732547?v=4&size=72" alt="rain84">
+        </a>
+      
         <a href="https://github.com/yanglbme" class="md-author" title="@yanglbme">
 
           <img src="https://avatars.githubusercontent.com/u/21008209?v=4&size=72" alt="yanglbme">

en/lc/974/index.html

@@ -27762,9 +27762,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-hash-table-prefix-sum" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Hash Table + Prefix Sum
     </span>
   </a>
 
@@ -81220,7 +81220,44 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-hash-table-prefix-sum">Solution 1: Hash Table + Prefix Sum</h3>
+<ol>
+<li>
+<p><strong>Key Insight</strong>:</p>
+<ul>
+<li>If there exist indices $i$ and $j$ such that $i \leq j$, and the sum of the subarray $nums[i, ..., j]$ is divisible by $k$, then $(s_j - s_i) \bmod k = 0$, this implies: $s_j \bmod k = s_i \bmod k$</li>
+<li>We can use a hash table to count the occurrences of prefix sums modulo $k$ to efficiently check for subarrays satisfying the condition.</li>
+</ul>
+</li>
+<li>
+<p><strong>Prefix Sum Modulo</strong>:</p>
+<ul>
+<li>Use a hash table $cnt$ to count occurrences of each prefix sum modulo $k$.</li>
+<li>$cnt[i]$ represents the number of prefix sums with modulo $k$ equal to $i$.</li>
+<li>Initialize $cnt[0] = 1$ to account for subarrays directly divisible by $k$.</li>
+</ul>
+</li>
+<li>
+<p><strong>Algorithm</strong>:</p>
+<ul>
+<li>Let a variable $s$ represent the running prefix sum, starting with $s = 0$.</li>
+<li>Traverse the array $nums$ from left to right.<ul>
+<li>For each element $x$:<ul>
+<li>Compute $s = (s + x) \bmod k$.</li>
+<li>Update the result: $ans += cnt[s]$.</li>
+<li>Increment $cnt[s]$ by $1$.</li>
+</ul>
+</li>
+</ul>
+</li>
+<li>Return the result $ans$.</li>
+</ul>
+</li>
+</ol>
+<blockquote>
+<p>Note: if $s$ is negative, adjust it to be non-negative by adding $k$ and taking modulo $k$ again.</p>
+</blockquote>
+<p>The time complexity is $O(n)$ and space complexity is $O(n)$ where $n$ is the length of the array $nums$.</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">
@@ -81380,6 +81417,11 @@ <h3 id="solution-1">Solution 1</h3>
 
     <nav>
 
+        <a href="https://github.com/Maddieee" class="md-author" title="@Maddieee">
+          
+          <img src="https://avatars.githubusercontent.com/u/10874742?v=4&size=72" alt="Maddieee">
+        </a>
+      
         <a href="https://github.com/yanglbme" class="md-author" title="@yanglbme">
 
           <img src="https://avatars.githubusercontent.com/u/21008209?v=4&size=72" alt="yanglbme">