deploy: 9cab9d7

Author: acbin

en/lc/3145/index.html

@@ -78377,8 +78377,8 @@ <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
 <h3 id="solution-1-binary-search-bit-manipulation">Solution 1: Binary Search + Bit Manipulation</h3>
-<p>The continuous positive integer numbers correspond to the strong integer array, forming the array $\textit{big_nums}$. The problem requires us to find the result of the product of the subarray $\textit{big_nums}[\textit{left}..\textit{right}]$ modulo $\textit{mod}$ for each query $[\textit{left}, \textit{right}, \textit{mod}]$. Since each element of the subarray is a power of 2, this is equivalent to finding the sum of the powers $\textit{power}$ of the subarray, and then calculating $2^{\textit{power}} \bmod \textit{mod}$. For example, for the subarray $[1, 4, 8]$, i.e., $[2^0, 2^2, 2^3]$, the sum of the powers is $0 + 2 + 3 = 5$, so $2^5 \bmod \textit{mod}$ is the result we need.</p>
-<p>Therefore, we can convert $\textit{big_nums}$ into an array of powers. For example, for the subarray $[1, 4, 8]$, we convert it to $[0, 2, 3]$. Thus, the problem is transformed into finding the sum of the subarray of powers, i.e., $\textit{power} = \textit{f}(\textit{right} + 1) - \textit{f}(\textit{left})$, where $\textit{f}(i)$ represents the sum of the powers of $\textit{big_nums}[0..i)$, which is the prefix sum.</p>
+<p>The continuous positive integer numbers correspond to the strong integer array, forming the array $\textit{bignums}$. The problem requires us to find the result of the product of the subarray $\textit{bignums}[\textit{left}..\textit{right}]$ modulo $\textit{mod}$ for each query $[\textit{left}, \textit{right}, \textit{mod}]$. Since each element of the subarray is a power of 2, this is equivalent to finding the sum of the powers $\textit{power}$ of the subarray, and then calculating $2^{\textit{power}} \bmod \textit{mod}$. For example, for the subarray $[1, 4, 8]$, i.e., $[2^0, 2^2, 2^3]$, the sum of the powers is $0 + 2 + 3 = 5$, so $2^5 \bmod \textit{mod}$ is the result we need.</p>
+<p>Therefore, we can convert $\textit{bignums}$ into an array of powers. For example, for the subarray $[1, 4, 8]$, we convert it to $[0, 2, 3]$. Thus, the problem is transformed into finding the sum of the subarray of powers, i.e., $\textit{power} = \textit{f}(\textit{right} + 1) - \textit{f}(\textit{left})$, where $\textit{f}(i)$ represents the sum of the powers of $\textit{bignums}[0..i)$, which is the prefix sum.</p>
 <p>Next, we calculate the value of $\textit{f}(i)$ based on the index $i$. We can use binary search to find the largest number whose strong array length is less than $i$, and then calculate the sum of the powers of the remaining numbers.</p>
 <p>According to the problem description, we list the strong integers for numbers $0..14$:</p>
 <table>
@@ -78499,7 +78499,7 @@ <h3 id="solution-1-binary-search-bit-manipulation">Solution 1: Binary Search + B
 </tr>
 </tbody>
 </table>
-<p>By dividing the numbers into different colors according to the interval $[2^i, 2^{i+1}-1]$, we can see that the numbers in the interval $[2^i, 2^{i+1}-1]$ are equivalent to adding $2^i$ to each number in the interval $[0, 2^i-1]$. Based on this pattern, we can calculate the total number of strong arrays $\textit{cnt}[i]$ and the sum of powers $\textit{s}[i]$ for the first $i$ groups of numbers in $\textit{big_nums}$.</p>
+<p>By dividing the numbers into different colors according to the interval $[2^i, 2^{i+1}-1]$, we can see that the numbers in the interval $[2^i, 2^{i+1}-1]$ are equivalent to adding $2^i$ to each number in the interval $[0, 2^i-1]$. Based on this pattern, we can calculate the total number of strong arrays $\textit{cnt}[i]$ and the sum of powers $\textit{s}[i]$ for the first $i$ groups of numbers in $\textit{bignums}$.</p>
 <p>Next, for any number, we consider how to calculate the number of strong arrays and the sum of powers. We can use the binary method, calculating from the highest bit. For example, for the number $13 = 2^3 + 2^2 + 2^0$, the result of the first $2^3$ numbers can be obtained from $\textit{cnt}[3]$ and $\textit{s}[3]$, and the result of the remaining $[2^3, 13]$ is equivalent to adding $3$ to all numbers in $[0, 13-2^3]$, i.e., $[0, 5]$. The problem is transformed into calculating the number of strong arrays and the sum of powers for $[0, 5]$. In this way, we can calculate the number of strong arrays and the sum of powers for any number.</p>
 <p>Finally, based on the value of $\textit{power}$, we use the fast exponentiation method to calculate the result of $2^{\textit{power}} \bmod \textit{mod}$.</p>
 <p>The time complexity is $O(q \times \log M)$, and the space complexity is $O(\log M)$. Here, $q$ is the number of queries, and $M$ is the upper bound of the number, with $M \le 10^{15}$ in this problem.</p>

en/lc/3146/index.html

@@ -73122,9 +73122,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-hash-table-or-array" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Hash Table or Array
     </span>
   </a>
 
@@ -78333,8 +78333,11 @@ <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="1:5"><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>
+<h3 id="solution-1-hash-table-or-array">Solution 1: Hash Table or Array</h3>
+<p>We can use a hash table or an array of length $26$, denoted as $\textit{d}$, to store the positions of each character in the string $\textit{s}$.</p>
+<p>Then, we traverse the string $\textit{t}$ and calculate the sum of the absolute differences between the positions of each character in the string $\textit{t}$ and the positions in the string $\textit{s}$.</p>
+<p>The time complexity is $O(n)$, where $n$ is the length of the string $\textit{s}$. The space complexity is $O(|\Sigma|)$, where $\Sigma$ is the character set. Here, it is lowercase English letters, so $|\Sigma| \leq 26$.</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:6"><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" /><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">C#</label></div>
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@@ -78446,16 +78449,46 @@ <h3 id="solution-1">Solution 1</h3>
 <span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">d</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="mf">26</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">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">s</span><span class="p">.</span><span class="nx">length</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">i</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">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<span class="w">        </span><span class="nx">d</span><span class="p">[</span><span class="nx">s</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">)]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
+<span class="w">        </span><span class="nx">d</span><span class="p">[</span><span class="nx">s</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">97</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
 <span class="w">    </span><span class="p">}</span>
 <span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">ans</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="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</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">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-<span class="w">        </span><span class="nx">ans</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">abs</span><span class="p">(</span><span class="nx">d</span><span class="p">[</span><span class="nx">t</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="mf">0</span><span class="p">)]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
+<span class="w">        </span><span class="nx">ans</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">abs</span><span class="p">(</span><span class="nx">d</span><span class="p">[</span><span class="nx">t</span><span class="p">.</span><span class="nx">charCodeAt</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">97</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">i</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">ans</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>
+<span class="normal">14</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">public</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">Solution</span><span class="w"> </span><span class="p">{</span>
+<span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">FindPermutationDifference</span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="m">26</span><span class="p">];</span>
+<span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span>
+<span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">            </span><span class="n">d</span><span class="p">[</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="sc">&#39;a&#39;</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<span class="w">        </span><span class="p">}</span>
+<span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ans</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">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="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">            </span><span class="n">ans</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="n">Abs</span><span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="sc">&#39;a&#39;</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</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="n">ans</span><span class="p">;</span>
+<span class="w">    </span><span class="p">}</span>
+<span class="p">}</span>
+</code></pre></div></td></tr></table></div>
+</div>
 </div>
 </div>
 <!-- solution:end -->