deploy: fd47409

Author: yanglbme

en/lc/1589/index.html

@@ -40695,9 +40695,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-difference-array-sorting-greedy" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Difference Array + Sorting + Greedy
     </span>
   </a>
 
@@ -81410,7 +81410,7 @@ <h2 id="description">Description</h2>
 <pre>
 <strong>Input:</strong> nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
 <strong>Output:</strong> 19
-<strong>Explanation:</strong> One permutation of nums is [2,1,3,4,5] with the following result: 
+<strong>Explanation:</strong> One permutation of nums is [2,1,3,4,5] with the following result:
 requests[0] -&gt; nums[1] + nums[2] + nums[3] = 1 + 3 + 4 = 8
 requests[1] -&gt; nums[0] + nums[1] = 2 + 1 = 3
 Total sum: 8 + 3 = 11.
@@ -81451,7 +81451,10 @@ <h2 id="description">Description</h2>
 <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
-<h3 id="solution-1">Solution 1</h3>
+<h3 id="solution-1-difference-array-sorting-greedy">Solution 1: Difference Array + Sorting + Greedy</h3>
+<p>We observe that for a query operation, it returns the sum of all elements in the query interval $[l, r]$. The problem requires the maximum sum of the results of all query operations, which means we need to accumulate the results of all query operations to maximize the sum. Therefore, if an index $i$ appears more frequently in the query operations, we should assign a larger value to index $i$ to maximize the sum of the results of all query operations.</p>
+<p>Therefore, we can use the idea of a difference array to count the number of times each index appears in the query operations, then sort these counts in ascending order, and also sort the array $\textit{nums}$ in ascending order. This ensures that the more frequently an index $i$ appears in the query operations, the larger the value $\textit{nums}[i]$ corresponding to that index will be. Next, we only need to multiply the values $\textit{nums}[i]$ corresponding to these indices by the number of times they appear in the query operations, and then sum them up to get the maximum sum of the results of all query operations.</p>
+<p>Time complexity $O(n \times \log n)$, space complexity $O(n)$. Where $n$ is the length of the array $\textit{nums}$.</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">

en/lc/1705/index.html

@@ -81438,9 +81438,9 @@ <h2 id="solutions">Solutions</h2>
 <!-- solution:start -->
 
 <h3 id="solution-1-greedy-priority-queue">Solution 1: Greedy + Priority Queue</h3>
-<p>We can greedily choose the apple that is most likely to rot among the unrotten apples, so that we can eat as many apples as possible.</p>
-<p>Therefore, we can use a priority queue (min heap) to store the rotting time of the apples and the corresponding number of apples. Each time we take out the apple with the smallest rotting time from the priority queue, then reduce its quantity by one. If the quantity of the apple is not zero after reduction, we put it back into the priority queue. If the apple has rotted, we pop it out from the priority queue.</p>
-<p>The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array <code>apples</code> or <code>days</code>.</p>
+<p>We can greedily choose the apples that are closest to rotting among the unrotten apples, so that we can eat as many apples as possible.</p>
+<p>Therefore, we can use a priority queue (min-heap) to store the rotting time of the apples and the corresponding number of apples. Each time, we take out the apples with the smallest rotting time from the priority queue, then decrement their quantity by one. If the quantity is not zero after decrementing, we put them back into the priority queue. If the apples have already rotted, we remove them from the priority queue.</p>
+<p>The time complexity is $O(n \times \log n + M)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $\textit{days}$, and $M = \max(\textit{days})$.</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">
@@ -81554,23 +81554,33 @@ <h3 id="solution-1-greedy-priority-queue">Solution 1: Greedy + Priority Queue</h
 <span class="normal">20</span>
 <span class="normal">21</span>
 <span class="normal">22</span>
-<span class="normal">23</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">using</span><span class="w"> </span><span class="n">pii</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="p">;</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="normal">23</span>
+<span class="normal">24</span>
+<span class="normal">25</span>
+<span class="normal">26</span>
+<span class="normal">27</span>
+<span class="normal">28</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="k">class</span><span class="w"> </span><span class="nc">Solution</span><span class="w"> </span><span class="p">{</span>
 <span class="k">public</span><span class="o">:</span>
 <span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">eatenApples</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span><span class="w"> </span><span class="n">apples</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&amp;</span><span class="w"> </span><span class="n">days</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<span class="w">        </span><span class="k">using</span><span class="w"> </span><span class="n">pii</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="p">;</span>
 <span class="w">        </span><span class="n">priority_queue</span><span class="o">&lt;</span><span class="n">pii</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">pii</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="n">pii</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">q</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">days</span><span class="p">.</span><span class="n">size</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="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
 <span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</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="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">q</span><span class="p">.</span><span class="n">empty</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="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">apples</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">days</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="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">apples</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-<span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">q</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">top</span><span class="p">().</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</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="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">apples</span><span class="p">[</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">q</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">days</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="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">apples</span><span class="p">[</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">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">q</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">top</span><span class="p">().</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;</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="n">q</span><span class="p">.</span><span class="n">pop</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="o">!</span><span class="n">q</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <span class="w">                </span><span class="k">auto</span><span class="w"> </span><span class="p">[</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">top</span><span class="p">();</span>
 <span class="w">                </span><span class="n">q</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
 <span class="w">                </span><span class="o">--</span><span class="n">v</span><span class="p">;</span>
 <span class="w">                </span><span class="o">++</span><span class="n">ans</span><span class="p">;</span>
-<span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">v</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="n">q</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">);</span>
+<span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">v</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="o">&gt;</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="n">q</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">v</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="o">++</span><span class="n">i</span><span class="p">;</span>
 <span class="w">        </span><span class="p">}</span>