deploy: f82785c

Author: yanglbme

en/lc/801/index.html

@@ -25071,9 +25071,9 @@
       <ul class="md-nav__list">
 
           <li class="md-nav__item">
-  <a href="#solution-1" class="md-nav__link">
+  <a href="#solution-1-dynamic-programming" class="md-nav__link">
     <span class="md-ellipsis">
-      Solution 1
+      Solution 1: Dynamic Programming
     </span>
   </a>
 
@@ -86378,7 +86378,7 @@ <h2 id="description">Description</h2>
 <pre>
 <strong>Input:</strong> nums1 = [1,3,5,4], nums2 = [1,2,3,7]
 <strong>Output:</strong> 1
-<strong>Explanation:</strong> 
+<strong>Explanation:</strong>
 Swap nums1[3] and nums2[3]. Then the sequences are:
 nums1 = [1, 3, 5, 7] and nums2 = [1, 2, 3, 4]
 which are both strictly increasing.
@@ -86405,8 +86405,15 @@ <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-dynamic-programming">Solution 1: Dynamic Programming</h3>
+<p>Define <span class="arithmatex">\(a\)</span> and <span class="arithmatex">\(b\)</span> to represent the minimum number of swaps needed to make the element sequences strictly increasing up to index <span class="arithmatex">\([0..i]\)</span>, with the <span class="arithmatex">\(i\)</span>-th element not swapped and swapped, respectively. The index starts from <span class="arithmatex">\(0\)</span>.</p>
+<p>When <span class="arithmatex">\(i=0\)</span>, we have <span class="arithmatex">\(a = 0\)</span> and <span class="arithmatex">\(b = 1\)</span>.</p>
+<p>When <span class="arithmatex">\(i \gt 0\)</span>, we first save the previous values of <span class="arithmatex">\(a\)</span> and <span class="arithmatex">\(b\)</span> in <span class="arithmatex">\(x\)</span> and <span class="arithmatex">\(y\)</span>, and then discuss the following cases:</p>
+<p>If <span class="arithmatex">\(nums1[i - 1] \ge nums1[i]\)</span> or <span class="arithmatex">\(nums2[i - 1] \ge nums2[i]\)</span>, to make both sequences strictly increasing, the relative positions of the elements at indices <span class="arithmatex">\(i-1\)</span> and <span class="arithmatex">\(i\)</span> must change. That is, if the previous position was swapped, then the current position should not be swapped, so <span class="arithmatex">\(a = y\)</span>; if the previous position was not swapped, then the current position must be swapped, so <span class="arithmatex">\(b = x + 1\)</span>.</p>
+<p>Otherwise, the relative positions of the elements at indices <span class="arithmatex">\(i-1\)</span> and <span class="arithmatex">\(i\)</span> do not need to change, so <span class="arithmatex">\(b = y + 1\)</span>. Additionally, if <span class="arithmatex">\(nums1[i - 1] \lt nums2[i]\)</span> and <span class="arithmatex">\(nums2[i - 1] \lt nums1[i]\)</span>, the relative positions of the elements at indices <span class="arithmatex">\(i-1\)</span> and <span class="arithmatex">\(i\)</span> can change, so <span class="arithmatex">\(a\)</span> and <span class="arithmatex">\(b\)</span> can take the smaller values, thus <span class="arithmatex">\(a = \min(a, y)\)</span> and <span class="arithmatex">\(b = \min(b, x + 1)\)</span>.</p>
+<p>Finally, return the smaller value between <span class="arithmatex">\(a\)</span> and <span class="arithmatex">\(b\)</span>.</p>
+<p>The time complexity is <span class="arithmatex">\(O(n)\)</span>, and the space complexity is <span class="arithmatex">\(O(1)\)</span>.</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>
@@ -86548,6 +86555,44 @@ <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>
+<span class="normal">17</span>
+<span class="normal">18</span></pre></div></td><td class="code"><div><pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">minSwap</span><span class="p">(</span><span class="nx">nums1</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">nums2</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">let</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="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">1</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">1</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">nums1</span><span class="p">.</span><span class="nx">length</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="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="nx">a</span><span class="p">,</span>
+<span class="w">            </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">b</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">nums1</span><span class="p">[</span><span class="nx">i</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="o">&gt;=</span><span class="w"> </span><span class="nx">nums1</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="nx">nums2</span><span class="p">[</span><span class="nx">i</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="o">&gt;=</span><span class="w"> </span><span class="nx">nums2</span><span class="p">[</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">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">;</span>
+<span class="w">            </span><span class="nx">b</span><span class="w"> </span><span class="o">=</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">1</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="p">{</span>
+<span class="w">            </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</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">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums1</span><span class="p">[</span><span class="nx">i</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="o">&lt;</span><span class="w"> </span><span class="nx">nums2</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums2</span><span class="p">[</span><span class="nx">i</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="o">&lt;</span><span class="w"> </span><span class="nx">nums1</span><span class="p">[</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">a</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">min</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="p">);</span>
+<span class="w">                </span><span class="nx">b</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">min</span><span class="p">(</span><span class="nx">b</span><span class="p">,</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">1</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="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">min</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="p">}</span>
+</code></pre></div></td></tr></table></div>
+</div>
 </div>
 </div>
 <!-- solution:end -->