deploy

2025-07-19 20:55:57 +08:00 · 2023-08-27 00:50:10 +08:00
parent 3bb4725cbb
commit 8350023f50
12 changed files with 239 additions and 230 deletions
--- a/chapter_dynamic_programming/intro_to_dynamic_programming/index.html
+++ b/chapter_dynamic_programming/intro_to_dynamic_programming/index.html
@ -2838,7 +2838,7 @@
      
        <li class="md-nav__item">
  <a href="#1414" class="md-nav__link">
-    14.1.4 &nbsp; 状态压缩
+    14.1.4 &nbsp; 空间优化
  </a>
  
 </li>
@ -3449,7 +3449,7 @@
      
        <li class="md-nav__item">
  <a href="#1414" class="md-nav__link">
-    14.1.4 &nbsp; 状态压缩
+    14.1.4 &nbsp; 空间优化
  </a>
  
 </li>
@ -4533,12 +4533,12 @@ dp[i] = dp[i-1] + dp[i-2]
 <li>将最小子问题对应的状态（即第 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(2\)</span> 阶楼梯）称为「初始状态」。</li>
 <li>将递推公式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> 称为「状态转移方程」。</li>
 </ul>
-<h2 id="1414">14.1.4 &nbsp; 状态压缩<a class="headerlink" href="#1414" title="Permanent link">&para;</a></h2>
+<h2 id="1414">14.1.4 &nbsp; 空间优化<a class="headerlink" href="#1414" title="Permanent link">&para;</a></h2>
 <p>细心的你可能发现，<strong>由于 <span class="arithmatex">\(dp[i]\)</span> 只与 <span class="arithmatex">\(dp[i-1]\)</span> 和 <span class="arithmatex">\(dp[i-2]\)</span> 有关，因此我们无须使用一个数组 <code>dp</code> 来存储所有子问题的解</strong>，而只需两个变量滚动前进即可。</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Java</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Python</label><label for="__tabbed_5_4">Go</label><label for="__tabbed_5_5">JS</label><label for="__tabbed_5_6">TS</label><label for="__tabbed_5_7">C</label><label for="__tabbed_5_8">C#</label><label for="__tabbed_5_9">Swift</label><label for="__tabbed_5_10">Zig</label><label for="__tabbed_5_11">Dart</label><label for="__tabbed_5_12">Rust</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
@ -4553,7 +4553,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
 <a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
@ -4569,7 +4569,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </div>
 <div class="tabbed-block">
 <div class="highlight"><span class="filename">climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="k">def</span> <span class="nf">climbing_stairs_dp_comp</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="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;爬楼梯：状态压缩后的动态规划&quot;&quot;&quot;</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;爬楼梯：空间优化后的动态规划&quot;&quot;&quot;</span>
 <a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
 <a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a>        <span class="k">return</span> <span class="n">n</span>
 <a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span>
@ -4579,7 +4579,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span>
@ -4594,7 +4594,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDPComp</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
 <a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
@ -4609,7 +4609,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">climbingStairsDPComp</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="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span>
 <a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span>
@ -4628,7 +4628,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span>
 <a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
@ -4643,7 +4643,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kd">func</span> <span class="nf">climbingStairsDPComp</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="p">-&gt;</span> <span class="nb">Int</span> <span class="p">{</span>
 <a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="o">||</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">2</span> <span class="p">{</span>
 <a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>        <span class="k">return</span> <span class="n">n</span>
@ -4658,7 +4658,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="c1">// 爬楼梯：状态压缩后的动态规划</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="c1">// 爬楼梯：空间优化后的动态规划</span>
 <a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">climbingStairsDPComp</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">@intCast</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
@ -4675,7 +4675,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
 <a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
@ -4689,7 +4689,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </code></pre></div>
 </div>
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 爬楼梯：状态压缩后的动态规划 */</span>
+<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 爬楼梯：空间优化后的动态规划 */</span>
 <a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">fn</span> <span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="kt">i32</span> <span class="p">{</span>
 <a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</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">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
 <a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
@ -4705,7 +4705,7 @@ dp[i] = dp[i-1] + dp[i-2]
 </div>
 </div>
 <p>观察以上代码，由于省去了数组 <code>dp</code> 占用的空间，因此空间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</p>
-<p><strong>这种空间优化技巧被称为「状态压缩」</strong>。在常见的动态规划问题中，当前状态仅与前面有限个状态有关，这时我们可以应用状态压缩，只保留必要的状态，通过“降维”来节省内存空间。</p>
+<p>在动态规划问题中，当前状态往往仅与前面有限个状态有关，这时我们可以只保留必要的状态，通过“降维”来节省内存空间。<strong>这种空间优化技巧被称为“滚动变量”或“滚动数组”</strong>。</p>