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@ -2970,7 +2970,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="p">}</span><span class="w"> </span>
<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
@ -3358,7 +3358,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="c1">// 指数阶（循环实现）</span>
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="p">{</span>
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">bas</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
@ -3372,7 +3372,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="p">}</span><span class="w"> </span>
<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
@ -3461,7 +3461,7 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="c1">// 指数阶（递归实现）</span>
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="p">{</span>
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</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-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></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="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</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="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</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="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="p">}</span>
@ -3586,17 +3586,16 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="c1">// 对数阶（循环实现）</span>
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="p">{</span>
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
<a id="__codelineno-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n_var</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_var</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-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></a><span class="p">}</span>
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</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-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n_var</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_var</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-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
@ -3685,11 +3684,10 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="c1">// 对数阶（递归实现）</span>
<a id="__codelineno-129-2" name="__codelineno-129-2" href="#__codelineno-129-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-129-3" name="__codelineno-129-3" href="#__codelineno-129-3"></a><span class="p">{</span>
<a id="__codelineno-129-4" name="__codelineno-129-4" href="#__codelineno-129-4"></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">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-129-5" name="__codelineno-129-5" href="#__codelineno-129-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</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">2</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>
<a id="__codelineno-129-6" name="__codelineno-129-6" href="#__codelineno-129-6"></a><span class="p">}</span>
<a id="__codelineno-129-2" name="__codelineno-129-2" href="#__codelineno-129-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</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-129-3" name="__codelineno-129-3" href="#__codelineno-129-3"></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">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-129-4" name="__codelineno-129-4" href="#__codelineno-129-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</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">2</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>
<a id="__codelineno-129-5" name="__codelineno-129-5" href="#__codelineno-129-5"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
@ -3819,17 +3817,16 @@ O((n - 1) \frac{n}{2}) = O(n^2)
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="c1">// 线性对数阶</span>
<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span>
<a id="__codelineno-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></a><span class="p">{</span>
<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></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">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</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">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a><span class="w"> </span><span class="n">linearLogRecur</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">2</span><span class="p">);</span>
<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-139-8" name="__codelineno-139-8" href="#__codelineno-139-8"></a><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="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</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="p">{</span>
<a id="__codelineno-139-9" name="__codelineno-139-9" href="#__codelineno-139-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-139-10" name="__codelineno-139-10" href="#__codelineno-139-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-139-11" name="__codelineno-139-11" href="#__codelineno-139-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-139-12" name="__codelineno-139-12" href="#__codelineno-139-12"></a><span class="p">}</span>
<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</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-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></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">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</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">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a><span class="w"> </span><span class="n">linearLogRecur</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">2</span><span class="p">);</span>
<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a><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="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</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="p">{</span>
<a id="__codelineno-139-8" name="__codelineno-139-8" href="#__codelineno-139-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
<a id="__codelineno-139-9" name="__codelineno-139-9" href="#__codelineno-139-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-139-10" name="__codelineno-139-10" href="#__codelineno-139-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
<a id="__codelineno-139-11" name="__codelineno-139-11" href="#__codelineno-139-11"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>