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@ -5914,7 +5914,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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<div class="tabbed-set tabbed-alternate" data-tabs="12:12"><input checked="checked" id="__tabbed_12_1" name="__tabbed_12" type="radio" /><input id="__tabbed_12_2" name="__tabbed_12" type="radio" /><input id="__tabbed_12_3" name="__tabbed_12" type="radio" /><input id="__tabbed_12_4" name="__tabbed_12" type="radio" /><input id="__tabbed_12_5" name="__tabbed_12" type="radio" /><input id="__tabbed_12_6" name="__tabbed_12" type="radio" /><input id="__tabbed_12_7" name="__tabbed_12" type="radio" /><input id="__tabbed_12_8" name="__tabbed_12" type="radio" /><input id="__tabbed_12_9" name="__tabbed_12" type="radio" /><input id="__tabbed_12_10" name="__tabbed_12" type="radio" /><input id="__tabbed_12_11" name="__tabbed_12" type="radio" /><input id="__tabbed_12_12" name="__tabbed_12" type="radio" /><div class="tabbed-labels"><label for="__tabbed_12_1">Python</label><label for="__tabbed_12_2">C++</label><label for="__tabbed_12_3">Java</label><label for="__tabbed_12_4">C#</label><label for="__tabbed_12_5">Go</label><label for="__tabbed_12_6">Swift</label><label for="__tabbed_12_7">JS</label><label for="__tabbed_12_8">TS</label><label for="__tabbed_12_9">Dart</label><label for="__tabbed_12_10">Rust</label><label for="__tabbed_12_11">C</label><label for="__tabbed_12_12">Zig</label></div>
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<div class="tabbed-content">
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="k">def</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="k">def</span> <span class="nf">logarithmic</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">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-132-2" name="__codelineno-132-2" href="#__codelineno-132-2"></a><span class="w"> </span><span class="sd">"""对数阶(循环实现)"""</span>
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<a id="__codelineno-132-3" name="__codelineno-132-3" href="#__codelineno-132-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-132-4" name="__codelineno-132-4" href="#__codelineno-132-4"></a> <span class="k">while</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
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@ -5925,7 +5925,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</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>
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<a id="__codelineno-133-3" name="__codelineno-133-3" href="#__codelineno-133-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
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<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></a><span class="w"> </span><span class="k">while</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="p">{</span>
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<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></a><span class="w"> </span><span class="n">n</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>
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@ -5937,7 +5937,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-134-2" name="__codelineno-134-2" href="#__codelineno-134-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-134-2" name="__codelineno-134-2" href="#__codelineno-134-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</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>
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<a id="__codelineno-134-3" name="__codelineno-134-3" href="#__codelineno-134-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
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<a id="__codelineno-134-4" name="__codelineno-134-4" href="#__codelineno-134-4"></a><span class="w"> </span><span class="k">while</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="p">{</span>
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<a id="__codelineno-134-5" name="__codelineno-134-5" href="#__codelineno-134-5"></a><span class="w"> </span><span class="n">n</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>
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@ -5949,7 +5949,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-135-2" name="__codelineno-135-2" href="#__codelineno-135-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-135-2" name="__codelineno-135-2" href="#__codelineno-135-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Logarithmic</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>
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<a id="__codelineno-135-3" name="__codelineno-135-3" href="#__codelineno-135-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
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<a id="__codelineno-135-4" name="__codelineno-135-4" href="#__codelineno-135-4"></a><span class="w"> </span><span class="k">while</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="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-135-5" name="__codelineno-135-5" href="#__codelineno-135-5"></a><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>
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@ -5961,7 +5961,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="cm">/* 对数阶(循环实现)*/</span>
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<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logarithmic</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>
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<a id="__codelineno-136-3" name="__codelineno-136-3" href="#__codelineno-136-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
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<a id="__codelineno-136-4" name="__codelineno-136-4" href="#__codelineno-136-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-136-5" name="__codelineno-136-5" href="#__codelineno-136-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">=</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>
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@ -5973,7 +5973,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kd">func</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kd">func</span> <span class="nf">logarithmic</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">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-137-3" name="__codelineno-137-3" href="#__codelineno-137-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
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<a id="__codelineno-137-4" name="__codelineno-137-4" href="#__codelineno-137-4"></a> <span class="kd">var</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">n</span>
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<a id="__codelineno-137-5" name="__codelineno-137-5" href="#__codelineno-137-5"></a> <span class="k">while</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span> <span class="p">{</span>
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@ -6010,10 +6010,10 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="kt">num</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logarithmic</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>
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<a id="__codelineno-140-3" name="__codelineno-140-3" href="#__codelineno-140-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
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<a id="__codelineno-140-4" name="__codelineno-140-4" href="#__codelineno-140-4"></a><span class="w"> </span><span class="k">while</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="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w"> </span><span class="n">n</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>
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<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w"> </span><span class="n">n</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>
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<a id="__codelineno-140-6" name="__codelineno-140-6" href="#__codelineno-140-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
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<a id="__codelineno-140-7" name="__codelineno-140-7" href="#__codelineno-140-7"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-140-8" name="__codelineno-140-8" href="#__codelineno-140-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
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@ -6022,10 +6022,10 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
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<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="k">fn</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
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||||
<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="k">fn</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">n</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-141-3" name="__codelineno-141-3" href="#__codelineno-141-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</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-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w"> </span><span class="n">n</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="mf">2.0</span><span class="p">;</span>
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||||
<a id="__codelineno-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w"> </span><span class="k">while</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="p">{</span>
|
||||
<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w"> </span><span class="n">n</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>
|
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<a id="__codelineno-141-6" name="__codelineno-141-6" href="#__codelineno-141-6"></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-141-7" name="__codelineno-141-7" href="#__codelineno-141-7"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-141-8" name="__codelineno-141-8" href="#__codelineno-141-8"></a><span class="w"> </span><span class="n">count</span>
|
||||
@ -6034,7 +6034,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="cm">/* 对数阶(循环实现) */</span>
|
||||
<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</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-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</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-142-3" name="__codelineno-142-3" href="#__codelineno-142-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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-142-4" name="__codelineno-142-4" href="#__codelineno-142-4"></a><span class="w"> </span><span class="k">while</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="p">{</span>
|
||||
<a id="__codelineno-142-5" name="__codelineno-142-5" href="#__codelineno-142-5"></a><span class="w"> </span><span class="n">n</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>
|
||||
@ -6046,7 +6046,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="c1">// 对数阶(循环实现)</span>
|
||||
<a id="__codelineno-143-2" name="__codelineno-143-2" href="#__codelineno-143-2"></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-143-2" name="__codelineno-143-2" href="#__codelineno-143-2"></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">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-143-3" name="__codelineno-143-3" href="#__codelineno-143-3"></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-143-4" name="__codelineno-143-4" href="#__codelineno-143-4"></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-143-5" name="__codelineno-143-5" href="#__codelineno-143-5"></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">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||||
@ -6062,8 +6062,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<details class="pythontutor">
|
||||
<summary>可视化运行</summary>
|
||||
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20/%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20/%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||||
<p><div style="height: 459px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20/%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20logarithmic%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20count%20%3D%200%0A%20%20%20%20while%20n%20%3E%201%3A%0A%20%20%20%20%20%20%20%20n%20%3D%20n%20/%202%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20logarithmic%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E5%BE%AA%E7%8E%AF%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||||
</details>
|
||||
<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="对数阶的时间复杂度" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic.png" /></a></p>
|
||||
<p align="center"> 图 2-12 对数阶的时间复杂度 </p>
|
||||
@ -6072,7 +6072,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="13:12"><input checked="checked" id="__tabbed_13_1" name="__tabbed_13" type="radio" /><input id="__tabbed_13_2" name="__tabbed_13" type="radio" /><input id="__tabbed_13_3" name="__tabbed_13" type="radio" /><input id="__tabbed_13_4" name="__tabbed_13" type="radio" /><input id="__tabbed_13_5" name="__tabbed_13" type="radio" /><input id="__tabbed_13_6" name="__tabbed_13" type="radio" /><input id="__tabbed_13_7" name="__tabbed_13" type="radio" /><input id="__tabbed_13_8" name="__tabbed_13" type="radio" /><input id="__tabbed_13_9" name="__tabbed_13" type="radio" /><input id="__tabbed_13_10" name="__tabbed_13" type="radio" /><input id="__tabbed_13_11" name="__tabbed_13" type="radio" /><input id="__tabbed_13_12" name="__tabbed_13" type="radio" /><div class="tabbed-labels"><label for="__tabbed_13_1">Python</label><label for="__tabbed_13_2">C++</label><label for="__tabbed_13_3">Java</label><label for="__tabbed_13_4">C#</label><label for="__tabbed_13_5">Go</label><label for="__tabbed_13_6">Swift</label><label for="__tabbed_13_7">JS</label><label for="__tabbed_13_8">TS</label><label for="__tabbed_13_9">Dart</label><label for="__tabbed_13_10">Rust</label><label for="__tabbed_13_11">C</label><label for="__tabbed_13_12">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="k">def</span> <span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="k">def</span> <span class="nf">log_recur</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">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-144-2" name="__codelineno-144-2" href="#__codelineno-144-2"></a><span class="w"> </span><span class="sd">"""对数阶(递归实现)"""</span>
|
||||
<a id="__codelineno-144-3" name="__codelineno-144-3" href="#__codelineno-144-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<a id="__codelineno-144-4" name="__codelineno-144-4" href="#__codelineno-144-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||||
@ -6081,7 +6081,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-145-2" name="__codelineno-145-2" href="#__codelineno-145-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</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-145-2" name="__codelineno-145-2" href="#__codelineno-145-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</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-145-3" name="__codelineno-145-3" href="#__codelineno-145-3"></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>
|
||||
<a id="__codelineno-145-4" name="__codelineno-145-4" href="#__codelineno-145-4"></a><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-145-5" name="__codelineno-145-5" href="#__codelineno-145-5"></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>
|
||||
@ -6090,7 +6090,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-146-2" name="__codelineno-146-2" href="#__codelineno-146-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</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-146-2" name="__codelineno-146-2" href="#__codelineno-146-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</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-146-3" name="__codelineno-146-3" href="#__codelineno-146-3"></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>
|
||||
<a id="__codelineno-146-4" name="__codelineno-146-4" href="#__codelineno-146-4"></a><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-146-5" name="__codelineno-146-5" href="#__codelineno-146-5"></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>
|
||||
@ -6099,7 +6099,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-147-2" name="__codelineno-147-2" href="#__codelineno-147-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LogRecur</span><span class="p">(</span><span class="kt">float</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-147-2" name="__codelineno-147-2" href="#__codelineno-147-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LogRecur</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-147-3" name="__codelineno-147-3" href="#__codelineno-147-3"></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="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-147-4" name="__codelineno-147-4" href="#__codelineno-147-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">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="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-147-5" name="__codelineno-147-5" href="#__codelineno-147-5"></a><span class="p">}</span>
|
||||
@ -6107,7 +6107,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="cm">/* 对数阶(递归实现)*/</span>
|
||||
<a id="__codelineno-148-2" name="__codelineno-148-2" href="#__codelineno-148-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</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-148-2" name="__codelineno-148-2" href="#__codelineno-148-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logRecur</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-148-3" name="__codelineno-148-3" href="#__codelineno-148-3"></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="p">{</span>
|
||||
<a id="__codelineno-148-4" name="__codelineno-148-4" href="#__codelineno-148-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||||
<a id="__codelineno-148-5" name="__codelineno-148-5" href="#__codelineno-148-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
@ -6117,7 +6117,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-149-2" name="__codelineno-149-2" href="#__codelineno-149-2"></a><span class="kd">func</span> <span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-149-2" name="__codelineno-149-2" href="#__codelineno-149-2"></a><span class="kd">func</span> <span class="nf">logRecur</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">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-149-3" name="__codelineno-149-3" href="#__codelineno-149-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span> <span class="p">{</span>
|
||||
<a id="__codelineno-149-4" name="__codelineno-149-4" href="#__codelineno-149-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-149-5" name="__codelineno-149-5" href="#__codelineno-149-5"></a> <span class="p">}</span>
|
||||
@ -6143,25 +6143,25 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="kt">num</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-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logRecur</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-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></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="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></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="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></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="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="k">fn</span> <span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></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="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="k">fn</span> <span class="nf">log_recur</span><span class="p">(</span><span class="n">n</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-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></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="p">{</span>
|
||||
<a id="__codelineno-153-4" name="__codelineno-153-4" href="#__codelineno-153-4"></a><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-153-5" name="__codelineno-153-5" href="#__codelineno-153-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="w"> </span><span class="n">log_recur</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>
|
||||
<a id="__codelineno-153-7" name="__codelineno-153-7" href="#__codelineno-153-7"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="cm">/* 对数阶(递归实现) */</span>
|
||||
<a id="__codelineno-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</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-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</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-154-3" name="__codelineno-154-3" href="#__codelineno-154-3"></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>
|
||||
<a id="__codelineno-154-4" name="__codelineno-154-4" href="#__codelineno-154-4"></a><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-154-5" name="__codelineno-154-5" href="#__codelineno-154-5"></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>
|
||||
@ -6170,7 +6170,7 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="c1">// 对数阶(递归实现)</span>
|
||||
<a id="__codelineno-155-2" name="__codelineno-155-2" href="#__codelineno-155-2"></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-155-2" name="__codelineno-155-2" href="#__codelineno-155-2"></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">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-155-3" name="__codelineno-155-3" href="#__codelineno-155-3"></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">0</span><span class="p">;</span>
|
||||
<a id="__codelineno-155-4" name="__codelineno-155-4" href="#__codelineno-155-4"></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-155-5" name="__codelineno-155-5" href="#__codelineno-155-5"></a><span class="p">}</span>
|
||||
@ -6180,8 +6180,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
|
||||
</div>
|
||||
<details class="pythontutor">
|
||||
<summary>可视化运行</summary>
|
||||
<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20/%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20/%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||||
<p><div style="height: 423px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20/%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20return%20log_recur%28n%20/%202%29%20%2B%201%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20log_recur%28n%29%0A%20%20%20%20print%28%22%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||||
</details>
|
||||
<p>对数阶常出现于基于分治策略的算法中,体现了“一分为多”和“化繁为简”的算法思想。它增长缓慢,是仅次于常数阶的理想的时间复杂度。</p>
|
||||
<div class="admonition tip">
|
||||
@ -6197,7 +6197,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="14:12"><input checked="checked" id="__tabbed_14_1" name="__tabbed_14" type="radio" /><input id="__tabbed_14_2" name="__tabbed_14" type="radio" /><input id="__tabbed_14_3" name="__tabbed_14" type="radio" /><input id="__tabbed_14_4" name="__tabbed_14" type="radio" /><input id="__tabbed_14_5" name="__tabbed_14" type="radio" /><input id="__tabbed_14_6" name="__tabbed_14" type="radio" /><input id="__tabbed_14_7" name="__tabbed_14" type="radio" /><input id="__tabbed_14_8" name="__tabbed_14" type="radio" /><input id="__tabbed_14_9" name="__tabbed_14" type="radio" /><input id="__tabbed_14_10" name="__tabbed_14" type="radio" /><input id="__tabbed_14_11" name="__tabbed_14" type="radio" /><input id="__tabbed_14_12" name="__tabbed_14" type="radio" /><div class="tabbed-labels"><label for="__tabbed_14_1">Python</label><label for="__tabbed_14_2">C++</label><label for="__tabbed_14_3">Java</label><label for="__tabbed_14_4">C#</label><label for="__tabbed_14_5">Go</label><label for="__tabbed_14_6">Swift</label><label for="__tabbed_14_7">JS</label><label for="__tabbed_14_8">TS</label><label for="__tabbed_14_9">Dart</label><label for="__tabbed_14_10">Rust</label><label for="__tabbed_14_11">C</label><label for="__tabbed_14_12">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="k">def</span> <span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="k">def</span> <span class="nf">linear_log_recur</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">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||
<a id="__codelineno-156-2" name="__codelineno-156-2" href="#__codelineno-156-2"></a><span class="w"> </span><span class="sd">"""线性对数阶"""</span>
|
||||
<a id="__codelineno-156-3" name="__codelineno-156-3" href="#__codelineno-156-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<a id="__codelineno-156-4" name="__codelineno-156-4" href="#__codelineno-156-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||||
@ -6209,7 +6209,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-157-2" name="__codelineno-157-2" href="#__codelineno-157-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</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-157-2" name="__codelineno-157-2" href="#__codelineno-157-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</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-157-3" name="__codelineno-157-3" href="#__codelineno-157-3"></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>
|
||||
<a id="__codelineno-157-4" name="__codelineno-157-4" href="#__codelineno-157-4"></a><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-157-5" name="__codelineno-157-5" href="#__codelineno-157-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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><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>
|
||||
@ -6222,7 +6222,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-158-2" name="__codelineno-158-2" href="#__codelineno-158-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</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-158-2" name="__codelineno-158-2" href="#__codelineno-158-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</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-158-3" name="__codelineno-158-3" href="#__codelineno-158-3"></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>
|
||||
<a id="__codelineno-158-4" name="__codelineno-158-4" href="#__codelineno-158-4"></a><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-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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><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>
|
||||
@ -6235,7 +6235,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-159-2" name="__codelineno-159-2" href="#__codelineno-159-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LinearLogRecur</span><span class="p">(</span><span class="kt">float</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-159-2" name="__codelineno-159-2" href="#__codelineno-159-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">LinearLogRecur</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-159-3" name="__codelineno-159-3" href="#__codelineno-159-3"></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="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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="m">2</span><span class="p">)</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="m">2</span><span class="p">);</span>
|
||||
<a id="__codelineno-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></a><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"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
@ -6247,12 +6247,12 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-160-2" name="__codelineno-160-2" href="#__codelineno-160-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</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-160-2" name="__codelineno-160-2" href="#__codelineno-160-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linearLogRecur</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-160-3" name="__codelineno-160-3" href="#__codelineno-160-3"></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="p">{</span>
|
||||
<a id="__codelineno-160-4" name="__codelineno-160-4" href="#__codelineno-160-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-160-5" name="__codelineno-160-5" href="#__codelineno-160-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
||||
<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><span class="w"> </span><span class="k">for</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">0.0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-160-8" name="__codelineno-160-8" href="#__codelineno-160-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||||
<a id="__codelineno-160-9" name="__codelineno-160-9" href="#__codelineno-160-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-160-10" name="__codelineno-160-10" href="#__codelineno-160-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||||
@ -6261,7 +6261,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-161-2" name="__codelineno-161-2" href="#__codelineno-161-2"></a><span class="kd">func</span> <span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-161-2" name="__codelineno-161-2" href="#__codelineno-161-2"></a><span class="kd">func</span> <span class="nf">linearLogRecur</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">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-161-3" name="__codelineno-161-3" href="#__codelineno-161-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span> <span class="p">{</span>
|
||||
<a id="__codelineno-161-4" name="__codelineno-161-4" href="#__codelineno-161-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-161-5" name="__codelineno-161-5" href="#__codelineno-161-5"></a> <span class="p">}</span>
|
||||
@ -6299,9 +6299,9 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="kt">num</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-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linearLogRecur</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-164-3" name="__codelineno-164-3" href="#__codelineno-164-3"></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="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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="m">2</span><span class="p">)</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="m">2</span><span class="p">);</span>
|
||||
<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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="m">2</span><span class="p">)</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="m">2</span><span class="p">);</span>
|
||||
<a id="__codelineno-164-5" name="__codelineno-164-5" href="#__codelineno-164-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</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"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-164-6" name="__codelineno-164-6" href="#__codelineno-164-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||||
<a id="__codelineno-164-7" name="__codelineno-164-7" href="#__codelineno-164-7"></a><span class="w"> </span><span class="p">}</span>
|
||||
@ -6311,11 +6311,11 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="k">fn</span> <span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||||
<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></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="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="k">fn</span> <span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</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-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></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="p">{</span>
|
||||
<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a><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-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">);</span>
|
||||
<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</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="n">linear_log_recur</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-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</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="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-165-8" name="__codelineno-165-8" href="#__codelineno-165-8"></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-165-9" name="__codelineno-165-9" href="#__codelineno-165-9"></a><span class="w"> </span><span class="p">}</span>
|
||||
@ -6325,7 +6325,7 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||||
<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</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-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</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-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></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>
|
||||
<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><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-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</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><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>
|
||||
@ -6338,10 +6338,10 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="c1">// 线性对数阶</span>
|
||||
<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></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-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></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">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-167-3" name="__codelineno-167-3" href="#__codelineno-167-3"></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-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></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><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-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></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">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-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></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>
|
||||
<a id="__codelineno-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></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"><</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-167-7" name="__codelineno-167-7" href="#__codelineno-167-7"></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-167-8" name="__codelineno-167-8" href="#__codelineno-167-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
@ -6353,8 +6353,8 @@ O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||||
</div>
|
||||
<details class="pythontutor">
|
||||
<summary>可视化运行</summary>
|
||||
<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20//%202%29%20%2B%20linear_log_recur%28n%20//%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20float%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20//%202%29%20%2B%20linear_log_recur%28n%20//%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
|
||||
<p><div style="height: 477px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20//%202%29%20%2B%20linear_log_recur%28n%20//%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
|
||||
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20linear_log_recur%28n%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%22%22%22%0A%20%20%20%20if%20n%20%3C%3D%201%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%20//%202%29%20%2B%20linear_log_recur%28n%20//%202%29%0A%20%20%20%20for%20_%20in%20range%28n%29%3A%0A%20%20%20%20%20%20%20%20count%20%2B%3D%201%0A%20%20%20%20return%20count%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20n%20%3D%208%0A%20%20%20%20print%28%22%E8%BE%93%E5%85%A5%E6%95%B0%E6%8D%AE%E5%A4%A7%E5%B0%8F%20n%20%3D%22,%20n%29%0A%0A%20%20%20%20count%20%3D%20linear_log_recur%28n%29%0A%20%20%20%20print%28%22%E7%BA%BF%E6%80%A7%E5%AF%B9%E6%95%B0%E9%98%B6%EF%BC%88%E9%80%92%E5%BD%92%E5%AE%9E%E7%8E%B0%EF%BC%89%E7%9A%84%E6%93%8D%E4%BD%9C%E6%95%B0%E9%87%8F%20%3D%22,%20count%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=4&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 ></a></div></p>
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</details>
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<p>图 2-13 展示了线性对数阶的生成方式。二叉树的每一层的操作总数都为 <span class="arithmatex">\(n\)</span> ,树共有 <span class="arithmatex">\(\log_2 n + 1\)</span> 层,因此时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。</p>
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<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic_linear.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="线性对数阶的时间复杂度" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></a></p>
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||||
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Reference in New Issue
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