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@ -2614,8 +2614,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="sd">""" 常数阶 """</span>
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<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="k">def</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</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-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">""" 常数阶 """</span>
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<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
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<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
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@ -2724,8 +2724,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="sd">""" 线性阶 """</span>
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<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="k">def</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</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-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w"> </span><span class="sd">""" 线性阶 """</span>
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<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
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@ -2833,8 +2833,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="sd">""" 线性阶（遍历数组）"""</span>
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<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="k">def</span> <span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</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-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="k">def</span> <span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
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<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="w"> </span><span class="sd">""" 线性阶（遍历数组）"""</span>
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<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a> <span class="c1"># 循环次数与数组长度成正比</span>
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<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
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@ -2955,8 +2955,8 @@ O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="sd">""" 平方阶 """</span>
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<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="k">def</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</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-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">def</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">""" 平方阶 """</span>
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<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a> <span class="c1"># 循环次数与数组长度成平方关系</span>
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<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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@ -3112,8 +3112,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="sd">""" 平方阶（冒泡排序）"""</span>
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<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</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-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
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<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="w"> </span><span class="sd">""" 平方阶（冒泡排序）"""</span>
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<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 计数器</span>
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<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a> <span class="c1"># 外循环：待排序元素数量为 n-1, n-2, ..., 1</span>
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<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
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@ -3307,8 +3307,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="sd">""" 指数阶（循环实现）"""</span>
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<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="k">def</span> <span class="nf">exponential</span><span class="p">(</span><span class="n">n</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-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="k">def</span> <span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="w"> </span><span class="sd">""" 指数阶（循环实现）"""</span>
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<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a> <span class="n">count</span><span class="p">,</span> <span class="n">base</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span>
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<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a> <span class="c1"># cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
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<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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@ -3453,8 +3453,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="sd">""" 指数阶（递归实现）"""</span>
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<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="k">def</span> <span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</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-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="k">def</span> <span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="w"> </span><span class="sd">""" 指数阶（递归实现）"""</span>
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<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="mi">1</span>
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<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a> <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
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</code></pre></div>
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@ -3549,8 +3549,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="sd">""" 对数阶（循环实现）"""</span>
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<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="k">def</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</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-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="k">def</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
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<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="w"> </span><span class="sd">""" 对数阶（循环实现）"""</span>
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<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
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<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></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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<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a> <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
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@ -3664,8 +3664,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="sd">""" 对数阶（递归实现）"""</span>
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<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></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>
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></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>
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<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="w"> </span><span class="sd">""" 对数阶（递归实现）"""</span>
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<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="mi">0</span>
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<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></a> <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
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</code></pre></div>
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@ -3761,8 +3761,8 @@ O((n - 1) \frac{n}{2}) = O(n^2)
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</code></pre></div>
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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.py</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="sd">""" 线性对数阶 """</span>
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<a id="__codelineno-132-2" name="__codelineno-132-2" href="#__codelineno-132-2"></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>
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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">linear_log_recur</span><span class="p">(</span><span class="n">n</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">""" 线性对数阶 """</span>
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<a id="__codelineno-132-3" name="__codelineno-132-3" href="#__codelineno-132-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span> <span class="k">return</span> <span class="mi">1</span>
|
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<a id="__codelineno-132-4" name="__codelineno-132-4" href="#__codelineno-132-4"></a> <span class="n">count</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
|
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<a id="__codelineno-132-5" name="__codelineno-132-5" href="#__codelineno-132-5"></a> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
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@ -3897,8 +3897,8 @@ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="sd">""" 阶乘阶（递归实现）"""</span>
|
||||
<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="k">def</span> <span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="k">def</span> <span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="w"> </span><span class="sd">""" 阶乘阶（递归实现）"""</span>
|
||||
<a id="__codelineno-142-3" name="__codelineno-142-3" href="#__codelineno-142-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="k">return</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-142-4" name="__codelineno-142-4" href="#__codelineno-142-4"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<a id="__codelineno-142-5" name="__codelineno-142-5" href="#__codelineno-142-5"></a> <span class="c1"># 从 1 个分裂出 n 个</span>
|
||||
@ -4068,16 +4068,16 @@ n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="sd">""" 生成一个数组，元素为: 1, 2, ..., n ，顺序被打乱 """</span>
|
||||
<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="k">def</span> <span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="k">def</span> <span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="w"> </span><span class="sd">""" 生成一个数组，元素为: 1, 2, ..., n ，顺序被打乱 """</span>
|
||||
<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a> <span class="c1"># 生成数组 nums =: 1, 2, 3, ..., n</span>
|
||||
<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
|
||||
<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a> <span class="c1"># 随机打乱数组元素</span>
|
||||
<a id="__codelineno-152-6" name="__codelineno-152-6" href="#__codelineno-152-6"></a> <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
|
||||
<a id="__codelineno-152-7" name="__codelineno-152-7" href="#__codelineno-152-7"></a> <span class="k">return</span> <span class="n">nums</span>
|
||||
<a id="__codelineno-152-8" name="__codelineno-152-8" href="#__codelineno-152-8"></a>
|
||||
<a id="__codelineno-152-9" name="__codelineno-152-9" href="#__codelineno-152-9"></a><span class="sd">""" 查找数组 nums 中数字 1 所在索引 """</span>
|
||||
<a id="__codelineno-152-10" name="__codelineno-152-10" href="#__codelineno-152-10"></a><span class="k">def</span> <span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
|
||||
<a id="__codelineno-152-9" name="__codelineno-152-9" href="#__codelineno-152-9"></a><span class="k">def</span> <span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
|
||||
<a id="__codelineno-152-10" name="__codelineno-152-10" href="#__codelineno-152-10"></a><span class="w"> </span><span class="sd">""" 查找数组 nums 中数字 1 所在索引 """</span>
|
||||
<a id="__codelineno-152-11" name="__codelineno-152-11" href="#__codelineno-152-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
|
||||
<a id="__codelineno-152-12" name="__codelineno-152-12" href="#__codelineno-152-12"></a> <span class="c1"># 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||||
<a id="__codelineno-152-13" name="__codelineno-152-13" href="#__codelineno-152-13"></a> <span class="c1"># 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||||
|
||||
Reference in New Issue
Block a user