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GeezerVison is showing github.com — python-doc-tw.github.io/library/bisect.html at master · python-doc-tw/python-doc-tw.github.io Expand file tree/ Copy pathbisect.htmlMore file actions 300 lines (271 loc) · 25.4 KB / Copy pathbisect.htmlFile metadata and controls300 lines (271 loc) · 25.4 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" lang="zh_TW"> <head> <meta http-equiv="X-UA-Compatible" content="IE=Edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>8.6. bisect — 陣列二分演算法 (Array bisection algorithm) — Python 3.7.0 說明文件</title> <link rel="stylesheet" href="../_static/pydoctheme.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/translations.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="在 Python 3.7.0 說明文件 中搜尋" href="../_static/opensearch.xml"/> <link rel="author" title="關於這些文件" href="../about.html" /> <link rel="index" title="索引" href="../genindex.html" /> <link rel="search" title="搜尋" href="../search.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="next" title="8.7. array — 高效率的數值型態陣列" href="array.html" /> <link rel="prev" title="8.5. heapq — 堆積佇列 (heap queue) 演算法" href="heapq.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="https://docs.python.org/3/library/bisect.html" /> <script type="text/javascript" src="../_static/copybutton.js"></script> <script type="text/javascript" src="../_static/switchers.js"></script> </head><body> <div class="related" role="navigation" aria-label="related navigation"> <h3>瀏覽</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">索引</a></li> <li class="right" > <a href="../py-modindex.html" title="Python 模組索引" >模組</a> |</li> <li class="right" > <a href="array.html" title="8.7. array — 高效率的數值型態陣列" accesskey="N">下一頁</a> |</li> <li class="right" > <a href="heapq.html" title="8.5. heapq — 堆積佇列 (heap queue) 演算法" accesskey="P">上一頁</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <span class="language_switcher_placeholder">zh_TW</span> <span class="version_switcher_placeholder">3.7.0</span> <a href="../index.html">Documentation </a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >Python 標準函式庫 (Standard Library)</a> »</li> <li class="nav-item nav-item-2"><a href="datatypes.html" accesskey="U">8. Data Types</a> »</li> <li class="right"> <div class="inline-search" style="display: none" role="search"> <form class="inline-search" action="../search.html" method="get"> <input placeholder="Quick search" type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </div> <script type="text/javascript">$('.inline-search').show(0);</script> | </li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="module-bisect"> <span id="bisect-array-bisection-algorithm"></span><h1>8.6. <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> — 陣列二分演算法 (Array bisection algorithm)<a class="headerlink" href="#module-bisect" title="本標題的永久連結">¶</a></h1> <p><strong>原始碼:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.7/Lib/bisect.py">Lib/bisect.py</a></p> <hr class="docutils" /> <p>這個模組維護一個已經排序過的 list ,當我們每次做完插入後不需要再次排序整個 list 。一個很長的 list 的比較操作很花費時間,為了改進這點,這個模組是其中一個常用的方法。這個模組被命名為 <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> 來自他使用一個基礎的 bisection 演算法實作。模組的原始碼是這個演算法的一個完善的實作(邊界條件已經是正確的了)。</p> <p>此模組提供下面的函式</p> <dl class="function"> <dt id="bisect.bisect_left"> <code class="descclassname">bisect.</code><code class="descname">bisect_left</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_left" title="本定義的永久連結">¶</a></dt> <dd><p>在 <em>a</em> 當中找到一個位置,讓 <em>x</em> 插入後 <em>a</em> 仍然是排序好的。參數 <em>lo</em> 和 <em>hi</em> 用來指定 list 中應該被考慮的子區間,預設是考慮整個 list 。如果 <em>a</em> 裡面已經有 <em>x</em> 出現,插入的位置會在所有 <em>x</em> 的前面(左邊)。回傳值可以被當作 <code class="docutils literal notranslate"><span class="pre">list.insert()</span></code> 的第一個參數,但列表 <em>a</em> 必須先排序過。</p> <p>回傳的插入位置 <em>i</em> 將陣列 <em>a</em> 分為兩半,使得 <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre"><</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> 都在左側且 <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">>=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> 都在右側。</p> </dd></dl> <dl class="function"> <dt id="bisect.bisect_right"> <code class="descclassname">bisect.</code><code class="descname">bisect_right</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_right" title="本定義的永久連結">¶</a></dt> <dt id="bisect.bisect"> <code class="descclassname">bisect.</code><code class="descname">bisect</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect" title="本定義的永久連結">¶</a></dt> <dd><p>類似 <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect_left()</span></code></a> ,但回傳的插入位置會在所有 <em>a</em> 當中的 <em>x</em> 的後面(右邊)。</p> <p>回傳的插入位置 <em>i</em> 將陣列 <em>a</em> 分為兩半,使得 <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre"><=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> 都在左側且 <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">></span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> 都在右側。</p> </dd></dl> <dl class="function"> <dt id="bisect.insort_left"> <code class="descclassname">bisect.</code><code class="descname">insort_left</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_left" title="本定義的永久連結">¶</a></dt> <dd><p>不破壞 <em>a</em> 的排序下插入 <em>x</em> ,這等價於 <code class="docutils literal notranslate"><span class="pre">a.insert(bisect.bisect_left(a,</span> <span class="pre">x,</span> <span class="pre">lo,</span> <span class="pre">hi),</span> <span class="pre">x)</span></code> ,注意 <em>a</em> 必須是已經排序過的 list 。注意搜尋只需要 O(log n) 時間而插入需要很慢的 O(n) 時間,這使得插入操作主導了需要的花費時間。</p> </dd></dl> <dl class="function"> <dt id="bisect.insort_right"> <code class="descclassname">bisect.</code><code class="descname">insort_right</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_right" title="本定義的永久連結">¶</a></dt> <dt id="bisect.insort"> <code class="descclassname">bisect.</code><code class="descname">insort</code><span class="sig-paren">(</span><em>a</em>, <em>x</em>, <em>lo=0</em>, <em>hi=len(a)</em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort" title="本定義的永久連結">¶</a></dt> <dd><p>類似 <a class="reference internal" href="#bisect.insort_left" title="bisect.insort_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">insort_left()</span></code></a> ,但插入的位置會在所有 <em>a</em> 當中的 <em>x</em> 的後面(右邊)。</p> </dd></dl> <div class="admonition seealso"> <p class="first admonition-title">也參考</p> <p class="last"><a class="reference external" href="https://code.activestate.com/recipes/577197-sortedcollection/">SortedCollection recipe</a> that uses bisect to build a full-featured collection class with straight-forward search methods and support for a key-function. The keys are precomputed to save unnecessary calls to the key function during searches.</p> </div> <div class="section" id="searching-sorted-lists"> <h2>8.6.1. Searching Sorted Lists<a class="headerlink" href="#searching-sorted-lists" title="本標題的永久連結">¶</a></h2> <p>The above <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions are useful for finding insertion points but can be tricky or awkward to use for common searching tasks. The following five functions show how to transform them into the standard lookups for sorted lists:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">index</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Locate the leftmost value exactly equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="ow">and</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">x</span><span class="p">:</span> <span class="k">return</span> <span class="n">i</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_lt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find rightmost value less than x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_le</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find rightmost value less than or equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_gt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find leftmost value greater than x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_ge</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find leftmost item greater than or equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> </pre></div> </div> </div> <div class="section" id="other-examples"> <h2>8.6.2. Other Examples<a class="headerlink" href="#other-examples" title="本標題的永久連結">¶</a></h2> <p id="bisect-example">The <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> function can be useful for numeric table lookups. This example uses <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> to look up a letter grade for an exam score (say) based on a set of ordered numeric breakpoints: 90 and up is an 『A』, 80 to 89 is a 『B』, and so on:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span> <span class="nf">grade</span><span class="p">(</span><span class="n">score</span><span class="p">,</span> <span class="n">breakpoints</span><span class="o">=</span><span class="p">[</span><span class="mi">60</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">80</span><span class="p">,</span> <span class="mi">90</span><span class="p">],</span> <span class="n">grades</span><span class="o">=</span><span class="s1">'FDCBA'</span><span class="p">):</span> <span class="gp">... </span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect</span><span class="p">(</span><span class="n">breakpoints</span><span class="p">,</span> <span class="n">score</span><span class="p">)</span> <span class="gp">... </span> <span class="k">return</span> <span class="n">grades</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="gp">...</span> <span class="gp">>>> </span><span class="p">[</span><span class="n">grade</span><span class="p">(</span><span class="n">score</span><span class="p">)</span> <span class="k">for</span> <span class="n">score</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">33</span><span class="p">,</span> <span class="mi">99</span><span class="p">,</span> <span class="mi">77</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">89</span><span class="p">,</span> <span class="mi">90</span><span class="p">,</span> <span class="mi">100</span><span class="p">]]</span> <span class="go">['F', 'A', 'C', 'C', 'B', 'A', 'A']</span> </pre></div> </div> <p>Unlike the <a class="reference internal" href="functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate"><span class="pre">sorted()</span></code></a> function, it does not make sense for the <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions to have <em>key</em> or <em>reversed</em> arguments because that would lead to an inefficient design (successive calls to bisect functions would not 「remember」 all of the previous key lookups).</p> <p>Instead, it is better to search a list of precomputed keys to find the index of the record in question:</p> <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">'red'</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="s1">'blue'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'yellow'</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span> <span class="p">(</span><span class="s1">'black'</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="gp">>>> </span><span class="n">data</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="gp">>>> </span><span class="n">keys</span> <span class="o">=</span> <span class="p">[</span><span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">data</span><span class="p">]</span> <span class="c1"># precomputed list of keys</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="go">('black', 0)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="go">('blue', 1)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">5</span><span class="p">)]</span> <span class="go">('red', 5)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">8</span><span class="p">)]</span> <span class="go">('yellow', 8)</span> </pre></div> </div> </div> </div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <h3><a href="../contents.html">目錄</a></h3> <ul> <li><a class="reference internal" href="#">8.6. <code class="docutils literal notranslate"><span class="pre">bisect</span></code> — 陣列二分演算法 (Array bisection algorithm)</a><ul> <li><a class="reference internal" href="#searching-sorted-lists">8.6.1. Searching Sorted Lists</a></li> <li><a class="reference internal" href="#other-examples">8.6.2. Other Examples</a></li> </ul> </li> </ul> <h4>上個主題</h4> <p class="topless"><a href="heapq.html" title="上一章">8.5. <code class="docutils literal notranslate"><span class="pre">heapq</span></code> — 堆積佇列 (heap queue) 演算法</a></p> <h4>下個主題</h4> <p class="topless"><a href="array.html" title="下一章">8.7. <code class="docutils literal notranslate"><span class="pre">array</span></code> — 高效率的數值型態陣列</a></p> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../bugs.html">Report a Bug</a></li> <li> <a href="https://github.com/python/cpython/blob/3.7/Doc/library/bisect.rst" rel="nofollow">Show Source </a> </li> </ul> </div> </div> </div> <div class="clearer"></div> </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>瀏覽</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >索引</a></li> <li class="right" > <a href="../py-modindex.html" title="Python 模組索引" >模組</a> |</li> <li class="right" > <a href="array.html" title="8.7. array — 高效率的數值型態陣列" >下一頁</a> |</li> <li class="right" > <a href="heapq.html" title="8.5. heapq — 堆積佇列 (heap queue) 演算法" >上一頁</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <span class="language_switcher_placeholder">zh_TW</span> <span class="version_switcher_placeholder">3.7.0</span> <a href="../index.html">Documentation </a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >Python 標準函式庫 (Standard Library)</a> »</li> <li class="nav-item nav-item-2"><a href="datatypes.html" >8. 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