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add doc: Binary search algorithms
2013-08-22 15:08:35 +00:00
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<div class="section" id="binary-search">
<h1>binary_search<a class="headerlink" href="#binary-search" title="Permalink to this headline"></a></h1>
<div class="section" id="interface">
<h2>Interface<a class="headerlink" href="#interface" title="Permalink to this headline"></a></h2>
<div class="highlight-c++"><div class="highlight"><pre><span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">ForwardIterator</span><span class="p">,</span> <span class="k">typename</span> <span class="n">T</span><span class="o">&gt;</span>
<span class="kr">inline</span> <span class="n">SPROUT_CONSTEXPR</span> <span class="kt">bool</span>
<span class="n">binary_search</span><span class="p">(</span><span class="n">ForwardIterator</span> <span class="n">first</span><span class="p">,</span> <span class="n">ForwardIterator</span> <span class="n">last</span><span class="p">,</span> <span class="n">T</span> <span class="k">const</span><span class="o">&amp;</span> <span class="n">value</span><span class="p">);</span>
<span class="k">template</span><span class="o">&lt;</span><span class="k">typename</span> <span class="n">ForwardIterator</span><span class="p">,</span> <span class="k">typename</span> <span class="n">T</span><span class="p">,</span> <span class="k">typename</span> <span class="n">Compare</span><span class="o">&gt;</span>
<span class="kr">inline</span> <span class="n">SPROUT_CONSTEXPR</span> <span class="kt">bool</span>
<span class="n">binary_search</span><span class="p">(</span><span class="n">ForwardIterator</span> <span class="n">first</span><span class="p">,</span> <span class="n">ForwardIterator</span> <span class="n">last</span><span class="p">,</span> <span class="n">T</span> <span class="k">const</span><span class="o">&amp;</span> <span class="n">value</span><span class="p">,</span> <span class="n">Compare</span> <span class="n">comp</span><span class="p">);</span>
</pre></div>
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<div class="section" id="requires">
<h2>Requires<a class="headerlink" href="#requires" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line">The elements e of [first,last) are partitioned with respect to the expressions <tt class="docutils literal"><span class="pre">e</span> <span class="pre">&lt;</span> <span class="pre">value</span></tt> and <tt class="docutils literal"><span class="pre">!(value</span> <span class="pre">&lt;</span> <span class="pre">e)</span></tt> or <tt class="docutils literal"><span class="pre">comp(e,</span> <span class="pre">value)</span></tt> and <tt class="docutils literal"><span class="pre">!comp(value,</span> <span class="pre">e)</span></tt>.</div>
<div class="line">Also, for all elements e of [first,last), <tt class="docutils literal"><span class="pre">e</span> <span class="pre">&lt;</span> <span class="pre">value</span></tt> implies <tt class="docutils literal"><span class="pre">!(value</span> <span class="pre">&lt;</span> <span class="pre">e)</span></tt> or <tt class="docutils literal"><span class="pre">comp(e,</span> <span class="pre">value)</span></tt> implies <tt class="docutils literal"><span class="pre">!comp(value,</span> <span class="pre">e)</span></tt>.</div>
</div>
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<div class="section" id="returns">
<h2>Returns<a class="headerlink" href="#returns" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line">true if there is an iterator i in the range [first,last) that satisfies the corresponding conditions: <tt class="docutils literal"><span class="pre">!(*i</span> <span class="pre">&lt;</span> <span class="pre">value)</span> <span class="pre">&amp;&amp;</span> <span class="pre">!(value</span> <span class="pre">&lt;</span> <span class="pre">*i)</span></tt> or <tt class="docutils literal"><span class="pre">comp(*i,</span> <span class="pre">value)</span> <span class="pre">&amp;&amp;</span> <span class="pre">comp(value,</span> <span class="pre">*i)</span></tt>.</div>
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<div class="section" id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h2>
<div class="highlight-c++"><div class="highlight"><pre><span class="cp">#include &lt;sprout/algorithm/binary_search.hpp&gt;</span>
<span class="cp">#include &lt;sprout/array.hpp&gt;</span>
<span class="cp">#include &lt;sprout/container.hpp&gt;</span>
<span class="k">using</span> <span class="k">namespace</span> <span class="n">sprout</span><span class="p">;</span>
<span class="n">SPROUT_STATIC_CONSTEXPR</span> <span class="k">auto</span> <span class="n">input</span> <span class="o">=</span> <span class="n">array</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span> <span class="mi">10</span><span class="o">&gt;</span><span class="p">{{</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">}};</span>
<span class="n">SPROUT_STATIC_CONSTEXPR</span> <span class="k">auto</span> <span class="n">result</span> <span class="o">=</span> <span class="n">sprout</span><span class="o">::</span><span class="n">binary_search</span><span class="p">(</span><span class="n">begin</span><span class="p">(</span><span class="n">input</span><span class="p">),</span> <span class="n">end</span><span class="p">(</span><span class="n">input</span><span class="p">),</span> <span class="mi">5</span><span class="p">);</span>
<span class="n">static_assert</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="s">&quot;found 5 by binary search.&quot;</span><span class="p">);</span>
</pre></div>
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<div class="section" id="complexity">
<h2>Complexity<a class="headerlink" href="#complexity" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line">At most <tt class="docutils literal"><span class="pre">log2(last</span> <span class="pre">-</span> <span class="pre">first)</span> <span class="pre">+</span> <span class="pre">O(1)</span></tt> comparisons.</div>
<div class="line">Recursive function invocations in <em>O(logN)</em> (logarithmic) depth.</div>
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<h2>Header<a class="headerlink" href="#header" title="Permalink to this headline"></a></h2>
<div class="line-block">
<div class="line"><tt class="docutils literal"><span class="pre">sprout/algorithm/binary_search.hpp</span></tt></div>
<div class="line">Convenience header: <tt class="docutils literal"><span class="pre">sprout/algorithm.hpp</span></tt></div>
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<li><a class="reference external" href="#">binary_search</a><ul>
<li><a class="reference external" href="#interface">Interface</a></li>
<li><a class="reference external" href="#requires">Requires</a></li>
<li><a class="reference external" href="#returns">Returns</a></li>
<li><a class="reference external" href="#examples">Examples</a></li>
<li><a class="reference external" href="#complexity">Complexity</a></li>
<li><a class="reference external" href="#header">Header</a></li>
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