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<div class="identifier-type">function template</div><div class="header"><numeric></div><h1 itemprop="name"><span class="namespace" title="namespace std">std::</span><span class="token">partial_sum</span></h1>
<div itemprop="articleBody"><p><div class="codehilite"><pre><span></span><code><span class="k">namespace</span><span class="w"> </span><span class="nn">std</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">InputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">OutputIterator</span><span class="o">></span>
<span class="w"> </span><span class="n">OutputIterator</span>
<span class="w"> </span><span class="n">partial_sum</span><span class="p">(</span><span class="n">InputIterator</span><span class="w"> </span><span class="n">first</span><span class="p">,</span>
<span class="w"> </span><span class="n">InputIterator</span><span class="w"> </span><span class="n">last</span><span class="p">,</span>
<span class="w"> </span><span class="n">OutputIterator</span><span class="w"> </span><span class="n">result</span><span class="p">);</span><span class="w"> </span><span class="c1">// (1) C++03</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">InputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">OutputIterator</span><span class="o">></span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">OutputIterator</span>
<span class="w"> </span><span class="n">partial_sum</span><span class="p">(</span><span class="n">InputIterator</span><span class="w"> </span><span class="n">first</span><span class="p">,</span>
<span class="w"> </span><span class="n">InputIterator</span><span class="w"> </span><span class="n">last</span><span class="p">,</span>
<span class="w"> </span><span class="n">OutputIterator</span><span class="w"> </span><span class="n">result</span><span class="p">);</span><span class="w"> </span><span class="c1">// (1) C++20</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">InputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">OutputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">BinaryOperation</span><span class="o">></span>
<span class="w"> </span><span class="n">OutputIterator</span>
<span class="w"> </span><span class="n">partial_sum</span><span class="p">(</span><span class="n">InputIterator</span><span class="w"> </span><span class="n">first</span><span class="p">,</span>
<span class="w"> </span><span class="n">InputIterator</span><span class="w"> </span><span class="n">last</span><span class="p">,</span>
<span class="w"> </span><span class="n">OutputIterator</span><span class="w"> </span><span class="n">result</span><span class="p">,</span>
<span class="w"> </span><span class="n">BinaryOperation</span><span class="w"> </span><span class="n">binary_op</span><span class="p">);</span><span class="w"> </span><span class="c1">// (2) C++03</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">InputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">OutputIterator</span><span class="p">,</span><span class="w"> </span><span class="k">class</span><span class="w"> </span><span class="nc">BinaryOperation</span><span class="o">></span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">OutputIterator</span>
<span class="w"> </span><span class="n">partial_sum</span><span class="p">(</span><span class="n">InputIterator</span><span class="w"> </span><span class="n">first</span><span class="p">,</span>
<span class="w"> </span><span class="n">InputIterator</span><span class="w"> </span><span class="n">last</span><span class="p">,</span>
<span class="w"> </span><span class="n">OutputIterator</span><span class="w"> </span><span class="n">result</span><span class="p">,</span>
<span class="w"> </span><span class="n">BinaryOperation</span><span class="w"> </span><span class="n">binary_op</span><span class="p">);</span><span class="w"> </span><span class="c1">// (2) C++20</span>
<span class="p">}</span>
</code></pre></div>
</p>
<h2>概要</h2>
<p><a class="cpprefjp-defined-word" data-desc="2つのイテレータで表現される半開区間を表す。C++20からイテレータと番兵で異なる型であっても指定可能になる">イテレータ範囲</a><code>[first, last)</code>の値の部分和を計算する。</p>
<p><code><a href="accumulate.html">accumulate()</a></code>は最終結果のみを得るが、<code>partial_sum()</code>は計算の途中結果のシーケンスを得る。</p>
<p><code>partial_sum()</code>の引数としてシーケンス<code>{0, 1, 2, 3}</code>が与えられた場合、以下のような計算が行われる：</p>
<p><div class="codehilite"><pre><span></span><code><span class="c1">// 計算の経過</span>
<span class="p">{</span>
<span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="c1">// (1)</span>
<span class="w"> </span><span class="mi">0</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="c1">// (2)</span>
<span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</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="c1">// (3)</span>
<span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// (4)</span>
<span class="p">}</span>
</code></pre></div>
</p>
<p>そして最終的に、以下のシーケンスが結果として出力される：</p>
<p><div class="codehilite"><pre><span></span><code><span class="p">{</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">}</span>
</code></pre></div>
</p>
<p>出力イテレータ<code>result</code>には、そのシーケンスが書き込まれる。</p>
<p>2項演算の関数オブジェクト<code>binary_op</code>には、第1引数として現在の集積値が渡され(「計算の経過」の(3)では、<code>0 + 1</code>した結果の<code>1</code>が渡される)、第2引数として新たに集積する値が渡される(「計算の経過」の(3)では、<code>2</code>が渡される)。</p>
<ul>
<li>(1) : 値を集積する方法として、<code>binary_op</code>をデフォルトで<code>operator+</code>とする</li>
<li>(2) : 値を集積する方法を<code>binary_op</code>として、任意にユーザーが決定する</li>
</ul>
<h2>要件</h2>
<ul>
<li>C++03まで : <code>binary_op</code>を呼び出した結果として、いかなる副作用も起こしてはならない</li>
<li>C++11から : <code>InputIterator</code>の値型は、<code>*first</code>の型から構築可能でなければならない</li>
<li>C++11から : <code>binary_op</code>の<a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a>が、<code>InputIterator</code>の値型に変換可能でなければならない</li>
<li>C++11から : <code>binary_op</code>の<a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a>が、<code>result</code>出力イテレータに書き込めなければならない</li>
<li>C++11から : <code>binary_op</code>は入力<a class="cpprefjp-defined-word" data-desc="2つのイテレータで表現される半開区間を表す。C++20からイテレータと番兵で異なる型であっても指定可能になる">イテレータ範囲</a><code>[first, last]</code>および出力<a class="cpprefjp-defined-word" data-desc="2つのイテレータで表現される半開区間を表す。C++20からイテレータと番兵で異なる型であっても指定可能になる">イテレータ範囲</a><code>[result, result + (last - first)]</code>の要素を変更してはならず、そのイテレータと部分範囲を無効化してはならない</li>
</ul>
<h2>効果</h2>
<ul>
<li>(1) : <code>binary_op</code>を<code>operator+</code>として、(2)の演算を行う</li>
<li>
<p>(2) : 出力結果の<a class="cpprefjp-defined-word" data-desc="2つのイテレータで表現される半開区間を表す。C++20からイテレータと番兵で異なる型であっても指定可能になる">イテレータ範囲</a><code>[result, result + (last - first))</code>には、以下が書き込まれる：</p>
<ul>
<li>C++03 :</li>
</ul>
<p><pre><code>*firstが書き込まれる // (1)
binary_op(*first, *(first + 1))が書き込まれる // (2)
binary_op((2)の結果, *(first + 2))が書き込まれる // (3)
binary_op((3)の結果, *(first + 3))が書き込まれる // (4)
…
binary_op((N-2)の結果, *(first + (N-1)))が書き込まれる
</code></pre></p>
<ul>
<li>C++20 :</li>
</ul>
<p><pre><code>*firstが書き込まれる // (1)
binary_op(<a href="../utility/move.html">std::move</a>(*first), *(first + 1))が書き込まれる // (2)
binary_op(<a href="../utility/move.html">std::move</a>((2)の結果), *(first + 2))が書き込まれる // (3)
binary_op(<a href="../utility/move.html">std::move</a>((3)の結果), *(first + 3))が書き込まれる // (4)
…
binary_op(<a href="../utility/move.html">std::move</a>((N-2)の結果), *(first + (N-1)))が書き込まれる
</code></pre></p>
</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a></h2>
<p><code>result + (last - first)</code></p>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Complexity。関数が使うアルゴリズムの空間計算量・時間計算量">計算量</a></h2>
<p>ちょうど<code>(last - first) - 1</code>回だけ<code>binary_op</code>を適用する</p>
<h2>備考</h2>
<p>この関数は、他の言語では<code>scan</code>という名前で提供されている。</p>
<h2>例</h2>
<p><div class="yata" id="94f28dbb3bfd3c6be5f2f54650576c0bd5b876ab"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="cp">#include <a href="../array.html"><array></a></span>
<span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">Range</span><span class="o">></span>
<span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">Range</span><span class="o">&</span><span class="w"> </span><span class="n">r</span><span class="p">)</span>
<span class="p">{</span>
<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="o">&</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" --> "</span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"end"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="p">}</span>
<span class="kt">int</span><span class="w"> </span><span class="n">main</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n"><a href="../array/array.html">std::array</a></span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="o">></span><span class="w"> </span><span class="n">ar</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mf">.0</span><span class="p">,</span><span class="mf">.2</span><span class="p">,</span><span class="mf">.4</span><span class="p">,</span><span class="mf">.6</span><span class="p">,</span><span class="mf">.8</span><span class="p">};</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../array/array.html">std::array</a></span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="o">></span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::partial_sum</span></span><span class="p">(</span><span class="n"><a href="../array/array/begin.html">ar.begin()</a></span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../array/array/end.html">ar.end()</a></span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../array/array/begin.html">result.begin()</a></span><span class="p">);</span>
<span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="n">result</span><span class="p">);</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="n"><a href="../array/array.html">std::array</a></span><span class="o"><</span><span class="kt">double</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="o">></span><span class="w"> </span><span class="n">result</span><span class="p">;</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::partial_sum</span></span><span class="p">(</span><span class="n"><a href="../array/array/begin.html">ar.begin()</a></span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../array/array/end.html">ar.end()</a></span><span class="p">,</span><span class="w"> </span><span class="n"><a href="../array/array/begin.html">result.begin()</a></span><span class="p">,</span>
<span class="w"> </span><span class="p">[](</span><span class="kt">double</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">b</span><span class="p">;</span><span class="w"> </span><span class="p">});</span>
<span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="n">result</span><span class="p">);</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h3>出力</h3>
<p><pre><code>0 --> 0.2 --> 0.6 --> 1.2 --> 2 --> end
0 --> -0.2 --> -0.8 --> -2.2 --> -5.2 --> end
</code></pre></p>
<h2>関連項目</h2>
<ul>
<li><code><a href="inclusive_scan.html">std::inclusive_scan()</a></code></li>
<li><code><a href="exclusive_scan.html">std::exclusive_scan()</a></code></li>
</ul>
<h2>参照</h2>
<ul>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2017/p0616r0.pdf" target="_blank">P0616R0 De-pessimize legacy <code><numeric></code> algorithms with <code>std::move</code></a></li>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p1645r1.html" target="_blank">P1645R1 <code>constexpr</code> for <code><numeric></code> algorithms</a><ul>
<li>C++20で、並列バージョン以外の数値計算アルゴリズムが<code>constexpr</code>対応した</li>
</ul>
</li>
</ul></div>
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