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<a class="post-title-link" href="/2019/05/11/强化学习基础/" itemprop="url">强化学习基础</a></h1>
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<h3 id="概念"><a href="#概念" class="headerlink" title="概念"></a>概念</h3><p>强化学习研究的是智能体agent与环境之间交互的任务，也就是让agent像人类一样通过试错，不断地学习在不同的环境下做出最优的动作，而不是有监督地直接告诉agent在什么环境下应该做出什么动作。既然与环境交互，必然会有反馈，也即回报。</p>
<p>强化学习和监督学习的区别主要有以下两点：</p>
<ol>
<li>强化学习是试错学习(Trail-and-error)，由于没有直接的指导信息，智能体要以不断与环境进行交互，通过试错的方式来获得最佳策略。（可以认为是交互产生样本）</li>
<li>延迟回报，强化学习的指导信息很少，而且往往是在事后（最后一个状态）才给出的，这就导致了一个问题，就是获得正回报或者负回报以后，如何将回报分配给前面的状态。</li>
</ol>
<h3 id="MDP"><a href="#MDP" class="headerlink" title="MDP"></a>MDP</h3><p>显然MDP是一个离散的过程，当前的执行的动作的回报依赖于未来的回报（延迟回报），一个使得在任意时刻和状态下的长期回报都是最大的策略是我们最终需要得到的。因此最简单的就是累计回报</p>
<p>$$G<em>{t}=R</em>{t+1}+R<em>{t+2}+R</em>{t+3}+\ldots=\sum<em>{k=t+1}^{\infty} R</em>{k}$$<br>但实际上我们一般会用下面更通用的公式来代替：</p>
<p>$$G<em>{t}=R</em>{t+1}+\gamma R<em>{t+2}+\gamma^{2} R</em>{t+3}+\ldots+\gamma^{T-t-1} R<em>{T}=\sum</em>{k=0}^{T-t-1} \gamma^{k} R_{t+k+1}$$</p>
<h3 id="马尔可夫决策过程"><a href="#马尔可夫决策过程" class="headerlink" title="马尔可夫决策过程"></a>马尔可夫决策过程</h3><p>一个有限马尔可夫决策过程由一个四元组构成 M=(S,A,P,R)。如上所述，S表示状态集空间，A表示动作集空间，P表示状态转移概率矩阵，R表示期望回报值。</p>
<p>给定当前状态和动作，转移到另一个状态的概率计算：</p>
<p>$$p\left(s^{\prime} | s, a\right)=\operatorname{Pr}\left{S<em>{t+1}=s^{\prime} | S</em>{t}=s, A_{t}=a\right} \in \mathbf{P}$$</p>
<p>在给定状态、动作和下一个状态的前提下，回报的计算：</p>
<p>$$r\left(s, a, s^{\prime}\right)=\mathbf{E}\left[R<em>{t+1} | S</em>{t}=s, A<em>{t}=a, S</em>{t+1}=s^{\prime}\right] \in \mathbf{R}$$</p>
<h3 id="值函数及贝尔曼公式"><a href="#值函数及贝尔曼公式" class="headerlink" title="值函数及贝尔曼公式"></a>值函数及贝尔曼公式</h3><p>增强学习的最终结果是找到一个环境到动作的映射—即策略$\pi(a|s)$，在几乎所有的强化学习理论中都会定义值函数来表示给定策略下期望的未来回报，并将值函数作为评估学习效果的指标。值函数有多种定义，目前常见的是将值函数直接定义为未来回报的期望：</p>
<p>$$v<em>{\pi}(s)=\mathbf{E}</em>{\pi}\left[G<em>{t} | S</em>{t}=s\right]=\mathbf{E}<em>{\pi}\left[\sum</em>{k=0}^{\infty} \gamma^{k} R<em>{t+k+1} | S</em>{t}=s\right]$$</p>
<p>上面表示的是在某个策略$\pi$下，当环境处于状态s时未来回报的期望，因此又叫做状态值函数(state-value function for policy)，只跟当前状态有关。同样，我们也可以定义动作值函数(action-value function for policy)，如下：</p>
<p>$$q<em>{\pi}(s, a)=\mathbf{E}</em>{\pi}\left[G<em>{t} | S</em>{t}=s, A<em>{t}=a\right]=\mathbf{E}</em>{\pi}\left[\sum<em>{k=0}^{\infty} \gamma^{k} R</em>{t+k+1} | S<em>{t}=s, A</em>{t}=a\right]$$</p>
<p>值函数和动作值函数的区别在于动作值是在给定动作下的期望回报，从形式上看，都可以写成递归的形式：</p>
<p>$$v<em>{\pi}(s)=\mathbf{E}</em>{\pi}\left[G<em>{t} | S</em>{t}=s\right]=\mathbf{E}<em>{\pi}\left[\sum</em>{k=0}^{\infty} \gamma^{k} R<em>{t+k+1} | S</em>{t}=s\right]$$</p>
<p>$$=\mathbf{E}<em>{\pi}\left[R</em>{t+1}+\gamma \sum<em>{k=0}^{\infty} \gamma^{k} R</em>{t+k+2} | S_{t}=s\right]$$</p>
<p>$$=\sum<em>{a} \pi(a | s) \cdot \mathbf{E}</em>{\pi}\left[R<em>{t+1}+\gamma \sum</em>{k=0}^{\infty} \gamma^{k} R<em>{t+k+2} | S</em>{t}=s, A_{t}\right]$$</p>
<p>$$=\sum<em>{a} \pi(a | s) \sum</em>{s^{\prime}} p\left(s^{\prime} | s, a\right)\left[r\left(s, a, s^{\prime}\right)+\gamma \mathbf{E}<em>{\pi}\left[\sum</em>{k=0}^{\infty} \gamma^{k} R<em>{t+k+2} | S</em>{t+1}=s^{\prime}\right]\right]$$</p>
<p>$$=\sum<em>{a} \pi(a | s) \sum</em>{s^{\prime}} p\left(s^{\prime} | s, a\right)\left[r\left(s, a, s^{\prime}\right)+\gamma v_{\pi}\left(s^{\prime}\right)\right]$$</p>
<p>因此当前状态下的回报可以用下一状态下的值函数求解，这个公式就是贝尔曼公式。</p>
<p>同理状态值函数也可以递归求解：</p>
<p>$$\begin{aligned} q<em>{\pi}(s, a) &=\mathbf{E}</em>{\pi}\left[G<em>{t} | S</em>{t}=s, A<em>{t}=a\right] \ &=\mathbf{E}</em>{\pi}\left[R<em>{t+1}+\gamma \sum</em>{k=0}^{\infty} \gamma^{k} R<em>{t+k+2} | S</em>{t}=s, A<em>{t}=a\right] \ &=\sum</em>{s^{\prime}} p\left(s^{\prime} | s, a\right)\left[r\left(s, a, s^{\prime}\right)+\gamma v_{\pi}\left(s^{\prime}\right)\right] \end{aligned}$$</p>
<p>根据贝叶斯公式可以把两者关联：</p>
<p>$$v<em>{\pi}(s)=\sum</em>{a} \pi(a | s) q_{\pi}(s, a)$$</p>
<h3 id="最优值函数及贝尔曼最优公式"><a href="#最优值函数及贝尔曼最优公式" class="headerlink" title="最优值函数及贝尔曼最优公式"></a>最优值函数及贝尔曼最优公式</h3><p>我们的目标就是使得任意时刻未来回报的期望值都是最大的，为此目标可以是：</p>
<p>$$\pi<em>{*}=\underset{\pi}{\arg \max } v</em>{\pi}(s)$$</p>
<p>策略可能有多个，但是最优的状态值函数和动作值函数是一致的：</p>
<p>$$v<em>{*}(s)=\max </em>{\pi} v_{\pi}(s)$$</p>
<p>$$q<em>{*}(s, a)=\max </em>{\pi} q_{\pi}(s, a)$$</p>
<p>目标函数有了，最重要的就是如何求解最优策略$\pi_*(a|s)$，由于状态之间的转义是依赖动作的，因此不需要求解状态转义的概率。</p>
<p>贝尔曼公式与贝尔曼最优公式是MDP求解的基础，下面主要介绍几种MDP求解的方法。</p>
<p><a href="https://blog.csdn.net/chenhoujiangsir/article/details/52909921" target="_blank" rel="external">参考链接</a></p>
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<center> <h3> FM算法 </h3> </center>
<ol>
<li><p>线性模型</p>
<p>$$y=\omega<em>{0}+\sum</em>{i=1}^{n} \omega<em>{i} x</em>{i}$$</p>
</li>
<li><p>因子模型</p>
<p>$$y=\omega<em>{0}+\sum</em>{i=1}^{n} \omega<em>{i} x</em>{i}+\sum<em>{i=1}^{n-1} \sum</em>{j=i+1}^{n}<v_{i}, v_{j}="">x<em>{i} x</em>{j}$$</v_{i},></p>
<p>其中$v \in \mathbb{R}^{n, k}$, $ \quad<\mathbf{v}<em>{i}, \mathbf{v}</em>{j}>$ <vi,vj>表示的是两个大小为$k$的向量之间的<strong>点积</strong>：</vi,vj></p>
<p>$$<\mathbf{v}<em>{i}, \mathbf{v}</em>{j}>=\sum<em>{f=1}^{k} v</em>{i, f} \cdot v_{j, f}$$</p>
</li>
<li><p>FM模型求解 </p>
<p>FM模型在基础的线性模型的基础上引入交叉项</p>
<p>$$y=\omega<em>{0}+\sum</em>{i=1}^{n} \omega<em>{i} x</em>{i}+\sum<em>{i=1}^{n-1} \sum</em>{j=1+1}^{n} \omega<em>{i j} x</em>{i} x_{j}$$</p>
<p>一般来说数据是非常稀疏的，$w_{i,j}$ 无法通过训练得到。因此，辅助向量$v<em>i$ 对$w</em>{i,j}$进行估计：</p>
<p>$$\hat{\omega}<em>{i j}=\mathbf{v}</em>{i} \mathbf{v}_{j}^{T}$$</p>
</li>
<li><p>交叉项的求解 （时间复杂度 $O(kn)$）</p>
</li>
</ol>
<p>$$\begin{aligned} & \sum<em>{i=1}^{n} \sum</em>{j=i+1}^{n}\left\langle\mathbf{v}<em>{i}, \mathbf{v}</em>{j}\right\rangle x<em>{i} x</em>{j} \=& \frac{1}{2} \sum<em>{i=1}^{n} \sum</em>{j=1}^{n}\left\langle\mathbf{v}<em>{i}, \mathbf{v}</em>{j}\right\rangle x<em>{i} x</em>{j}-\frac{1}{2} \sum<em>{i=1}^{n}\left\langle\mathbf{v}</em>{i}, \mathbf{v}<em>{i}\right\rangle x</em>{i} x_{i} \end{aligned}$$</p>
<p>$$=\frac{1}{2}\left(\sum<em>{i=1}^{n} \sum</em>{j=1}^{n} \sum<em>{f=1}^{k} v</em>{i, f} v<em>{j, f} x</em>{i} x<em>{j}-\sum</em>{i=1}^{n} \sum<em>{f=1}^{k} v</em>{i, f} v<em>{i, f} x</em>{i} x_{i}\right)$$</p>
<p>$$=\frac{1}{2} \sum<em>{f=1}^{k}\left(\left(\sum</em>{i=1}^{n} v<em>{i, f} x</em>{i}\right)\left(\sum<em>{j=1}^{n} v</em>{j, f} x<em>{j}\right)-\sum</em>{i=1}^{n} v<em>{i, f}^{2} x</em>{i}^{2}\right)$$</p>
<p>$$=\frac{1}{2} \sum<em>{f=1}^{k}\left(\left(\sum</em>{i=1}^{n} v<em>{i, f} x</em>{i}\right)^{2}-\sum<em>{i=1}^{n} v</em>{i, f}^{2} x_{i}^{2}\right)$$</p>
<ol>
<li><p>反向梯度</p>
<p>损失函数（假设是MSE）</p>
<p>$$\operatorname{loss}^{R}(\hat{y}, y)=\frac{1}{2} \sum_{i=1}^{m}\left(\hat{y}^{(i)}-y^{(i)}\right)^{2}$$</p>
<p>梯度：</p>
<p>$$\frac{\partial \operatorname{loss}^{R}(\hat{y}, y)}{\partial \theta}=(\hat{y}-y) \frac{\partial \hat{y}}{\partial \theta}$$</p>
<p>$$\frac{\partial}{\partial \theta} \hat{y}(\mathbf{x})=\left{\begin{array}{ll}{1,} & {\text { if } \theta \text { is } w<em>{0}} \ {x</em>{i},} & {\text { if } \theta \text { is } w<em>{i}} \ {x</em>{i} \sum<em>{j=1}^{n} v</em>{j, f} x<em>{j}-v</em>{i, f} x<em>{i}^{2},} & {\text { if } \theta \text { is } v</em>{i, f}}\end{array}\right.$$</p>
</li>
<li><p>c++代码实现</p>
</li>
</ol>
<p>fm.h</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><vector></span></span></div><div class="line"></div><div class="line"><span class="meta"># <span class="meta-keyword">ifndef</span> SRC_FM_</span></div><div class="line"><span class="meta"># <span class="meta-keyword">define</span> SRC_FM_</span></div><div class="line"></div><div class="line"><span class="keyword">using</span> <span class="built_in">std</span>::<span class="built_in">vector</span>;</div><div class="line"><span class="keyword">using</span> <span class="built_in">std</span>::<span class="built_in">string</span>;</div><div class="line"></div><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">FM</span> {</span></div><div class="line"> <span class="keyword">public</span>:</div><div class="line"> FM();</div><div class="line"> ~FM();</div><div class="line"> <span class="function"><span class="keyword">void</span> <span class="title">Init</span><span class="params">(<span class="built_in">string</span> file_name, <span class="keyword">int</span> n_sample, <span class="keyword">int</span> n, <span class="keyword">int</span> k)</span></span>;</div><div class="line"> <span class="function"><span class="keyword">void</span> <span class="title">Fit</span><span class="params">(<span class="keyword">int</span> epoch)</span></span>;</div><div class="line"> <span class="function"><span class="keyword">float</span> <span class="title">Predict</span><span class="params">(<span class="built_in">vector</span><<span class="keyword">float</span>> &sample)</span></span>;</div><div class="line"> <span class="keyword">private</span>:</div><div class="line"> <span class="function"><span class="keyword">float</span> <span class="title">GradYToTheta</span><span class="params">(<span class="keyword">int</span> sample, <span class="keyword">int</span> i, <span class="keyword">int</span> f)</span></span>;</div><div class="line"> <span class="function"><span class="keyword">void</span> <span class="title">CalcVDot</span><span class="params">()</span></span>;</div><div class="line"> <span class="keyword">private</span>:</div><div class="line"> <span class="built_in">vector</span><<span class="built_in">vector</span><<span class="keyword">float</span>> > data_;</div><div class="line"> <span class="built_in">vector</span><<span class="keyword">float</span>> y_;</div><div class="line"> <span class="built_in">vector</span><<span class="keyword">float</span>> w_;</div><div class="line"> <span class="built_in">vector</span><<span class="built_in">vector</span><<span class="keyword">float</span>> > v_;</div><div class="line"> <span class="built_in">vector</span><<span class="built_in">vector</span><<span class="keyword">float</span>> > v_dot_;</div><div class="line">};</div><div class="line"></div><div class="line"><span class="meta">#<span class="meta-keyword">endif</span></span></div></pre></td></tr></table></figure>
<p>fm.cpp</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div><div class="line">28</div><div class="line">29</div><div class="line">30</div><div class="line">31</div><div class="line">32</div><div class="line">33</div><div class="line">34</div><div class="line">35</div><div class="line">36</div><div class="line">37</div><div class="line">38</div><div class="line">39</div><div class="line">40</div><div class="line">41</div><div class="line">42</div><div class="line">43</div><div class="line">44</div><div class="line">45</div><div class="line">46</div><div class="line">47</div><div class="line">48</div><div class="line">49</div><div class="line">50</div><div class="line">51</div><div class="line">52</div><div class="line">53</div><div class="line">54</div><div class="line">55</div><div class="line">56</div><div class="line">57</div><div class="line">58</div><div class="line">59</div><div class="line">60</div><div class="line">61</div><div class="line">62</div><div class="line">63</div><div class="line">64</div><div class="line">65</div><div class="line">66</div><div class="line">67</div><div class="line">68</div><div class="line">69</div><div class="line">70</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string"><fstream></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string"><iomanip></span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"fm.h"</span></span></div><div class="line"></div><div class="line"><span class="keyword">using</span> <span class="built_in">std</span>::ifstream;</div><div class="line"></div><div class="line">FM::FM() {}</div><div class="line"></div><div class="line">FM::~FM() {}</div><div class="line"></div><div class="line"><span class="keyword">void</span> FM::Init(<span class="built_in">string</span> file_name, <span class="keyword">int</span> n_sample, <span class="keyword">int</span> n, <span class="keyword">int</span> k) {</div><div class="line"> ifstream fin(file_name.c_str());</div><div class="line"> <span class="keyword">if</span>(!fin.is_open()) {</div><div class="line"> <span class="built_in">std</span>::<span class="built_in">cerr</span> << <span class="string">"opep file failure"</span> << <span class="built_in">std</span>::<span class="built_in">endl</span>;</div><div class="line"> }</div><div class="line"></div><div class="line">}</div><div class="line"><span class="keyword">void</span> FM::Fit(<span class="keyword">int</span> epoch) {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> ep = <span class="number">0</span>; ep < epoch; ep++) {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < data_.size(); i++) {</div><div class="line"> <span class="keyword">float</span> y_p = Predict(data_[i]);</div><div class="line"> <span class="keyword">float</span> resid = y_p - y_[i];</div><div class="line"> w_[<span class="number">0</span>] += resid;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">1</span>; j < w_.size(); j++) {</div><div class="line"> w_[j] = resid*data_[i][j<span class="number">-1</span>];</div><div class="line"> }</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> iter_i = <span class="number">0</span>; iter_i < v_.size(); iter_i++) {</div><div class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> f = <span class="number">0</span>; f < v_[iter_i].size(); f++) {</div><div class="line"> v_[iter_i][f] += resid*GradYToTheta(i, iter_i, f);</div><div class="line"> }</div><div class="line"> }</div><div class="line"> CalcVDot();</div><div class="line"> }</div><div class="line"></div><div class="line"> }</div><div class="line"></div><div class="line">}</div><div class="line"></div><div class="line"><span class="keyword">float</span> FM::Predict(<span class="built_in">vector</span><<span class="keyword">float</span>>& sample) {</div><div class="line"> <span class="keyword">float</span> result = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">0</span>; i < w_.size(); i++) {</div><div class="line"> result += sample[i]*w_[i];</div><div class="line"> }</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < sample.size(); i++) {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j= i+<span class="number">1</span>; j < sample.size(); j++) {</div><div class="line"> result += v_dot_[i][j]*sample[i]*sample[j];</div><div class="line"> }</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> result;</div><div class="line">}</div><div class="line"></div><div class="line"><span class="keyword">void</span> FM::CalcVDot() {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < v_.size(); i++) {</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">0</span>; j < v_.size(); j++) {</div><div class="line"> <span class="keyword">float</span> temp = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> f = <span class="number">0</span>; f < v_[i].size(); f++) {</div><div class="line"> temp += v_[i][f]*v_[j][f];</div><div class="line"> }</div><div class="line"> v_dot_[i][j] = temp;</div><div class="line"> }</div><div class="line"> }</div><div class="line">}</div><div class="line"><span class="keyword">float</span> FM::GradYToTheta(<span class="keyword">int</span> sample, <span class="keyword">int</span> i, <span class="keyword">int</span> f) {</div><div class="line"> <span class="keyword">float</span> sum = <span class="number">0</span>;</div><div class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> iter_j; iter_j < v_.size(); iter_j++) {</div><div class="line"> sum += v_[iter_j][f]*data_[sample][iter_j];</div><div class="line"> }</div><div class="line"></div><div class="line"> <span class="keyword">return</span> data_[sample][i]*(sum - v_[i][f]*data_[sample][i]);</div><div class="line">}</div></pre></td></tr></table></figure>
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<h3 id="简单工厂模式"><a href="#简单工厂模式" class="headerlink" title="简单工厂模式"></a>简单工厂模式</h3><h3 id="工厂模式"><a href="#工厂模式" class="headerlink" title="工厂模式"></a>工厂模式</h3><h3 id="抽象工厂模式"><a href="#抽象工厂模式" class="headerlink" title="抽象工厂模式"></a>抽象工厂模式</h3><p><a href="https://www.cnblogs.com/cxjchen/p/3143633.html" target="_blank" rel="external">link</a></p>
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<h3 id="单例模式"><a href="#单例模式" class="headerlink" title="单例模式"></a>单例模式</h3><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">ifndef</span> _SINGLETON_H_</span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> _SINGLETON_H_</span></div><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">Singleton</span>{</span></div><div class="line"><span class="keyword">public</span>:</div><div class="line"> <span class="function"><span class="keyword">static</span> Singleton* <span class="title">getInstance</span><span class="params">()</span></span>;</div><div class="line"></div><div class="line"><span class="keyword">private</span>:</div><div class="line"> Singleton();</div><div class="line"> <span class="comment">//把复制构造函数和=操作符也设为私有,防止被复制</span></div><div class="line"> Singleton(<span class="keyword">const</span> Singleton&);</div><div class="line"> Singleton& <span class="keyword">operator</span>=(<span class="keyword">const</span> Singleton&);</div><div class="line"></div><div class="line"> <span class="keyword">static</span> Singleton* instance;</div><div class="line">};</div><div class="line"></div><div class="line"><span class="meta">#<span class="meta-keyword">endif</span></span></div></pre></td></tr></table></figure>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"Singleton.h"</span></span></div><div class="line"></div><div class="line">Singleton::Singleton(){</div><div class="line"></div><div class="line">}</div><div class="line"></div><div class="line">Singleton::Singleton(<span class="keyword">const</span> Singleton&){</div><div class="line"></div><div class="line">}</div><div class="line"></div><div class="line">Singleton& Singleton::<span class="keyword">operator</span>=(<span class="keyword">const</span> Singleton&){</div><div class="line"></div><div class="line">}</div><div class="line"></div><div class="line"><span class="comment">//在此处初始化, 饿汉实现</span></div><div class="line">Singleton* Singleton::instance = <span class="keyword">new</span> Singleton();</div><div class="line">Singleton* Singleton::getInstance(){</div><div class="line"> <span class="keyword">return</span> instance;</div><div class="line">}</div></pre></td></tr></table></figure>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div></pre></td><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"Singleton.h"</span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><stdio.h></span></span></div><div class="line"></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span>{</div><div class="line"> Singleton* singleton1 = Singleton::getInstance();</div><div class="line"> Singleton* singleton2 = Singleton::getInstance();</div><div class="line"> <span class="built_in">std</span>::<span class="built_in">cout</span> << singleton1 << <span class="string">"=="</span><< singleton2<< <span class="built_in">std</span>::<span class="built_in">endl</span>;</div><div class="line"> <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">}</div></pre></td></tr></table></figure>
<h3 id="线程安全的懒汉实现"><a href="#线程安全的懒汉实现" class="headerlink" title="线程安全的懒汉实现"></a>线程安全的懒汉实现</h3><h4 id="经典实现"><a href="#经典实现" class="headerlink" title="经典实现"></a>经典实现</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div><div class="line">22</div><div class="line">23</div><div class="line">24</div><div class="line">25</div><div class="line">26</div><div class="line">27</div></pre></td><td class="code"><pre><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">singleton</span></span></div><div class="line"><span class="class">{</span></div><div class="line"><span class="keyword">protected</span>:</div><div class="line"> singleton()</div><div class="line"> {</div><div class="line"> pthread_mutex_init(&mutex);</div><div class="line"> }</div><div class="line"><span class="keyword">private</span>:</div><div class="line"> <span class="keyword">static</span> singleton* p;</div><div class="line"><span class="keyword">public</span>:</div><div class="line"> <span class="keyword">static</span> <span class="keyword">pthread_mutex_t</span> mutex;</div><div class="line"> <span class="function"><span class="keyword">static</span> singleton* <span class="title">initance</span><span class="params">()</span></span>;</div><div class="line">};</div><div class="line"></div><div class="line"><span class="keyword">pthread_mutex_t</span> singleton::mutex;</div><div class="line">singleton* singleton::p = <span class="literal">NULL</span>;</div><div class="line">singleton* singleton::initance()</div><div class="line">{</div><div class="line"> <span class="keyword">if</span> (p == <span class="literal">NULL</span>)</div><div class="line"> {</div><div class="line"> pthread_mutex_lock(&mutex);</div><div class="line"> <span class="keyword">if</span> (p == <span class="literal">NULL</span>)</div><div class="line"> p = <span class="keyword">new</span> singleton();</div><div class="line"> pthread_mutex_unlock(&mutex);</div><div class="line"> }</div><div class="line"> <span class="keyword">return</span> p;</div><div class="line">}</div></pre></td></tr></table></figure>
<h4 id="内部静态变量的懒汉实现"><a href="#内部静态变量的懒汉实现" class="headerlink" title="内部静态变量的懒汉实现"></a>内部静态变量的懒汉实现</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div><div class="line">5</div><div class="line">6</div><div class="line">7</div><div class="line">8</div><div class="line">9</div><div class="line">10</div><div class="line">11</div><div class="line">12</div><div class="line">13</div><div class="line">14</div><div class="line">15</div><div class="line">16</div><div class="line">17</div><div class="line">18</div><div class="line">19</div><div class="line">20</div><div class="line">21</div></pre></td><td class="code"><pre><div class="line"><span class="class"><span class="keyword">class</span> <span class="title">singleton</span></span></div><div class="line"><span class="class">{</span></div><div class="line"><span class="keyword">protected</span>:</div><div class="line"> singleton()</div><div class="line"> {</div><div class="line"> pthread_mutex_init(&mutex);</div><div class="line"> }</div><div class="line"><span class="keyword">public</span>:</div><div class="line"> <span class="keyword">static</span> <span class="keyword">pthread_mutex_t</span> mutex;</div><div class="line"> <span class="function"><span class="keyword">static</span> singleton* <span class="title">initance</span><span class="params">()</span></span>;</div><div class="line"> <span class="keyword">int</span> a;</div><div class="line">};</div><div class="line"></div><div class="line"><span class="keyword">pthread_mutex_t</span> singleton::mutex;</div><div class="line">singleton* singleton::initance()</div><div class="line">{</div><div class="line"> pthread_mutex_lock(&mutex);</div><div class="line"> <span class="keyword">static</span> singleton obj;</div><div class="line"> pthread_mutex_unlock(&mutex);</div><div class="line"> <span class="keyword">return</span> &obj;</div><div class="line">}</div></pre></td></tr></table></figure>
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<h3 id="amp-（左值引用）-和-amp-amp-右值引用"><a href="#amp-（左值引用）-和-amp-amp-右值引用" class="headerlink" title="&（左值引用） 和 && 右值引用"></a>&（左值引用） 和 && 右值引用</h3><figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">test</span><span class="params">(<span class="keyword">int</span> & i)</span> </span>{</div><div class="line"> i++;</div><div class="line">}</div><div class="line">test(<span class="number">1</span>) <span class="comment">// 编译不通过，非常量的引用值必须是左值。</span></div></pre></td></tr></table></figure>
<p>&（左值引用）：需要注意的是生命周期，<br>c++ 中的左值就像指针，它可以捕获实实在在的实体，但是我们要注意被捕获值的生命周期。不要随便把生命周期和栈同步的实体传给了它；</p>
<p>&& 右值引用<br>右值其实也是指针，但是它功能是专门捕获匿名的实体（可以理解为编译产生的中间变量）。同时我们要注意，右值在定义时捕获了实体以后，右值的名字就变成了被捕获的实体。</p>
<h3 id="类类型"><a href="#类类型" class="headerlink" title="类类型"></a>类类型</h3><p>类的声明：仅声明类暂时不定义它</p>
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<li><p>这种声明被称作 “前向声明”，在它声明之后定义之前是一个不完全类型（incomplete type），即我们知道是个类型，但是不知道内部情况</p>
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<li><p>不完全类型只能在非常有限的情况下使用：指针或者引用，参数或者返回值（都不会创建类型对象）</p>
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<li><p>只有类被定义之后，数据成员才能才能被申明成这种类型，所以一个类的成员类型不能是自己（如果可以的话，就会无限循环了）</p>
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<h3 id="static"><a href="#static" class="headerlink" title="static"></a>static</h3><ol>
<li>静态成员的定义和声明要加个关键static。静态成员可以通过双冒号来使用，即<类名>::<静态成员名>。</li>
<li>初始化静态成员变量要在类的外面进行。初始化的格式如下：数据类型 类名::静态成员变量名 = 初值；<figure class="highlight c++"><table><tr><td class="gutter"><pre><div class="line">1</div><div class="line">2</div><div class="line">3</div><div class="line">4</div></pre></td><td class="code"><pre><div class="line"><span class="function"><span class="keyword">static</span> <span class="keyword">void</span> <span class="title">test</span><span class="params">(<span class="keyword">int</span> i)</span> </span>{</div><div class="line"> <span class="keyword">static</span> j = <span class="number">0</span>;</div><div class="line"> <span class="built_in">std</span>::<span class="built_in">cout</span> << i << <span class="string">" static j 地址"</span> << &j<< <span class="built_in">std</span>::<span class="built_in">endl</span>;</div><div class="line">}</div></pre></td></tr></table></figure>
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