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            <h1 id="seo-header">【探索】利用后缀表达式解方程</h1>
            
              <p id="updated-time" class="note note-info" style="">
                
                  
                    Last updated on March 19, 2024 pm
                  
                
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                <figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> re</span><br><span class="line"><span class="keyword">from</span> fractions <span class="keyword">import</span> Fraction</span><br><span class="line"></span><br><span class="line"><span class="keyword">class</span> <span class="title class_">Stack</span>(<span class="title class_ inherited__">list</span>):</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">isEmpty</span>(<span class="params">self</span>):</span><br><span class="line">        <span class="keyword">return</span> self == []</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">peek</span>(<span class="params">self</span>):</span><br><span class="line">        <span class="keyword">if</span> self == []: <span class="keyword">return</span> <span class="literal">None</span></span><br><span class="line">        <span class="keyword">else</span>: <span class="keyword">return</span> self[-<span class="number">1</span>]</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">size</span>(<span class="params">self</span>):</span><br><span class="line">        <span class="keyword">return</span> <span class="built_in">len</span>(self)</span><br><span class="line">    push = <span class="built_in">list</span>.append</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">pop</span>(<span class="params">self</span>):</span><br><span class="line">        <span class="keyword">if</span> self == []: <span class="keyword">return</span> <span class="literal">None</span></span><br><span class="line">        <span class="keyword">else</span>: <span class="keyword">return</span> <span class="built_in">super</span>().pop()</span><br><span class="line"></span><br><span class="line"><span class="keyword">class</span> <span class="title class_">Polynomial</span>(<span class="title class_ inherited__">list</span>):</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">__init__</span>(<span class="params">self, value</span>):</span><br><span class="line">        <span class="keyword">for</span> item <span class="keyword">in</span> value: self.append(Fraction(item))</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">add</span>(<span class="params">self, value</span>):</span><br><span class="line">        <span class="keyword">if</span> <span class="built_in">len</span>(self) &lt; <span class="built_in">len</span>(value): self += [Fraction(<span class="number">0</span>)]*(<span class="built_in">len</span>(value)-<span class="built_in">len</span>(self))</span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(value)): self[i] += value[i]</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">sub</span>(<span class="params">self, value</span>):</span><br><span class="line">        <span class="keyword">if</span> <span class="built_in">len</span>(self) &lt; <span class="built_in">len</span>(value): self += [Fraction(<span class="number">0</span>)]*(<span class="built_in">len</span>(value)-<span class="built_in">len</span>(self))</span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(value)): self[i] -= value[i]</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">mul</span>(<span class="params">self, value</span>):</span><br><span class="line">        tmp = self.copy()</span><br><span class="line">        size = <span class="built_in">len</span>(self)</span><br><span class="line">        self.clear()</span><br><span class="line">        self += [Fraction(<span class="number">0</span>)]*(size+<span class="built_in">len</span>(value)-<span class="number">1</span>)</span><br><span class="line">        <span class="keyword">for</span> i,item <span class="keyword">in</span> <span class="built_in">enumerate</span>(value):</span><br><span class="line">            <span class="keyword">for</span> j <span class="keyword">in</span> <span class="built_in">range</span>(size):</span><br><span class="line">                self[i+j] += tmp[j]*item</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">divn</span>(<span class="params">self, n</span>):</span><br><span class="line">        <span class="keyword">if</span> <span class="built_in">type</span>(n) <span class="keyword">is</span> Polynomial:</span><br><span class="line">            <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(self)): self[i] /= n[<span class="number">0</span>]</span><br><span class="line">        <span class="keyword">else</span>:</span><br><span class="line">            _n = Fraction(n)</span><br><span class="line">            <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(<span class="built_in">len</span>(self)): self[i] /= _n</span><br><span class="line">    <span class="keyword">def</span> <span class="title function_">__str__</span>(<span class="params">self</span>):</span><br><span class="line">        <span class="keyword">if</span> self == []:</span><br><span class="line">            <span class="keyword">return</span> <span class="string">&#x27;0&#x27;</span></span><br><span class="line">        <span class="keyword">elif</span> <span class="built_in">len</span>(self) == <span class="number">1</span>:</span><br><span class="line">            <span class="keyword">return</span> <span class="built_in">str</span>(self[<span class="number">0</span>])</span><br><span class="line">        <span class="keyword">elif</span> <span class="built_in">len</span>(self) == <span class="number">2</span>:</span><br><span class="line">            <span class="keyword">return</span> <span class="string">f&#x27;(<span class="subst">&#123;self[<span class="number">1</span>]&#125;</span>)x + <span class="subst">&#123;self[<span class="number">0</span>]&#125;</span>&#x27;</span></span><br><span class="line">        <span class="keyword">else</span>: <span class="keyword">pass</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">def</span> <span class="title function_">get_Formula</span>(<span class="params">equation</span>):</span><br><span class="line">    <span class="keyword">return</span> equation.replace(<span class="string">&#x27; &#x27;</span>,<span class="string">&#x27;&#x27;</span>).split(<span class="string">&#x27;=&#x27;</span>)</span><br><span class="line"></span><br><span class="line">_ep = re.<span class="built_in">compile</span>(<span class="string">r&#x27;([\+\-\*/()][^\+\-\*/()]+)&#x27;</span>)</span><br><span class="line">_op = &#123;</span><br><span class="line">    <span class="string">&#x27;+&#x27;</span>: <span class="keyword">lambda</span> x,y:x.add(y),</span><br><span class="line">    <span class="string">&#x27;-&#x27;</span>: <span class="keyword">lambda</span> x,y:x.sub(y),</span><br><span class="line">    <span class="string">&#x27;*&#x27;</span>: <span class="keyword">lambda</span> x,y:x.mul(y),</span><br><span class="line">    <span class="string">&#x27;/&#x27;</span>: <span class="keyword">lambda</span> x,y:x.divn(y)</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">_middle2behind</span>(<span class="params">Fma, res, s, e</span>):</span><br><span class="line">    sta = Stack()</span><br><span class="line">    _s = s</span><br><span class="line">    <span class="keyword">while</span> s &lt; e:</span><br><span class="line">        <span class="keyword">if</span> Fma[s] <span class="keyword">in</span> <span class="string">&#x27;+-&#x27;</span>:</span><br><span class="line">            <span class="keyword">if</span> sta.isEmpty():</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">            <span class="keyword">elif</span> sta.peek() <span class="keyword">in</span> <span class="string">&#x27;*/&#x27;</span>:</span><br><span class="line">                <span class="keyword">while</span> sta: res.push(sta.pop())</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">            <span class="keyword">elif</span> sta.peek() <span class="keyword">in</span> <span class="string">&#x27;+-&#x27;</span>:</span><br><span class="line">                res.push(sta.pop())</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">        <span class="keyword">elif</span> Fma[s] <span class="keyword">in</span> <span class="string">&#x27;*/&#x27;</span>:</span><br><span class="line">            <span class="keyword">if</span> sta.isEmpty():</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">            <span class="keyword">elif</span> sta.peek() <span class="keyword">in</span> <span class="string">&#x27;+-&#x27;</span>:</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">            <span class="keyword">elif</span> sta.peek() <span class="keyword">in</span> <span class="string">&#x27;*/&#x27;</span>:</span><br><span class="line">                res.push(sta.pop())</span><br><span class="line">                sta.push(Fma[s])</span><br><span class="line">                s += <span class="number">1</span></span><br><span class="line">        <span class="keyword">elif</span> Fma[s] == <span class="string">&#x27;(&#x27;</span>:</span><br><span class="line">            s += <span class="number">1</span></span><br><span class="line">            d = _middle2behind(Fma, res, s, e)</span><br><span class="line">            s += d</span><br><span class="line">        <span class="keyword">elif</span> Fma[s] == <span class="string">&#x27;)&#x27;</span>:</span><br><span class="line">            s += <span class="number">1</span></span><br><span class="line">            <span class="keyword">break</span></span><br><span class="line">        <span class="keyword">else</span>:</span><br><span class="line">            res.push(Fma[s])</span><br><span class="line">            s += <span class="number">1</span></span><br><span class="line">    <span class="keyword">while</span> sta: res.push(sta.pop())</span><br><span class="line">    <span class="keyword">return</span> s-_s</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">middle2behind</span>(<span class="params">Formula</span>):</span><br><span class="line">    <span class="keyword">if</span> Formula.startswith(<span class="string">&#x27;-&#x27;</span>): Formula = <span class="string">&#x27;0&#x27;</span> + Formula</span><br><span class="line">    expr = _ep.findall(Formula.replace(<span class="string">&#x27;(-&#x27;</span>,<span class="string">&#x27;(0-&#x27;</span>))</span><br><span class="line">    res = Stack()</span><br><span class="line">    _middle2behind(expr, res, <span class="number">0</span>, <span class="built_in">len</span>(expr))</span><br><span class="line">    <span class="keyword">return</span> res</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">str2polynomial</span>(<span class="params">_<span class="built_in">str</span></span>):</span><br><span class="line">    <span class="keyword">if</span> _<span class="built_in">str</span>.endswith(<span class="string">&#x27;x&#x27;</span>):</span><br><span class="line">        <span class="keyword">if</span> _<span class="built_in">str</span> == <span class="string">&#x27;x&#x27;</span>: <span class="keyword">return</span> Polynomial((<span class="number">0</span>, <span class="number">1</span>))</span><br><span class="line">        <span class="keyword">return</span> Polynomial((<span class="number">0</span>, _<span class="built_in">str</span>.rstrip(<span class="string">&#x27;x&#x27;</span>)))</span><br><span class="line">    <span class="keyword">else</span>: <span class="keyword">return</span> Polynomial((_<span class="built_in">str</span>,))</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">not_eval</span>(<span class="params">Formula</span>):</span><br><span class="line">    expr = middle2behind(Formula)</span><br><span class="line">    <span class="comment">#print(expr)</span></span><br><span class="line">    sta = Stack()</span><br><span class="line">    <span class="keyword">for</span> item <span class="keyword">in</span> expr:</span><br><span class="line">        <span class="keyword">if</span> item <span class="keyword">in</span> _op:</span><br><span class="line">            y = sta.pop()</span><br><span class="line">            x = sta.pop()</span><br><span class="line">            _op[item](x, y)</span><br><span class="line">            sta.push(x)</span><br><span class="line">        <span class="keyword">else</span>: sta.push(str2polynomial(item))</span><br><span class="line">        <span class="comment">#print(sta)</span></span><br><span class="line">    <span class="keyword">return</span> sta.pop()</span><br><span class="line"></span><br><span class="line">_x = re.<span class="built_in">compile</span>(<span class="string">r&#x27;[a-zA-Z]+&#x27;</span>)</span><br><span class="line"><span class="keyword">def</span> <span class="title function_">solve_eq</span>(<span class="params">equation</span>):</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&#x27;equation is \t\t<span class="subst">&#123;equation&#125;</span>&#x27;</span>)</span><br><span class="line">    xname = <span class="built_in">set</span>(_x.findall(equation))</span><br><span class="line">    <span class="keyword">if</span> <span class="built_in">len</span>(xname) != <span class="number">1</span>: </span><br><span class="line">        <span class="comment">#print(xname)</span></span><br><span class="line">        <span class="built_in">print</span>(<span class="string">f&#x27;别逗，<span class="subst">&#123;equation&#125;</span>是一元一次方程吗?&#x27;</span>)</span><br><span class="line">        <span class="keyword">return</span></span><br><span class="line">    xname = xname.pop()</span><br><span class="line">    Fma = get_Formula(_x.sub(<span class="string">&#x27;x&#x27;</span>, equation))</span><br><span class="line">    <span class="keyword">if</span> <span class="built_in">len</span>(Fma) != <span class="number">2</span>:</span><br><span class="line">        <span class="built_in">print</span>(<span class="string">&#x27;&#123;equation&#125;不是标准方程！&#x27;</span>)</span><br><span class="line">        <span class="keyword">return</span></span><br><span class="line">    Fma = [not_eval(expr) <span class="keyword">for</span> expr <span class="keyword">in</span> Fma]</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&#x27;Simplification is \t<span class="subst">&#123;Fma[<span class="number">0</span>]&#125;</span> = <span class="subst">&#123;Fma[<span class="number">1</span>]&#125;</span>&#x27;</span>)</span><br><span class="line">    tmp = Fma[<span class="number">0</span>]</span><br><span class="line">    tmp.sub(Fma[<span class="number">1</span>])</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&#x27;Transposition is \t<span class="subst">&#123;tmp&#125;</span> = 0&#x27;</span>)</span><br><span class="line">    <span class="keyword">if</span> <span class="built_in">len</span>(tmp) &lt; <span class="number">2</span> <span class="keyword">or</span> tmp[<span class="number">1</span>] == <span class="number">0</span>:</span><br><span class="line">        <span class="built_in">print</span>(<span class="string">f&#x27;<span class="subst">&#123;xname&#125;</span> 无解&#x27;</span>)</span><br><span class="line">    <span class="keyword">else</span>:</span><br><span class="line">        x = -tmp[<span class="number">0</span>]/tmp[<span class="number">1</span>]</span><br><span class="line">        <span class="built_in">print</span>(<span class="string">f&#x27;<span class="subst">&#123;xname&#125;</span> = x = <span class="subst">&#123;x&#125;</span>&#x27;</span>)</span><br></pre></td></tr></table></figure>
                
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      <div>【探索】利用后缀表达式解方程</div>
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