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<!doctype html>
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<div id='write' class = 'is-node'><h1><a name='header-n0' class='md-header-anchor '></a>Midterm 1 Review</h1><h2><a name='header-n2' class='md-header-anchor '></a>Question 1</h2><pre class="md-fences md-end-block" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 4.16667px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 308px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre>x</pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">f_g_times</span>(<span class="cm-variable">f</span>, <span class="cm-variable">g</span>):</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-string">""" Define a function which returns a function that when applied</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> to x, applies f to x, g(x) number of times.</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> You may assume g(x) >= 0 for all x</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> h = f_g_times(lambda x: x+5, lambda x: x**2)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> h(3) # 3 + 5 * (3**2)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 48</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> h = f_g_times(lambda x: x**9, lambda x: 0)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> h(8)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 8</span></span></pre><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> """</span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 308px;"></div><div class="CodeMirror-gutters" style="display: none; height: 338px;"></div></div></div></pre><h2><a name='header-n4' class='md-header-anchor '></a>Question 2 (Modified Su17 MT Q8b)</h2><pre class="md-fences md-end-block" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 4.16667px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 360px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre>x</pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">hof_curry_add</span>(<span class="cm-variable">x</span>):</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-string">""" Define a function which accepts a number and returns a function</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> that also accepts a number and returns a function.</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> This process should repeated until x is the string 'Done' in which case</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> it should return the sum of all previous values</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> hof_curry_add(4)(6)(18)('Done') # 4 + 6 + 18</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 28</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> """</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">def</span> <span class="cm-def">helper</span>(<span class="cm-variable">______</span>):</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">if</span> <span class="cm-variable">________</span>:</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">return</span> <span class="cm-variable">________</span></span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">return</span> <span class="cm-keyword">lambda</span> <span class="cm-variable">x</span>: <span class="cm-variable">helper</span>(<span class="cm-variable">____________</span>)</span></pre></div><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">return</span> <span class="cm-keyword">lambda</span> <span class="cm-variable">y</span>: <span class="cm-variable">helper</span>(<span class="cm-variable">_________</span>)</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 360px;"></div><div class="CodeMirror-gutters" style="display: none; height: 390px;"></div></div></div></pre><h3><a name='header-n6' class='md-header-anchor '></a>Question 3</h3><pre class="md-fences md-end-block" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 4.16667px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 257px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre>x</pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">swap_digits</span>(<span class="cm-variable">x</span>):</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-string">""" Define a function which reverses each pair of digits</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> swap_digits(1234) # 1 <-> 2, 3 <-> 4</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 2143</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> swap_digits(13131)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 11313</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> swap_digits(123)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> 132</span></span></pre><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> """</span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 257px;"></div><div class="CodeMirror-gutters" style="display: none; height: 287px;"></div></div></div></pre><h2><a name='header-n8' class='md-header-anchor '></a>Question 4</h2><pre class="md-fences md-end-block md-focus" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap CodeMirror-focused"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 231.249px; left: 76.9206px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 257px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre>x</pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="" style="position: relative;"><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">div_digits</span>(<span class="cm-variable">x</span>, <span class="cm-variable">y</span>):</span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-string">""" Returns a binary string (string with only 0s and 1s) such that</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> the ith item in the string is 1 if the ith digit in x is divisible by</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> the ith digit in y (assume x and y are of same length)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> div_digits(66485, 28274)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> '10100'</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> >>> div_digits(999999, 332323)</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> '110101'</span></span></pre><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-string"> """</span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 257px;"></div><div class="CodeMirror-gutters" style="display: none; height: 287px;"></div></div></div></pre><p></p><h2><a name='header-n12' class='md-header-anchor '></a>Question 5</h2><p>Draw Environment Diagram for:</p><pre class="md-fences md-end-block" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 3.99306px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 180px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">x</span> = <span class="cm-number">10</span></span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">f</span>(<span class="cm-variable">x</span>):</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-variable">x</span> += <span class="cm-number">8</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-variable">g</span> = <span class="cm-keyword">lambda</span> <span class="cm-variable">y</span>: <span class="cm-variable">x</span> <span class="cm-operator">+</span> <span class="cm-variable">y</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"> <span class="cm-keyword">return</span> <span class="cm-variable">g</span></span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">h</span> = <span class="cm-variable">f</span>(<span class="cm-number">10</span>)</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">n</span> = <span class="cm-variable">h</span>(<span class="cm-number">6</span>)</span></pre></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 180px;"></div><div class="CodeMirror-gutters" style="display: none; height: 210px;"></div></div></div></pre><h2><a name='header-n16' class='md-header-anchor '></a>Question 6</h2><h3><a name='header-n17' class='md-header-anchor '></a>I don't like this one but try it if you'd like</h3><p>Draw Environment Diagram for: (callable returns <code>True</code> if <code>f</code> is a function)</p><pre class="md-fences md-end-block" lang="python"> <div class="CodeMirror cm-s-inner CodeMirror-wrap"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 0px; left: 3.99306px;"></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 0px; margin-bottom: 0px; border-right-width: 30px; min-height: 128px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: 0px; width: 0px;"></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">f</span> = <span class="cm-number">87</span></span></pre></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">def</span> <span class="cm-def">f</span>(<span class="cm-variable">f</span>):</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-variable">f</span> = <span class="cm-variable">f</span>(<span class="cm-variable">f</span>)</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-tab" role="presentation" cm-text=" "> </span><span class="cm-keyword">return</span> <span class="cm-variable">f</span>(<span class="cm-number">1</span>)</span></pre><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">f</span> = <span class="cm-variable">f</span>(<span class="cm-keyword">lambda</span> <span class="cm-variable">f</span>: (<span class="cm-keyword">lambda</span> <span class="cm-variable">x</span>: <span class="cm-variable">f</span>(<span class="cm-number">42</span>) <span class="cm-operator">+</span> <span class="cm-number">2</span><span class="cm-operator">*</span><span class="cm-variable">x</span><span class="cm-operator">**</span><span class="cm-number">3</span>) <span class="cm-keyword">if</span> <span class="cm-builtin">callable</span>(<span class="cm-variable">f</span>) <span class="cm-keyword">else</span> <span class="cm-variable">f</span> <span class="cm-operator">-</span> <span class="cm-number">25</span>)</span></pre></div></div></div></div></div><div style="position: absolute; height: 30px; width: 1px; border-bottom: 0px solid transparent; top: 128px;"></div><div class="CodeMirror-gutters" style="display: none; height: 158px;"></div></div></div></pre><p></p></div>
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