PAT/source/html/a1002.html

A+B for Polynomials
<div class="ques-view"><p>This time, you are supposed to find <span class="katex"><span class="katex-mathml"><math><mrow><mi>A</mi><mo>+</mo><mi>B</mi></mrow>A+B</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathit">A</span><span class="mbin">+</span><span class="mord mathit" style="margin-right:0.05017em;">B</span></span></span></span> where <span class="katex"><span class="katex-mathml"><math><mrow><mi>A</mi></mrow>A</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">A</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><mi>B</mi></mrow>B</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05017em;">B</span></span></span></span> are two polynomials.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case. Each case occupies 2 lines, and each line contains the information of a polynomial: </p>
<p><span class="katex"><span class="katex-mathml"><math><mrow><mi>K</mi></mrow>K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>1</mn></msub></mrow>N_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>a</mi><mrow><msub><mi>N</mi><mn>1</mn></msub></mrow></msub></mrow>a_{N_1}</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>2</mn></msub></mrow>N_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>a</mi><mrow><msub><mi>N</mi><mn>2</mn></msub></mrow></msub></mrow>a_{N_2}</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> ... <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>K</mi></msub></mrow>N_K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.07153em;">K</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>a</mi><mrow><msub><mi>N</mi><mi>K</mi></msub></mrow></msub></mrow>a_{N_K}</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.680865em;vertical-align:-0.250305em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.14329285714285717em;margin-right:0.07142857142857144em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.07153em;">K</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span></p>
<p>where <span class="katex"><span class="katex-mathml"><math><mrow><mi>K</mi></mrow>K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span> is the number of nonzero terms in the polynomial, <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow>N_i</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>a</mi><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow></msub></mrow>a_{N_i}</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.68066em;vertical-align:-0.2501em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15000000000000002em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mtight"><span class="mord mathit mtight" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.143em;margin-right:0.07142857142857144em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-scriptstyle scriptscriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>⋯</mo><mo separator="true">,</mo><mi>K</mi></mrow>i=1, 2, \cdots , K</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="minner">⋯</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.07153em;">K</span></span></span></span>) are the exponents and coefficients, respectively. It is given that <span class="katex"><span class="katex-mathml"><math><mrow><mn>1</mn><mo>≤</mo><mi>K</mi><mo>≤</mo><mn>1</mn><mn>0</mn></mrow>1 \le K \le 10</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8193em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.07153em;">K</span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math><mrow><mn>0</mn><mo>≤</mo><msub><mi>N</mi><mi>K</mi></msub><mo>&lt;</mo><mo>⋯</mo><mo>&lt;</mo><msub><mi>N</mi><mn>2</mn></msub><mo>&lt;</mo><msub><mi>N</mi><mn>1</mn></msub><mo>≤</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow>0 \le N_K &lt; \cdots &lt; N_2 &lt; N_1 \le 1000</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span><span class="mrel">≤</span><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.07153em;">K</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mrel">&lt;</span><span class="minner">⋯</span><span class="mrel">&lt;</span><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mrel">&lt;</span><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.10903em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span></span></span></span>.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case you should output the sum of <span class="katex"><span class="katex-mathml"><math><mrow><mi>A</mi></mrow>A</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">A</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><mi>B</mi></mrow>B</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05017em;">B</span></span></span></span> in one line, with the same format as the input. Notice that there must be NO extra space at the end of each line. Please be accurate to 1 decimal place.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">2 1 2.4 0 3.2
2 2 1.5 1 0.5
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">3 2 1.5 1 2.9 0 3.2
</code></pre>
</div>