PAT/source/html/a1060.html

Are They Equal
<div class="ques-view"><p>If a machine can save only 3 significant digits, the float numbers 12300 and 12358.9 are considered equal since they are both saved as <span class="katex"><span class="katex-mathml"><math><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>1</mn><mn>2</mn><mn>3</mn><mo>×</mo><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup></mrow>0.123\times 10^5</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">1</span><span class="mord mathrm">2</span><span class="mord mathrm">3</span><span class="mbin">×</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">5</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> with simple chopping. Now given the number of significant digits on a machine and two float numbers, you are supposed to tell if they are treated equal in that machine.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case which gives three numbers <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</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:0.10903em;">N</span></span></span></span>, <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>, where <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</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:0.10903em;">N</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mo>&lt;</mo><mn>1</mn><mn>0</mn><mn>0</mn></mrow>&lt;100</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.68354em;vertical-align:-0.0391em;"></span><span class="base textstyle uncramped"><span class="mrel">&lt;</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span></span></span></span>) is the number of significant digits, and <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 the two float numbers to be compared. Each float number is non-negative, no greater than <span class="katex"><span class="katex-mathml"><math><mrow><mn>1</mn><msup><mn>0</mn><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></msup></mrow>10^{100}</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord scriptstyle uncramped mtight"><span class="mord mathrm mtight">1</span><span class="mord mathrm mtight">0</span><span class="mord mathrm mtight">0</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>, and that its total digit number is less than 100.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case, print in a line <code>YES</code> if the two numbers are treated equal, and then the number in the standard form <code>0.d[1]...d[N]*10^k</code> (<code>d[1]</code>&gt;0 unless the number is 0); or <code>NO</code> if they are not treated equal, and then the two numbers in their standard form. All the terms must be separated by a space, with no extra space at the end of a line.</p>
<p>Note: Simple chopping is assumed without rounding.</p>
<h3 id="sample-input-1-">Sample Input 1:</h3>
<pre><code class="lang-in">3 12300 12358.9
</code></pre>
<h3 id="sample-output-1-">Sample Output 1:</h3>
<pre><code class="lang-out">YES 0.123*10^5
</code></pre>
<h3 id="sample-input-2-">Sample Input 2:</h3>
<pre><code class="lang-in">3 120 128
</code></pre>
<h3 id="sample-output-2-">Sample Output 2:</h3>
<pre><code class="lang-out">NO 0.120*10^3 0.128*10^3
</code></pre>
</div>