PAT/source/html/b1062.html

最简分数
<div class="ques-view"><p>一个分数一般写成两个整数相除的形式：<span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mi mathvariant="normal">/</mi><mi>M</mi></mrow>N/M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mord mathrm">/</span><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span>，其中 <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi></mrow>M</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;">M</span></span></span></span> 不为0。最简分数是指分子和分母没有公约数的分数表示形式。</p>
<p>现给定两个不相等的正分数 <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>1</mn></msub><mi mathvariant="normal">/</mi><msub><mi>M</mi><mn>1</mn></msub></mrow>N_1/M_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></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 class="mord mathrm">/</span><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">M</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> 和 <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>N</mi><mn>2</mn></msub><mi mathvariant="normal">/</mi><msub><mi>M</mi><mn>2</mn></msub></mrow>N_2/M_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></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 class="mord mathrm">/</span><span class="mord"><span class="mord mathit" style="margin-right:0.10903em;">M</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>，要求你按从小到大的顺序列出它们之间分母为 <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> 的最简分数。</p>
<h3 id="-">输入格式：</h3>
<p>输入在一行中按 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mi mathvariant="normal">/</mi><mi>M</mi></mrow>N/M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mord mathrm">/</span><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span> 的格式给出两个正分数，随后是一个正整数分母 <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>，其间以空格分隔。题目保证给出的所有整数都不超过 1000。</p>
<h3 id="-">输出格式：</h3>
<p>在一行中按 <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mi mathvariant="normal">/</mi><mi>M</mi></mrow>N/M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mord mathrm">/</span><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span> 的格式列出两个给定分数之间分母为 <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> 的所有最简分数，按从小到大的顺序，其间以 1 个空格分隔。行首尾不得有多余空格。题目保证至少有 1 个输出。</p>
<h3 id="-">输入样例：</h3>
<pre><code class="lang-in">7/18 13/20 12
</code></pre>
<h3 id="-">输出样例：</h3>
<pre><code class="lang-out">5/12 7/12
</code></pre>
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