PAT/source/html/b1063.html

计算谱半径
<div class="ques-view"><p>在数学中，矩阵的“谱半径”是指其特征值的模集合的上确界。换言之，对于给定的 <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:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">n</span></span></span></span> 个复数空间的特征值 { <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>a</mi><mn>1</mn></msub><mo>+</mo><msub><mi>b</mi><mn>1</mn></msub><mi>i</mi><mo separator="true">,</mo><mo>⋯</mo><mo separator="true">,</mo><msub><mi>a</mi><mi>n</mi></msub><mo>+</mo><msub><mi>b</mi><mi>n</mi></msub><mi>i</mi></mrow>a_1+b_1i, \cdots , a_n+b_ni</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></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 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="mbin">+</span><span class="mord"><span class="mord mathit">b</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 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 mathit">i</span><span class="mpunct">,</span><span class="minner">⋯</span><span class="mpunct">,</span><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 mathit mtight">n</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="mbin">+</span><span class="mord"><span class="mord mathit">b</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 mathit mtight">n</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 mathit">i</span></span></span></span> }，它们的模为实部与虚部的平方和的开方，而“谱半径”就是最大模。</p>
<p>现在给定一些复数空间的特征值，请你计算并输出这些特征值的谱半径。</p>
<h3 id="-">输入格式：</h3>
<p>输入第一行给出正整数 N（<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo></mrow>\le</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.63597em;"></span><span class="strut bottom" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span></span></span></span> 10 000）是输入的特征值的个数。随后 N 行，每行给出 1 个特征值的实部和虚部，其间以空格分隔。注意：题目保证实部和虚部均为绝对值不超过 1000 的整数。</p>
<h3 id="-">输出格式：</h3>
<p>在一行中输出谱半径，四舍五入保留小数点后 2 位。</p>
<h3 id="-">输入样例：</h3>
<pre><code class="lang-in">5
0 1
2 0
-1 0
3 3
0 -3
</code></pre>
<h3 id="-">输出样例：</h3>
<pre><code class="lang-out">4.24
</code></pre>
</div>