【C++】B2069 求分数序列和题目解析与优化详解

news/2024/12/26 18:24:41 标签: c, c

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文章目录

💯前言
💯题目描述
- 输入格式
- 输出格式
- 输入输出样例
- - 输入：
  - 输出：
💯解题思路
- 分析题目
- 解题步骤
💯代码实现
- 我的代码实现
- - 实现特点
- 老师的代码实现
- - 实现特点
  - 优点
  - 缺点
💯对比分析
💯优化方案
- - 改进点
💯小结

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💯前言

本篇文章将详细解析洛谷B2069题“求分数列和”的解题过程࿰class="tags" href="/tags/C.html" title=c>c;包括题目的详细描述、解题思路、不同代码实现方案的比较与优化࿰class="tags" href="/tags/C.html" title=c>c;以及对相关概念的深入拓展。文章的目标是帮助读者全面掌握此类题目的解法࿰class="tags" href="/tags/C.html" title=c>c;并提升在C++编程中的逻辑分析与代码优化能力。
C++ 参考手册
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💯题目描述

B2069 求分数序列和
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有一个分数序列：

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margin-left: -0.0359em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">4class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.4811em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mpunclass="tags" href="/tags/C.html" title=c>ct">,class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.1667em;">class="tags" href="/tags/C.html" title=c>class="minner">⋯

其中࿰class="tags" href="/tags/C.html" title=c>c;满足递推关系：

class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q i + 1 = q i + p i q_{i+1} = q_i + p_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.7778em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">
class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p i + 1 = q i p_{i+1} = q_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">
初始值 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q 1 = 2 q_1 = 2 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3011em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">2, class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p 1 = 1 p_1 = 1 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3011em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">1。

例如࿰class="tags" href="/tags/C.html" title=c>c;前6项依次为：
class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> 2 1 , 3 2 , 5 3 , 8 5 , 13 8 , 21 13 \fraclass="tags" href="/tags/C.html" title=c>c{2}{1}, \fraclass="tags" href="/tags/C.html" title=c>c{3}{2}, \fraclass="tags" href="/tags/C.html" title=c>c{5}{3}, \fraclass="tags" href="/tags/C.html" title=c>c{8}{5}, \fraclass="tags" href="/tags/C.html" title=c>c{13}{8}, \fraclass="tags" href="/tags/C.html" title=c>c{21}{13} class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 1.1901em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.345em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.394em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">2class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.345em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mpunclass="tags" href="/tags/C.html" title=c>ct">,class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.1667em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">2class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.394em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">3class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.345em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mpunclass="tags" href="/tags/C.html" title=c>ct">,class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.1667em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">3class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.394em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">5class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.345em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mpunclass="tags" href="/tags/C.html" title=c>ct">,class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.1667em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">5class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" 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title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">8class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" 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href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.8451em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">13class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.394em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">21class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.345em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">

任务是计算分数序列前 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n n class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">n 项的和。结果保留4位小数。

输入格式

输入一行包含一个正整数 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n n class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">n（class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n ≤ 30 n \leq 30 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.7719em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.136em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">nclass="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">≤class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">30）。

输出格式

输出一行浮点数࿰class="tags" href="/tags/C.html" title=c>c;表示分数序列前 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n n class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">n 项之和࿰class="tags" href="/tags/C.html" title=c>c;精确到小数点后4位。

输入输出样例

输入：

<class="tags" href="/tags/C.html" title=c>code>2
class="tags" href="/tags/C.html" title=c>code>

输出：

<class="tags" href="/tags/C.html" title=c>code>3.5000
class="tags" href="/tags/C.html" title=c>code>

💯解题思路

分析题目

递推关系：
- 序列的分子和分母满足递推关系：
  class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q i + 1 = q i + p i q_{i+1} = q_i + p_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.7778em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">
  class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p i + 1 = q i p_{i+1} = q_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">
- 初始条件为 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q 1 = 2 q_1 = 2 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3011em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">2, class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p 1 = 1 p_1 = 1 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3011em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">1。
目标：
- 计算前 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n n class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">n 项的分数和：
  class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> sum = q 1 p 1 + q 2 p 2 + ⋯ + q n p n \text{sum} = \fraclass="tags" href="/tags/C.html" title=c>c{q_1}{p_1} + \fraclass="tags" href="/tags/C.html" title=c>c{q_2}{p_2} + \class="tags" href="/tags/C.html" title=c>cdots + \fraclass="tags" href="/tags/C.html" title=c>c{q_n}{p_n} class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord text">class="tags" href="/tags/C.html" title=c>class="mord">sumclass="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 1.2286em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.4811em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.7475em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3173em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.4461em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3173em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: -0.0359em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.4811em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 1.2286em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.4811em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.7475em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3173em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">2class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.4461em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3173em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: -0.0359em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">2class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.4811em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6667em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.0833em;">class="tags" href="/tags/C.html" title=c>class="minner">⋯class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 1.2286em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.4811em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.7475em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.1645em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: 0em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">nclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.4461em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.1645em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.357em; margin-left: -0.0359em; margin-right: 0.0714em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.5em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size3 size1 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">nclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.143em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.4811em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">
数据范围：
- class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> n ≤ 30 n \leq 30 class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.7719em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.136em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">nclass="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">≤class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6444em;">class="tags" href="/tags/C.html" title=c>class="mord">30࿰class="tags" href="/tags/C.html" title=c>c;意味着序列递推和累加的规模较小࿰class="tags" href="/tags/C.html" title=c>c;可以采用简单的迭代方式解决。
精度要求：
- 输出结果保留小数点后4位。

解题步骤

初始化变量：
- 定义两个变量分别表示分子 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q q class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">q 和分母 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p p class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">p。
- 定义一个变量 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> s u m sum class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.4306em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">sclass="tags" href="/tags/C.html" title=c>class="mord mathnormal">uclass="tags" href="/tags/C.html" title=c>class="mord mathnormal">m 用于累加结果。
递推计算：
- 根据公式更新 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q q class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">q 和 class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p p class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">p。
- 累加当前项的分数值：class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q p \fraclass="tags" href="/tags/C.html" title=c>c{q}{p} class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 1.2286em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.4811em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mopen nulldelimiter">class="tags" href="/tags/C.html" title=c>class="mfraclass="tags" href="/tags/C.html" title=c>c">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.7475em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.655em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">pclass="tags" href="/tags/C.html" title=c>class="" style="top: -3.23em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="fraclass="tags" href="/tags/C.html" title=c>c-line" style="border-bottom-width: 0.04em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -3.4461em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 3em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.4811em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mclass="tags" href="/tags/C.html" title=c>close nulldelimiter">。
输出结果：
- 使用浮点数输出࿰class="tags" href="/tags/C.html" title=c>c;保留小数点后4位。

💯代码实现

我的代码实现

以下是我的代码实现：

<class="tags" href="/tags/C.html" title=c>code class="tags" href="/tags/C.html" title=c>class="prism language-class="tags" href="/tags/C.html" title=c>cpp">class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><iostream>
class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><class="tags" href="/tags/C.html" title=c>cstdio>
class="tags" href="/tags/C.html" title=c>class="token keyword">using class="tags" href="/tags/C.html" title=c>class="token keyword">namespaclass="tags" href="/tags/C.html" title=c>ce stdclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;

class="tags" href="/tags/C.html" title=c>class="token keyword">int class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">mainclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
    class="tags" href="/tags/C.html" title=c>class="token keyword">double sum class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 累加和࿰class="tags" href="/tags/C.html" title=c>c;双精度浮点数
    class="tags" href="/tags/C.html" title=c>class="token keyword">int n class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">, temp class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
    class="tags" href="/tags/C.html" title=c>class="token keyword">int z class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">2class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">, m class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">1class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 初始化分子和分母

    class="tags" href="/tags/C.html" title=c>cin class="tags" href="/tags/C.html" title=c>class="token operator">>> nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
    class="tags" href="/tags/C.html" title=c>class="token keyword">for class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token keyword">int i class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; i class="tags" href="/tags/C.html" title=c>class="token operator">< nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; iclass="tags" href="/tags/C.html" title=c>class="token operator">++class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
        sum class="tags" href="/tags/C.html" title=c>class="token operator">+= z class="tags" href="/tags/C.html" title=c>class="token operator">* class="tags" href="/tags/C.html" title=c>class="token number">1.0 class="tags" href="/tags/C.html" title=c>class="token operator">/ mclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 累加当前项
        temp class="tags" href="/tags/C.html" title=c>class="token operator">= zclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;           class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 暂存当前分子
        z class="tags" href="/tags/C.html" title=c>class="token operator">= z class="tags" href="/tags/C.html" title=c>class="token operator">+ mclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;          class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 计算新的分子
        m class="tags" href="/tags/C.html" title=c>class="token operator">= tempclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;           class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 更新分母为旧的分子
    class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}

    class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">printfclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token string">"%.4lf"class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">, sumclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">)class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 输出结果࿰class="tags" href="/tags/C.html" title=c>c;保留 4 位小数
    class="tags" href="/tags/C.html" title=c>class="token keyword">return class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}
class="tags" href="/tags/C.html" title=c>code>

实现特点

变量设计：
- 使用 <class="tags" href="/tags/C.html" title=c>code>zclass="tags" href="/tags/C.html" title=c>code> 表示当前分子࿰class="tags" href="/tags/C.html" title=c>c;<class="tags" href="/tags/C.html" title=c>code>mclass="tags" href="/tags/C.html" title=c>code> 表示当前分母。
- 使用 <class="tags" href="/tags/C.html" title=c>code>tempclass="tags" href="/tags/C.html" title=c>code> 保存中间变量࿰class="tags" href="/tags/C.html" title=c>c;避免覆盖数据。
核心递推逻辑：
- class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> q i + 1 = q i + p i q_{i+1} = q_i + p_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.7778em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="mbin">+class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2222em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class=""> 用 <class="tags" href="/tags/C.html" title=c>code>z = z + mclass="tags" href="/tags/C.html" title=c>code> 实现。
- class="tags" href="/tags/C.html" title=c>class="katex--inline">class="tags" href="/tags/C.html" title=c>class="katex">class="tags" href="/tags/C.html" title=c>class="katex-mathml"> p i + 1 = q i p_{i+1} = q_i class="tags" href="/tags/C.html" title=c>class="katex-html">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.6389em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.2083em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal">pclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="mbin mtight">+class="tags" href="/tags/C.html" title=c>class="mord mtight">1class="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.2083em;">class="tags" href="/tags/C.html" title=c>class="">class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="mrel">=class="tags" href="/tags/C.html" title=c>class="mspaclass="tags" href="/tags/C.html" title=c>ce" style="margin-right: 0.2778em;">class="tags" href="/tags/C.html" title=c>class="base">class="tags" href="/tags/C.html" title=c>class="strut" style="height: 0.625em; verticlass="tags" href="/tags/C.html" title=c>cal-align: -0.1944em;">class="tags" href="/tags/C.html" title=c>class="mord">class="tags" href="/tags/C.html" title=c>class="mord mathnormal" style="margin-right: 0.0359em;">qclass="tags" href="/tags/C.html" title=c>class="msupsub">class="tags" href="/tags/C.html" title=c>class="vlist-t vlist-t2">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.3117em;">class="tags" href="/tags/C.html" title=c>class="" style="top: -2.55em; margin-left: -0.0359em; margin-right: 0.05em;">class="tags" href="/tags/C.html" title=c>class="pstrut" style="height: 2.7em;">class="tags" href="/tags/C.html" title=c>class="sizing reset-size6 size3 mtight">class="tags" href="/tags/C.html" title=c>class="mord mathnormal mtight">iclass="tags" href="/tags/C.html" title=c>class="vlist-s">class="tags" href="/tags/C.html" title=c>class="vlist-r">class="tags" href="/tags/C.html" title=c>class="vlist" style="height: 0.15em;">class="tags" href="/tags/C.html" title=c>class=""> 用 <class="tags" href="/tags/C.html" title=c>code>m = tempclass="tags" href="/tags/C.html" title=c>code> 实现。
浮点数计算：
- 显式将 <class="tags" href="/tags/C.html" title=c>code>z / mclass="tags" href="/tags/C.html" title=c>code> 转换为浮点数计算࿰class="tags" href="/tags/C.html" title=c>c;确保精度。
结果输出：
- 使用 <class="tags" href="/tags/C.html" title=c>code>printfclass="tags" href="/tags/C.html" title=c>code> 保留4位小数。

老师的代码实现

以下是老师给出的代码实现：

<class="tags" href="/tags/C.html" title=c>code class="tags" href="/tags/C.html" title=c>class="prism language-class="tags" href="/tags/C.html" title=c>cpp">class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><iostream>
class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><class="tags" href="/tags/C.html" title=c>cstdio> class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 用于 printf
class="tags" href="/tags/C.html" title=c>class="token keyword">using class="tags" href="/tags/C.html" title=c>class="token keyword">namespaclass="tags" href="/tags/C.html" title=c>ce stdclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;

class="tags" href="/tags/C.html" title=c>class="token keyword">int class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">mainclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
    class="tags" href="/tags/C.html" title=c>class="token keyword">int n class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
    class="tags" href="/tags/C.html" title=c>cin class="tags" href="/tags/C.html" title=c>class="token operator">>> nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;

    class="tags" href="/tags/C.html" title=c>class="token keyword">float sum class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 累加和࿰class="tags" href="/tags/C.html" title=c>c;浮点类型
    class="tags" href="/tags/C.html" title=c>class="token keyword">float q class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">2class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;   class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 初始化分子 q
    class="tags" href="/tags/C.html" title=c>class="token keyword">float p class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">1class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;   class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 初始化分母 p

    class="tags" href="/tags/C.html" title=c>class="token keyword">for class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token keyword">int i class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; i class="tags" href="/tags/C.html" title=c>class="token operator">< nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; iclass="tags" href="/tags/C.html" title=c>class="token operator">++class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
        sum class="tags" href="/tags/C.html" title=c>class="token operator">+= q class="tags" href="/tags/C.html" title=c>class="token operator">/ pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 累加当前项
        q class="tags" href="/tags/C.html" title=c>class="token operator">= q class="tags" href="/tags/C.html" title=c>class="token operator">+ pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;    class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 计算新的 q
        p class="tags" href="/tags/C.html" title=c>class="token operator">= q class="tags" href="/tags/C.html" title=c>class="token operator">- pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;    class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 计算新的 p
    class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}

    class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">printfclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token string">"%.4f\n"class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">, sumclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">)class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 输出结果࿰class="tags" href="/tags/C.html" title=c>c;保留 4 位小数
    class="tags" href="/tags/C.html" title=c>class="token keyword">return class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}
class="tags" href="/tags/C.html" title=c>code>

实现特点

变量优化：
- 直接使用 <class="tags" href="/tags/C.html" title=c>code>floatclass="tags" href="/tags/C.html" title=c>code> 类型计算࿰class="tags" href="/tags/C.html" title=c>c;避免临时变量。
核心递推逻辑：
- 使用 <class="tags" href="/tags/C.html" title=c>code>q = q + pclass="tags" href="/tags/C.html" title=c>code> 和 <class="tags" href="/tags/C.html" title=c>code>p = q - pclass="tags" href="/tags/C.html" title=c>code> 通过数学公式简化更新。
结果输出：
- 同样使用 <class="tags" href="/tags/C.html" title=c>code>printfclass="tags" href="/tags/C.html" title=c>code> 保留4位小数。

优点

代码简洁：
- 变量数量少࿰class="tags" href="/tags/C.html" title=c>c;通过数学公式避免了中间变量。
逻辑紧凑：
- 更新 <class="tags" href="/tags/C.html" title=c>code>pclass="tags" href="/tags/C.html" title=c>code> 的方式非常简练࿰class="tags" href="/tags/C.html" title=c>c;体现了数学上的优化。

缺点

可读性较差：
- <class="tags" href="/tags/C.html" title=c>code>p = q - pclass="tags" href="/tags/C.html" title=c>code> 的逻辑不够直观࿰class="tags" href="/tags/C.html" title=c>c;对初学者不够友好。
精度问题：
- 使用 <class="tags" href="/tags/C.html" title=c>code>floatclass="tags" href="/tags/C.html" title=c>code> 类型可能导致精度不足。

💯对比分析

对比点	我的代码	老师的代码
变量数量	多一个临时变量 <class="tags" href="/tags/C.html" title=c>code>tempclass="tags" href="/tags/C.html" title=c>code>	仅用两个变量 <class="tags" href="/tags/C.html" title=c>code>qclass="tags" href="/tags/C.html" title=c>code> 和 <class="tags" href="/tags/C.html" title=c>code>pclass="tags" href="/tags/C.html" title=c>code>
代码可读性	逻辑清晰࿰class="tags" href="/tags/C.html" title=c>c;易于理解	数学简化逻辑不直观
浮点精度	使用 <class="tags" href="/tags/C.html" title=c>code>doubleclass="tags" href="/tags/C.html" title=c>code>࿰class="tags" href="/tags/C.html" title=c>c;精度更高	使用 <class="tags" href="/tags/C.html" title=c>code>floatclass="tags" href="/tags/C.html" title=c>code>࿰class="tags" href="/tags/C.html" title=c>c;精度稍低
内存使用	稍高࿰class="tags" href="/tags/C.html" title=c>c;多用了一个变量	更低࿰class="tags" href="/tags/C.html" title=c>c;只用了必要的变量
实现复杂度	适中࿰class="tags" href="/tags/C.html" title=c>c;易于实现和调试	较低࿰class="tags" href="/tags/C.html" title=c>c;但对理解有一定要求

💯优化方案

结合两者的优点࿰class="tags" href="/tags/C.html" title=c>c;我们可以进一步优化代码：

<class="tags" href="/tags/C.html" title=c>code class="tags" href="/tags/C.html" title=c>class="prism language-class="tags" href="/tags/C.html" title=c>cpp">class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><iostream>
class="tags" href="/tags/C.html" title=c>class="token maclass="tags" href="/tags/C.html" title=c>cro property">class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive-hash">#class="tags" href="/tags/C.html" title=c>class="token direclass="tags" href="/tags/C.html" title=c>ctive keyword">inclass="tags" href="/tags/C.html" title=c>clude class="tags" href="/tags/C.html" title=c>class="token string"><iomanip> class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 用于控制输出精度
class="tags" href="/tags/C.html" title=c>class="token keyword">using class="tags" href="/tags/C.html" title=c>class="token keyword">namespaclass="tags" href="/tags/C.html" title=c>ce stdclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;

class="tags" href="/tags/C.html" title=c>class="token keyword">int class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">mainclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
    class="tags" href="/tags/C.html" title=c>class="token keyword">int nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
    class="tags" href="/tags/C.html" title=c>cin class="tags" href="/tags/C.html" title=c>class="token operator">>> nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;

    class="tags" href="/tags/C.html" title=c>class="token keyword">double sum class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0.0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 使用 double 提高精度
    class="tags" href="/tags/C.html" title=c>class="token keyword">int q class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">2class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">, p class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">1class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 分子和分母初始化

    class="tags" href="/tags/C.html" title=c>class="token keyword">for class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token keyword">int i class="tags" href="/tags/C.html" title=c>class="token operator">= class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; i class="tags" href="/tags/C.html" title=c>class="token operator">< nclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; iclass="tags" href="/tags/C.html" title=c>class="token operator">++class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">{
        sum class="tags" href="/tags/C.html" title=c>class="token operator">+= class="tags" href="/tags/C.html" title=c>class="token genericlass="tags" href="/tags/C.html" title=c>c-funclass="tags" href="/tags/C.html" title=c>ction">class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">staticlass="tags" href="/tags/C.html" title=c>c_class="tags" href="/tags/C.html" title=c>castclass="tags" href="/tags/C.html" title=c>class="token genericlass="tags" href="/tags/C.html" title=c>c class="tags" href="/tags/C.html" title=c>class-name">class="tags" href="/tags/C.html" title=c>class="token operator"><class="tags" href="/tags/C.html" title=c>class="token keyword">doubleclass="tags" href="/tags/C.html" title=c>class="token operator">>class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(qclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token operator">/ pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 显式类型转换
        q class="tags" href="/tags/C.html" title=c>class="token operator">= q class="tags" href="/tags/C.html" title=c>class="token operator">+ pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 直接更新分子
        p class="tags" href="/tags/C.html" title=c>class="token operator">= q class="tags" href="/tags/C.html" title=c>class="token operator">- pclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 通过差值更新分母
    class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}

    class="tags" href="/tags/C.html" title=c>cout class="tags" href="/tags/C.html" title=c>class="token operator"><< fixed class="tags" href="/tags/C.html" title=c>class="token operator"><< class="tags" href="/tags/C.html" title=c>class="token funclass="tags" href="/tags/C.html" title=c>ction">setpreclass="tags" href="/tags/C.html" title=c>cisionclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">(class="tags" href="/tags/C.html" title=c>class="token number">4class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">) class="tags" href="/tags/C.html" title=c>class="token operator"><< sum class="tags" href="/tags/C.html" title=c>class="token operator"><< endlclass="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">; class="tags" href="/tags/C.html" title=c>class="token class="tags" href="/tags/C.html" title=c>comment">// 使用现代化流输出
    class="tags" href="/tags/C.html" title=c>class="token keyword">return class="tags" href="/tags/C.html" title=c>class="token number">0class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">;
class="tags" href="/tags/C.html" title=c>class="token punclass="tags" href="/tags/C.html" title=c>ctuation">}
class="tags" href="/tags/C.html" title=c>code>

改进点

精度提升：
- 使用 <class="tags" href="/tags/C.html" title=c>code>doubleclass="tags" href="/tags/C.html" title=c>code> 类型以提高浮点运算的精度。
代码简化：
- 去掉了临时变量࿰class="tags" href="/tags/C.html" title=c>c;简化逻辑。
现代化风格：
- 使用 <class="tags" href="/tags/C.html" title=c>code>class="tags" href="/tags/C.html" title=c>coutclass="tags" href="/tags/C.html" title=c>code> 和 <class="tags" href="/tags/C.html" title=c>code>setpreclass="tags" href="/tags/C.html" title=c>cisionclass="tags" href="/tags/C.html" title=c>code> 替代 <class="tags" href="/tags/C.html" title=c>code>printfclass="tags" href="/tags/C.html" title=c>code>࿰class="tags" href="/tags/C.html" title=c>c;更符合 C++ 标准。

💯小结

本题主要考察递推关系的理解与实现能力࿰class="tags" href="/tags/C.html" title=c>c;同时对浮点数精度控制和代码优化提出了要求。在解题过程中࿰class="tags" href="/tags/C.html" title=c>c;我们需要：

明确数列的递推关系。
合理设计变量以实现递推计算。
结合题目需求选择合适的浮点类型与输出方式。

通过对不同代码实现方案的比较与优化࿰class="tags" href="/tags/C.html" title=c>c;我们不仅学会了更高效的解题方法࿰class="tags" href="/tags/C.html" title=c>c;还理解了代码设计中的权衡取舍。希望本文能为读者提供帮助࿰class="tags" href="/tags/C.html" title=c>c;在未来的编程学习中取得更大的进步！

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