build_notes_simengweb/assets/index.html-D9EAuU7p.js

import{_ as i,c as a,a as n,o as h}from"./app-Bph9hmvC.js";const k={};function l(p,s){return h(),a("div",null,[...s[0]||(s[0]=[n(`<h2 id="一、x-质数" tabindex="-1"><a class="header-anchor" href="#一、x-质数"><span>一、X 质数</span></a></h2><h3 id="题目" tabindex="-1"><a class="header-anchor" href="#题目"><span>题目</span></a></h3><p>题目链接：0X质数 - 蓝桥云课</p><h3 id="问题描述" tabindex="-1"><a class="header-anchor" href="#问题描述"><span>问题描述</span></a></h3><p>对于一个含有 M 个数位的正整数 N ，任意选中其中 K 个不同的数位（0≤K&lt;M），将这些选中的数位删除之后，余下的数位按照原来的顺序组成了一个新的数字 P 。如果至少存在一个 P 是质数，我们就称 N 是一个 X 质数。例如，对于整数 7869 ，我们可以删去 7 和 6 ，得到一个新的数字 89 ，由于 89 是一个质数，因此 7869 是一个 X 质数。又如，对于整数 77 ，可以删去一个 7 后变为质数 7 ，因此 77 也是一个 X 质数。</p><p>请问 1 （含）至 1000000（含）中一共有多少个不同的 X 质数。</p><h3 id="解析" tabindex="-1"><a class="header-anchor" href="#解析"><span>解析</span></a></h3><p>先通过埃氏筛，获取到范围内的所有质数。然后遍历每个数字的所有子串，查看是否满足 X 质数的定义，我们只要找到一个符合条件的子串即可退出循环，只要子串是质数或者 X 质数，我们都可以认定当前数字为 X 质数。</p><p>这里在寻找每个数的子串的时候，可以采用二进制的方式，详情查看：通过位运算快速生成所有的子序列|祀梦的个人博客</p><h3 id="答案" tabindex="-1"><a class="header-anchor" href="#答案"><span>答案</span></a></h3><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># import os</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># import sys</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># def is_prime(n):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     _nums = [True] * (n + 1)</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     _nums[0] = _nums[1] = False</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     for i in range(2, n):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#         if _nums[i]:</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#             for j in range(i ** 2, n + 1, i):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#                 _nums[j] = False</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     return _nums</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># N = 1000000</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># nums = is_prime(N)</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># ans = 0</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># for num in range(N + 1):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     digits = [int(n) for n in str(num)]</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     length = len(str(num))</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#     for mask in range(1,1 &lt;&lt; length):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#         subseq = 0</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#         for i in range(length):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#             if mask &amp; ( 1 &lt;&lt; i ):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#                 subseq = subseq * 10 + digits[i]</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#         if nums[subseq]:</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#             nums[num] = True</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#             ans += 1</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">#             break</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># print(ans) # 989457</span></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">989457</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="二、顶板上的正方形" tabindex="-1"><a class="header-anchor" href="#二、顶板上的正方形"><span>二、顶板上的正方形</span></a></h2><h3 id="题目-1" tabindex="-1"><a class="header-anchor" href="#题目-1"><span>题目</span></a></h3><p>题目链接：0钉板上的正方形 - 蓝桥云课</p><h3 id="问题描述-1" tabindex="-1"><a class="header-anchor" href="#问题描述-1"><span>问题描述</span></a></h3><p>小蓝有一个大小为 10×1010×10 钉板，如下图所示，上面等距分布着 10×1010×10 个钉槽(上下/左右相邻的钉槽之间的距离均相同)。其中有一些钉槽上面有钉子， 在图中用红色来进行标注，白色则表示此处没有钉子。小蓝喜欢用橡皮筋在钉 子上围出正方形图案，即选择钉板上的四个钉子，将其作为正方形的四个顶点， 从而把橡皮筋拉伸为一个正方形。</p><p>现在，小蓝想要知道在这个钉板上，可以围出多少种边长不同的正方 形?(相同边长的正方形均视作是同一种，不用考虑正方形的位置)。图中展示 了三种不同边长的正方形，其中蓝色线条表示橡皮筋。</p><h3 id="解析-1" tabindex="-1"><a class="header-anchor" href="#解析-1"><span>解析</span></a></h3><p>参考了评论区的大哥（马国良的个人主页 - 蓝桥云课）的思路，如下图所示</p><p>dr 为行之间的差距</p><p>dc 为列之间的差距</p><p>我们遍历 A 和 B，计算 C 和 D 的坐标，分别为 ( x2 + dr , y2 - dc )，( x1 + dr , y1 - dc )</p><p>然后确保CD没有超过棋盘范围并且都有钉子即可</p><h3 id="答案-1" tabindex="-1"><a class="header-anchor" href="#答案-1"><span>答案</span></a></h3><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> os</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> sys</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">from</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> itertools </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> combinations</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">arr </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">],</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">    [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span></span>
<span class="line"><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">points </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> j</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">10</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> j </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">10</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> arr</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">j</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]]</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">squares </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> set</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">()</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">for</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">),</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> in</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> combinations</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">points</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        dx</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dy </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x1 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x2</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y1 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y2</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        x3 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x2 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dy</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        y3 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y2 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dx</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        x4 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x1 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dy</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        y4 </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y1 </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dx</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        if</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> all</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> &lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> coord </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 10</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> coord </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x3</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y3</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x4</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> y4</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]):</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> arr</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x3</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">y3</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> and</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> arr</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x4</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">y4</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">                squares</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">add</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">dx</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">dx </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> dy</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">dy</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">len</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">squares</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">))</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="三、整数变换" tabindex="-1"><a class="header-anchor" href="#三、整数变换"><span>三、整数变换</span></a></h2><h3 id="题目-2" tabindex="-1"><a class="header-anchor" href="#题目-2"><span>题目</span></a></h3><p>题目链接：0整数变换 - 蓝桥云课</p><h3 id="问题描述-2" tabindex="-1"><a class="header-anchor" href="#问题描述-2"><span>问题描述</span></a></h3><p>小蓝有一个整数 n。每分钟，小蓝的数都会发生变化，变为上一分钟的数减去上一分钟的数的各个数位和。</p><p>例如，如果小蓝开始时的数为 23，则下一分钟变为 23−(2+3)=18，再下一分钟变为 18−(1+8)=9，再下一分钟变为 9−9=0，共经过了 3 分钟变为 0。</p><p>给定一个正整数，请问这个数多少分钟后变为 0。</p><h3 id="解析-2" tabindex="-1"><a class="header-anchor" href="#解析-2"><span>解析</span></a></h3><p>这题直接暴力就过了。</p><p>Python3 跑出来只能通过 60% 的测试用例，用 PyPy3 就好了。</p><h3 id="答案-2" tabindex="-1"><a class="header-anchor" href="#答案-2"><span>答案</span></a></h3><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> os</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> sys</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">input</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">())</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">count </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">while</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">!=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">    num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">-=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> sum</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">map</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)))</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">    count </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">+=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">count</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3 id="整数变换的第二种做法" tabindex="-1"><a class="header-anchor" href="#整数变换的第二种做法"><span>整数变换的第二种做法</span></a></h3><h3 id="答案-3" tabindex="-1"><a class="header-anchor" href="#答案-3"><span>答案</span></a></h3><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> os</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> sys</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 对 1000 以内的数进行预处理</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># difference[i][j] 代表每次减去 sum_digits(i) + j 之后，剩余的值，可能为负数</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># step[i][j] 记录最终结果</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 题目中数字的最大值范围为 10的9 次方，我们每一步多减去的 j 值代表的其实是前六位的和</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># j 最大也就是 54（ 前六位都是9 ）</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">difference </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [[</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> _ </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">55</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> _ </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1000</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">step </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [[</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> _ </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">55</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> _ </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1000</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 这里要考虑一下边界情况，有可能后三位为 0 前六位还有</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 这个时候要减去前六位的值</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 并且步数需要加一步</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">difference</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">55</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">step</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> +</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> [</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">54</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)]</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 先计算出 0 ~ 999 以内的数的值</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1000</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">    # 遍历所有可能的 j 值</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">    for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> j </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">55</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        while</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&gt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">            num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">-=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> sum</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">map</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)))</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> +</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> j </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">            ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">+=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        difference</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">j</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        step</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">j</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> =</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> ans</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;"># 当 num 小于 1000 的时候直接返回</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">input</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">())</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1000</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">    print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">step</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">])</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">else</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">    ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">    while</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">        if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">&lt;</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1000</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">            ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">+=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> step</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">num</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">            break</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">        # x 为前六位</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">        # y 为后三位</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        x </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">//</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1000</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        y </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> num </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">%</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1000</span></span>
<span class="line"><span style="--shiki-light:#A0ADA0;--shiki-dark:#758575DD;">        # 直接加上步数，以及溢出的值即可</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">+=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> step</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">y</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">sum</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">map</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)))]</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        num </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> x </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">*</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1000</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> +</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> difference</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">y</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">][</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">sum</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">map</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">str</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">x</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)))]</span></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">    print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="四、火车运输" tabindex="-1"><a class="header-anchor" href="#四、火车运输"><span>四、火车运输</span></a></h2><h2 id="五、最大区间" tabindex="-1"><a class="header-anchor" href="#五、最大区间"><span>五、最大区间</span></a></h2><h3 id="题目-3" tabindex="-1"><a class="header-anchor" href="#题目-3"><span>题目</span></a></h3><p>题目链接：0最大区间 - 蓝桥云课</p><h3 id="问题描述-3" tabindex="-1"><a class="header-anchor" href="#问题描述-3"><span>问题描述</span></a></h3><p>给定一个长度为 n 的序列 Ai​，求 L,R 使 (R−L+1)⋅min⁡(AL,AL+1,…,AR) 尽可能大，其中 min⁡ 表示最小值。</p><p>你只需要输出最大的值即可，不需要输出具体的 L,R。</p><h3 id="解析-3" tabindex="-1"><a class="header-anchor" href="#解析-3"><span>解析</span></a></h3><p>这道题要求给定字符串中的 (R−L+1)⋅min⁡(AL,AL+1,…,AR) 的最大值，每次计算区间内的最小值再扩展区间很麻烦，我们可以转换一下思路以当前元素为区间内的最小元素，视为右边界，然后不断向左边扩展，一直到小于当前元素的位置停下，就可以得到当前区间的结果。（这里为什么不用向右边扩展，因为如果存在这种情况的话，右边向左扩展的时候会包括这一段）我们可以采用单调递增栈来加快寻找的速度，0 是为了确保清空栈。</p><p>可以用下面这个例子 debug 一下程序查看运行过程。</p><p>n = 6</p><p>A = [1,2,3,2,3,2]</p><p>（感觉解释的还是不太够清楚，有啥问题可以直接评论）</p><h3 id="答案-4" tabindex="-1"><a class="header-anchor" href="#答案-4"><span>答案</span></a></h3><div class="language-python line-numbers-mode" data-highlighter="shiki" data-ext="python" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-python"><span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> os</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">import</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> sys</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">n </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">input</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">())</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">A </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> list</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">map</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">int</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">,</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">input</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">().</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">split</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">()))</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">A</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">append</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">0</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">stack </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> []</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 0</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">for</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">in</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> range</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">n</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">+</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">):</span></span>
<span class="line"><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">    while</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> stack </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">and</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> A</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> &lt;=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> A</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">stack</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]]:</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        prev_i </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> stack</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">pop</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">()</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        L </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> stack</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;"> if</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> stack </span><span style="--shiki-light:#1E754F;--shiki-dark:#4D9375;">else</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> -</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;">1</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">        ans </span><span style="--shiki-light:#999999;--shiki-dark:#666666;">=</span><span style="--shiki-light:#998418;--shiki-dark:#B8A965;"> max</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> (</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> i </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> L </span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;">-</span><span style="--shiki-light:#2F798A;--shiki-dark:#4C9A91;"> 1</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> )</span><span style="--shiki-light:#AB5959;--shiki-dark:#CB7676;"> *</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;"> A</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">[</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">prev_i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">]</span><span style="--shiki-light:#999999;--shiki-dark:#666666;"> ,</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
<span class="line"><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">    stack</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">.</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">append</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">i</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#998418;--shiki-dark:#B8A965;">print</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">(</span><span style="--shiki-light:#393A34;--shiki-dark:#DBD7CAEE;">ans</span><span style="--shiki-light:#999999;--shiki-dark:#666666;">)</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2 id="六、等腰三角形" tabindex="-1"><a class="header-anchor" href="#六、等腰三角形"><span>六、等腰三角形</span></a></h2><h2 id="七、连续数组" tabindex="-1"><a class="header-anchor" href="#七、连续数组"><span>七、连续数组</span></a></h2><h2 id="八、质数排序" tabindex="-1"><a class="header-anchor" href="#八、质数排序"><span>八、质数排序</span></a></h2><h2 id="九、选段排序" tabindex="-1"><a class="header-anchor" href="#九、选段排序"><span>九、选段排序</span></a></h2><h2 id="十、最长同类子串" tabindex="-1"><a class="header-anchor" href="#十、最长同类子串"><span>十、最长同类子串</span></a></h2>`,60)])])}const e=i(k,[["render",l]]),d=JSON.parse('{"path":"/archives/b1c77a1d-d402-4788-8049-fa3aeb12ebd0/","title":"第十四届蓝桥杯大赛软件赛国赛 Python 研究生组（正在更新）","lang":"zh-CN","frontmatter":{"title":"第十四届蓝桥杯大赛软件赛国赛 Python 研究生组（正在更新）","createTime":"2026/01/09 15:57:22","cover":"/images/elysia/8.jpg","coverStyle":{"layout":"right"},"permalink":"/archives/b1c77a1d-d402-4788-8049-fa3aeb12ebd0/","description":"一、X 质数 题目 题目链接：0X质数 - 蓝桥云课 问题描述 对于一个含有 M 个数位的正整数 N ，任意选中其中 K 个不同的数位（0≤K<M），将这些选中的数位删除之后，余下的数位按照原来的顺序组成了一个新的数字 P 。如果至少存在一个 P 是质数，我们就称 N 是一个 X 质数。例如，对于整数 7869 ，我们可以删去 7 和 6 ，得到一个新...","head":[["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"第十四届蓝桥杯大赛软件赛国赛 Python 研究生组（正在更新）\\",\\"image\\":[\\"https://www.simengweb.com/images/elysia/8.jpg\\"],\\"dateModified\\":\\"2026-01-09T08:10:29.000Z\\",\\"author\\":[]}"],["meta",{"property":"og:url","content":"https://www.simengweb.com/archives/b1c77a1d-d402-4788-8049-fa3aeb12ebd0/"}],["meta",{"property":"og:site_name","content":"仲夏夜之梦"}],["meta",{"property":"og:title","content":"第十四届蓝桥杯大赛软件赛国赛 Python 研究生组（正在更新）"}],["meta",{"property":"og:description","content":"一、X 质数 题目 题目链接：0X质数 - 蓝桥云课 问题描述 对于一个含有 M 个数位的正整数 N ，任意选中其中 K 个不同的数位（0≤K<M），将这些选中的数位删除之后，余下的数位按照原来的顺序组成了一个新的数字 P 。如果至少存在一个 P 是质数，我们就称 N 是一个 X 质数。例如，对于整数 7869 ，我们可以删去 7 和 6 ，得到一个新..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:image","content":"https://www.simengweb.com/images/elysia/8.jpg"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"og:updated_time","content":"2026-01-09T08:10:29.000Z"}],["meta",{"name":"twitter:card","content":"summary_large_image"}],["meta",{"name":"twitter:image:src","content":"https://www.simengweb.com/images/elysia/8.jpg"}],["meta",{"name":"twitter:image:alt","content":"第十四届蓝桥杯大赛软件赛国赛 Python 研究生组（正在更新）"}],["meta",{"property":"article:modified_time","content":"2026-01-09T08:10:29.000Z"}]]},"readingTime":{"minutes":6.49,"words":1947},"git":{"createdTime":1767946229000,"updatedTime":1767946229000,"contributors":[{"name":"祀梦","username":"","email":"3501646051@qq.com","commits":1,"avatar":"https://gravatar.com/avatar/6406a81eeddc359cf3d3ce018797689fc6d014ff06215c27d0210b42e8f5a8ab?d=retro"}]},"autoDesc":true,"filePathRelative":"blog/competition/14th-lanqiaocup-python-grad.md","headers":[],"categoryList":[{"id":"126ac9","sort":10000,"name":"blog"},{"id":"83ee8d","sort":10002,"name":"competition"}]}');export{e as comp,d as data};