题目描述

或许你并不知道，你的某个朋友是你的亲戚。他可能是你的曾祖父的外公的女婿的外甥女的表姐的孙子。如果能得到完整的家谱，判断两个人是否亲戚应该是可行的，但如果两个人的最近公共祖先与他们相隔好几代，使得家谱十分庞大，那么检验亲戚关系实非人力所能及。在这种情况下，最好的帮手就是计算机。为了将问题简化，你将得到一些亲戚关系的信息，如Marry和Tom是亲戚，Tom和Ben是亲戚，等等。从这些信息中，你可以推出Marry和Ben是亲戚。请写一个程序，对于我们的关于亲戚关系的提问，以最快的速度给出答案。

输入格式

输入由两部分组成。

第一部分以N，M开始。N为问题涉及的人的个数(1  N  20000)。这些人的编号为1,2,3,…, N。下面有M行(1  M  1 000 000)，每行有两个数ai, bi，表示已知ai和bi是亲戚。第二部分以Q开始。以下Q行有Q个询问(1 <=  Q < = 1 000 000)，每行为ci, di，表示询问ci和di是否为亲戚。

输出格式

对于每个询问ci, di，输出一行：若ci和di为亲戚，则输出“Yes”，否则输出“No”。

闲来无事肝一肝并查集......

明显的并查集裸题。其思路是：对于每对亲戚关系，我们都将两人所在的集合合并为一个集合，查询时若两人再同一个集合就说明是亲戚了。

 
 
 
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#include<iostream>
#include<cstring>
#include<cstdio>
#define maxn 1000001
using namespace std;


int fa[maxn],n,m,q;




inline int read(){


    register int x(0),f(1); register char c(getchar());


    while(c<'0'||'9'<c){ if(c=='-') f=-1; c=getchar(); }


    while('0'<=c&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();


    return x*f;


}




int get(int x){


    if(fa[x]==x) return x;


    return fa[x]=get(fa[x]);


}




int main(){


    n=read(),m=read();


    for(register int i=1;i<=n;i++) fa[i]=i;


    for(register int i=1;i<=m;i++){


        int u=read(),v=read();


        u=get(u),v=get(v);


        fa[u]=v;


    }


     


    q=read();


    for(register int i=1;i<=q;i++){


        int u=read(),v=read();


        if(get(u)==get(v)) puts("Yes");


        else puts("No");


    }


    return 0;




}














 


 






时间复杂度为O((m+q)logn)


虽然是log级别，但这是上界，实际是远远达不到的




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a { text-decoration: none; outline: 0 }

a:hover { outline: 0 }

a:focus { outline: 1px dotted }

sup.md-footnote { background-color: rgba(85, 85, 85, 1); color: rgba(221, 221, 221, 1) }

p { word-wrap: break-word }

p, ul, dd, ol, hr, address, pre, table, iframe, .wp-caption, .wp-audio-shortcode, .wp-video-shortcode { margin-top: 0; margin-bottom: 1.5rem }

li>blockquote { margin-bottom: 0 }

audio:not([controls]) { display: none }

[hidden] { display: none }

.in-text-selection, ::selection { background: rgba(74, 137, 220, 1); color: rgba(255, 255, 255, 1); text-shadow: none }

ul, ol { padding: 0 0 0 1.875rem }

ul { list-style: square }

ol { list-style: decimal }

ul ul, ol ol, ul ol, ol ul { margin: 0 }

b, th, dt, strong { font-weight: bold }

i, em, dfn, cite { font-style: italic }

blockquote { margin: 35px 0 1.875rem 1.875rem; border-left: 2px solid rgba(71, 77, 84, 1); padding-left: 30px }

pre, code, kbd, tt, var { background: rgba(0, 0, 0, 0.05); font-size: 0.875rem; font-family: Monaco, Consolas, "Andale Mono", "DejaVu Sans Mono", monospace }

kbd { padding: 2px 4px; font-size: 90%; color: rgba(255, 255, 255, 1); background-color: rgba(51, 51, 51, 1); border-radius: 3px; box-shadow: inset 0 -1px rgba(0, 0, 0, 0.25) }

pre.md-fences { padding: 10px 30px; margin-bottom: 20px; border: 1px solid }

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.enable-diagrams pre.md-fences[lang="sequence"] .code-tooltip, .enable-diagrams pre.md-fences[lang="flow"] .code-tooltip, .enable-diagrams pre.md-fences[lang="mermaid"] .code-tooltip { bottom: -2.2em; right: 4px }

code, kbd, tt, var { padding: 2px 5px }

table { max-width: 100%; width: 100%; border-collapse: collapse; border-spacing: 0 }

th, td { padding: 5px 10px; vertical-align: top }

a { transition: all 0.2s ease-in-out }

hr { background: rgba(71, 77, 84, 1) }

h1 { margin-top: 2em }

a { color: rgba(224, 224, 224, 1); text-decoration: underline }

a:hover { color: rgba(255, 255, 255, 1) }

.md-inline-math script { color: rgba(129, 177, 219, 1) }

b, th, dt, strong { color: rgba(222, 222, 222, 1) }

mark { background: rgba(211, 212, 14, 1) }

blockquote { color: rgba(157, 162, 166, 1) }

table a { color: rgba(222, 222, 222, 1) }

th, td { border: 1px solid rgba(71, 77, 84, 1) }

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.md-task-list-item>input::before { content: ""; display: inline-block; width: 0.875rem; height: 0.875rem; vertical-align: middle; text-align: center; border: 1px solid rgba(184, 191, 198, 1); background-color: rgba(54, 59, 64, 1); margin-top: -0.4rem }

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.btn, .btn .btn-default { background: rgba(0, 0, 0, 0); color: rgba(184, 191, 198, 1) }

.ty-table-edit { border-top: 1px solid rgba(128, 128, 128, 1); background-color: rgba(54, 59, 64, 1) }

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#write>h4.md-focus::before { top: 2px }

.md-toc-item { color: rgba(168, 194, 220, 1) }

#write div.md-toc-tooltip { background-color: rgba(54, 59, 64, 1) }

.dropdown-menu .btn:hover, .dropdown-menu .btn:focus, .md-toc .btn:hover, .md-toc .btn:focus { color: rgba(255, 255, 255, 1); background: rgba(0, 0, 0, 1) }

#toc-dropmenu { background: rgba(50, 54, 59, 0.93); border: 1px solid rgba(253, 253, 253, 0.15) }

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h1.md-focus .md-attr, h2.md-focus .md-attr, h3.md-focus .md-attr, h4.md-focus .md-attr, h5.md-focus .md-attr, h6.md-focus .md-attr, .md-header-span .md-attr { color: rgba(140, 142, 146, 1); display: inline }

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.modal-content { background: var(--bg-color); border: 0 }

.modal-title { font-size: 1.5em }

.modal-content input { background-color: rgba(26, 21, 21, 0.51); color: rgba(255, 255, 255, 1) }

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.modal-backdrop { background-color: rgba(174, 174, 174, 0.7) }

.modal-content .btn-primary { border-color: var(--primary-color) }

.md-table-resize-popover { background-color: rgba(75, 83, 90, 1) }

.form-inline .input-group .input-group-addon { color: rgba(255, 255, 255, 1) }

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#file-info-file-path .file-info-field-value:hover { background-color: rgba(85, 85, 85, 1); color: rgba(222, 222, 222, 1) }

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.btn-default:hover, .btn-default:focus, .btn-default.focus, .btn-default:active, .btn-default.active, .open>.dropdown-toggle.btn-default { color: rgba(255, 255, 255, 1); border: 1px solid rgba(221, 221, 221, 1); background-color: inherit }

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.megamenu-menu-panel .btn { border: 1px solid rgba(238, 238, 238, 1); background: rgba(0, 0, 0, 0) }

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.file-list-item { border-bottom: none }

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.file-node-background { height: 32px }

.file-library-node.active>.file-node-content, .file-list-item.active { color: var(--active-file-text-color) }

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