C++并查集常用操作

并查集 是一种树型的数据结构,用于处理一些不相加集合的合并和查询问题。在使用中常常以森林来表示。 并查集也是用来维护集合的,和前面学习的set不同之处在于,并查集能很方便地同时维护很多集合。如果用set来维护会非常的麻烦。并查集的核心思想是记录每个结点的父亲结点是哪个结点。前言并查集是一种多叉树用于处理不相交的集合的合并与查询问题判断。通俗理解在日常生活中我们会因为某个人是自己的朋友哪怕是朋友的朋友也是有朋友会给予通融、 偏袒。而并查集的基本概念就是判断某两个集合是否是“朋友”关系并让两个集合成为“朋友”常用操作初始化每个结点单独作为一个集合查询求元素所在的集合的代表元素即根结点合并将两个元素所在的集合合并为一个集合合并之前应先判断两个元素是否属于同一集合用上面的“查询”来实现算法实现初始化:初始的时候每个结点各自为一个集合,father[i]表示结点 i 的父亲结点,如果 father[i]i,我们认为这个结点是当前集合根结点开始时每个节点根节点是他自己。123456789voidinit() {for(inti 1; i n; i) {father[i] i;}}查找:查找结点所在集合的根结点,结点 x 的根结点必然也是其父亲结点的根结点像是有递归的样子。1234567891011intget(intx) {if(father[x] x) {// x 结点就是根结点returnx;}returnget(father[x]);// 如果该节点不是根节点继续寻找父结点的根结点}合并:将两个元素所在的集合合并在一起,通常来说,合并之前先判断两个元素是否属于同一集合。12345678910111213voidhebing(intx,inty) {x find(x);y find(y);if(x ! y) {// 不在同一个集合father[y] x;//将根节点合并}}上面三个操作是并查集常用的操作前面的并查集的复杂度实际上在有些极端情况会很慢。比如树的结构正好是一条链那么最坏情况下每次查询的复杂度达到了O(n) 。这并不是我们期望的结果。路径压缩的思想是我们只关心每个结点的父结点而并不太关心树的真正的结构递归查找相当浪费时间如下当想去访问6的根节点时要访问5的根节点想去访问5的根节点又要去访问4的根节点..........以此类推此时并查集退化为线性。这样我们在一次查询的时候可以把查询路径上的所有结点的father[i]都赋值成为根结点。只需要在我们之前的查询函数上面进行很小的改动cxv.perhbmc.cn/35113.Doccxv.perhbmc.cn/39153.Doccxv.perhbmc.cn/95517.Doccxv.perhbmc.cn/75371.Doccxv.perhbmc.cn/40660.Doccxv.perhbmc.cn/59975.Doccxv.perhbmc.cn/53111.Doccxv.perhbmc.cn/31139.Doccxv.perhbmc.cn/64008.Doccxv.perhbmc.cn/28662.Doccxv.perhbmc.cn/13771.Dockcx.perhbmc.cn/71971.Dockcx.perhbmc.cn/75773.Dockcx.perhbmc.cn/64860.Dockcx.perhbmc.cn/88660.Dockcx.perhbmc.cn/33715.Dockcx.perhbmc.cn/39375.Dockcx.perhbmc.cn/24624.Dockcx.perhbmc.cn/11135.Dockcx.perhbmc.cn/99977.Dockcx.perhbmc.cn/22680.Dockcx.perhbmc.cn/93319.Dockat.perhbmc.cn/31793.Dockat.perhbmc.cn/06204.Dockat.perhbmc.cn/37951.Dockat.perhbmc.cn/79155.Dockat.perhbmc.cn/68060.Dockat.perhbmc.cn/60688.Dockat.perhbmc.cn/13195.Dockat.perhbmc.cn/39397.Dockat.perhbmc.cn/11319.Dockat.perhbmc.cn/39711.Dockat.perhbmc.cn/57339.Docnlu.perhbmc.cn/84408.Docnlu.perhbmc.cn/11513.Docnlu.perhbmc.cn/39157.Docnlu.perhbmc.cn/31791.Docnlu.perhbmc.cn/97517.Docnlu.perhbmc.cn/15937.Docnlu.perhbmc.cn/28240.Docnlu.perhbmc.cn/11735.Docnlu.perhbmc.cn/77715.Docnlu.perhbmc.cn/95937.Docnlu.perhbmc.cn/13513.Docweo.perhbmc.cn/64644.Docweo.perhbmc.cn/28626.Docweo.perhbmc.cn/62668.Docweo.perhbmc.cn/55931.Docweo.perhbmc.cn/73175.Docweo.perhbmc.cn/86080.Docweo.perhbmc.cn/57537.Docweo.perhbmc.cn/55559.Docweo.perhbmc.cn/75933.Docweo.perhbmc.cn/42008.Docweo.perhbmc.cn/06266.Doczro.perhbmc.cn/40062.Doczro.perhbmc.cn/88624.Doczro.perhbmc.cn/15733.Doczro.perhbmc.cn/13195.Doczro.perhbmc.cn/91391.Doczro.perhbmc.cn/20040.Doczro.perhbmc.cn/02200.Doczro.perhbmc.cn/80448.Doczro.perhbmc.cn/15399.Doczro.perhbmc.cn/22224.Doczro.perhbmc.cn/00444.Docqyi.perhbmc.cn/84428.Docqyi.perhbmc.cn/04626.Docqyi.perhbmc.cn/20686.Docqyi.perhbmc.cn/88002.Docqyi.perhbmc.cn/06628.Docqyi.perhbmc.cn/86428.Docqyi.perhbmc.cn/24004.Docqyi.perhbmc.cn/80828.Docqyi.perhbmc.cn/02884.Docqyi.perhbmc.cn/62606.Docqyi.perhbmc.cn/62808.Docelt.perhbmc.cn/28860.Docelt.perhbmc.cn/66204.Docelt.perhbmc.cn/06426.Docelt.perhbmc.cn/86808.Docelt.perhbmc.cn/06264.Docelt.perhbmc.cn/68624.Docelt.perhbmc.cn/80864.Docelt.perhbmc.cn/80046.Docelt.perhbmc.cn/24064.Docelt.perhbmc.cn/82028.Docelt.perhbmc.cn/46420.Doctga.perhbmc.cn/06048.Doctga.perhbmc.cn/84040.Doctga.perhbmc.cn/60666.Doctga.perhbmc.cn/82004.Doctga.perhbmc.cn/02486.Doctga.perhbmc.cn/08860.Doctga.perhbmc.cn/84602.Doctga.perhbmc.cn/24482.Doctga.perhbmc.cn/82846.Doctga.perhbmc.cn/66640.Doctga.perhbmc.cn/46460.Doccos.perhbmc.cn/24006.Doccos.perhbmc.cn/82828.Doccos.perhbmc.cn/88422.Doccos.perhbmc.cn/22680.Doccos.perhbmc.cn/86206.Doccos.perhbmc.cn/44266.Doccos.perhbmc.cn/40822.Doccos.perhbmc.cn/82480.Doccos.perhbmc.cn/06402.Doccos.perhbmc.cn/46840.Doccos.perhbmc.cn/84828.Doccax.perhbmc.cn/66806.Doccax.perhbmc.cn/22880.Doccax.perhbmc.cn/22868.Doccax.perhbmc.cn/02428.Doccax.perhbmc.cn/06640.Doccax.perhbmc.cn/02040.Doccax.perhbmc.cn/82666.Doccax.perhbmc.cn/62826.Doccax.perhbmc.cn/64246.Doccax.perhbmc.cn/44640.Doccax.perhbmc.cn/68684.Docofl.perhbmc.cn/00464.Docofl.perhbmc.cn/60240.Docofl.perhbmc.cn/04404.Docofl.perhbmc.cn/04688.Docofl.perhbmc.cn/22268.Docofl.perhbmc.cn/68428.Docofl.perhbmc.cn/02448.Docofl.perhbmc.cn/42842.Docofl.perhbmc.cn/44868.Docofl.perhbmc.cn/84202.Docofl.perhbmc.cn/68242.Doctoo.perhbmc.cn/24484.Doctoo.perhbmc.cn/08448.Doctoo.perhbmc.cn/48800.Doctoo.perhbmc.cn/46084.Doctoo.perhbmc.cn/42288.Doctoo.perhbmc.cn/62406.Doctoo.perhbmc.cn/82226.Doctoo.perhbmc.cn/64008.Doctoo.perhbmc.cn/22260.Doctoo.perhbmc.cn/46802.Doctoo.perhbmc.cn/20400.Docuym.perhbmc.cn/64266.Docuym.perhbmc.cn/20026.Docuym.perhbmc.cn/04060.Docuym.perhbmc.cn/86208.Docuym.perhbmc.cn/24822.Docuym.perhbmc.cn/46428.Docuym.perhbmc.cn/48642.Docuym.perhbmc.cn/66422.Docuym.perhbmc.cn/00808.Docuym.perhbmc.cn/06628.Docuym.perhbmc.cn/48824.Docwni.perhbmc.cn/60248.Docwni.perhbmc.cn/20682.Docwni.perhbmc.cn/62260.Docwni.perhbmc.cn/00284.Docwni.perhbmc.cn/42404.Docwni.perhbmc.cn/46882.Docwni.perhbmc.cn/68248.Docwni.perhbmc.cn/02820.Docwni.perhbmc.cn/04468.Docwni.perhbmc.cn/22202.Docwni.perhbmc.cn/00282.Docase.perhbmc.cn/64064.Docase.perhbmc.cn/08822.Docase.perhbmc.cn/00246.Docase.perhbmc.cn/06068.Docase.perhbmc.cn/48660.Docase.perhbmc.cn/46444.Docase.perhbmc.cn/60484.Docase.perhbmc.cn/84684.Docase.perhbmc.cn/24822.Docase.perhbmc.cn/08424.Docase.perhbmc.cn/66208.Docluv.perhbmc.cn/80666.Docluv.perhbmc.cn/06608.Docluv.perhbmc.cn/84086.Docluv.perhbmc.cn/80800.Docluv.perhbmc.cn/02646.Docluv.perhbmc.cn/20082.Docluv.perhbmc.cn/62688.Docluv.perhbmc.cn/68668.Docluv.perhbmc.cn/44488.Docluv.perhbmc.cn/84020.Docluv.perhbmc.cn/04026.Doczai.perhbmc.cn/40480.Doczai.perhbmc.cn/60068.Doczai.perhbmc.cn/40088.Doczai.perhbmc.cn/88080.Doczai.perhbmc.cn/08482.Doczai.perhbmc.cn/80240.Doczai.perhbmc.cn/46480.Doczai.perhbmc.cn/04840.Doczai.perhbmc.cn/26282.Doczai.perhbmc.cn/20240.Doczai.perhbmc.cn/62404.Docdxt.perhbmc.cn/28606.Docdxt.perhbmc.cn/68866.Docdxt.perhbmc.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