# Kruskal algorithm + and check set

Source: Internet
Author: User

Algorithm Essentials: the most difficult point of the Kruskal algorithm is how to determine whether to join the edge (x, Y) after the formation of a ring.

The problem can be as follows: judging the two vertices x, y of the Edge (x, Y) is the most connected in the graph (actually forest) Mst. If it is already connected, the joining Edge will form a ring;

In the Kruskal algorithm, the merging and finding of the set is Used.

and check the Set:

`1 intGETFA (intK//find the most ancestors2 {3     if(fa[k]==k)returnk;4fa[k]=GETFA (fa[k]);5     returnfa[k];6 }7 8 voidMergeintXintY//Merging Ancestors9 {Ten     intfx=GETFA (x); one     intfy=GETFA (y); afa[fx]=fy; - } -  the BOOLJudgeintXintY//judgment is not an ancestor - { -     intfx=GETFA (x); -     intfy=GETFA (y); +     returnfx==fy; -}`

Kruskal algorithm Core:

`1  for(intI=1; i<=n;i++)2fa[i]=i;3Sort (e+1, e+1+len,mys);4 intCal=0;5  for(intI=1; i<=len;i++)6 {7     intv=GETFA (e[i].x);8     intu=GETFA (e[i].y);9     if(v!=U)Ten     { one Merge (v,u); a                 //Add according to test instructions -         if(++cal==n-1) -         { the              break; -         } -     } -}`

Input:

`1 intfa[maxn];2 intlen=0;3 structnode4 {5     intx,y,v;6 }e[maxn];7 8 voidInitintXxintYyintVv)9 {Ten     if(yy<0|| Yy>n*m)return; onee[++len].y=yy; ae[len].x=xx;e[len].v=vv; - } -  the intMain () - { -Memset (e,0,sizeof(e)); -Cin>>n>>m; +      for(intI=1; i<=m;i++) -     { +         intxx,yy,vv; aCin>>xx>>yy>>vv; at Init (xx,yy,vv); - Init (yy,xx,vv); -}`

Kruskal algorithm + and check set

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