The-kruskal solution of ACM/ICPC's distinguishing MST uniqueness (POJ1679)

An example of whether the MST is unique.

Poj1679-the Unique MST

　

Test instructions: For the given graph, the MST (minimum spanning tree) is unique, the unique output path is long, otherwise the output is not unique!

The puzzle: Whether the MST is unique depends on whether the weights are the same on both sides (where one edge is in the MST for the first time and the other outside the MST).

If such an edge exists, you will need to delete that edge from the MST one at a time, and then seek the MST again, and if this is the same as the first MST, there does not exist a unique MST

Otherwise, there must be no more than one MST.

1 //kruskal-determine if MST is unique2 //time:0ms memory:868k3#include <iostream>4#include <cstring>5#include <cstdio>6#include <algorithm>7 using namespacestd;8 9 #defineMAX 101Ten  One structEdge { A     intu, v; -     intW; -     BOOLUsed;//First used the     BOOLDel//Kruskal Whether this edge is not considered -FriendBOOL operator< (Edge e1, Edge E2) {returnE1.W <E2.W;} -}e[max*MAX]; -  + intN, M; - BOOLFirst//whether to ask for MST for the first time + intFa[max]; A intDel[max*max], Len;//edges to be removed successively at intMinroad;//First MST results -  - intFind (intx) - { -     returnFA[X] <0? X:FA[X] =Find (fa[x]); - } in  - voidUnion (intR1,intR2) to { +R1 =Find (R1); -r2 =Find (R2); the     intnum = Fa[r1] +FA[R2]; *     if(Fa[r1] <FA[R2]) $     {Panax NotoginsengFA[R2] =R1; -FA[R1] =num; the     } +     Else { AFA[R1] =R2; theFA[R2] =num; +     } - } $  $ BOOLKruskal () - { -memset (FA,-1,sizeof(FA)); the     intnum =0; -     intMind =0;Wuyi      for(inti =0; I < m; i++) the     { -         if(E[i].del)Continue; Wu         if(Find (e[i].u) = = Find (E[I].V))Continue; - Union (e[i].u, E[I].V); About         if(first) { $Minroad + =E[I].W; -e[i].used =true; -         } -Mind + =E[I].W; A         if(Mind > Minroad)return true; +         if(++num = = N-1) Break; the     } -      $     return false; the } the  the intMain () the { -     intT; inscanf"%d", &T); the      while(t--) the     { Aboutscanf"%d%d", &n, &m); theMemset (E,0,sizeof(e)); the          for(inti =0; I < m; i++) thescanf"%d%d%d", &e[i].u, &AMP;E[I].V, &E[I].W); +  -Len =0; theSort (E, E +m);Bayi          for(inti =0; I < m; i++) the             if(E[I].W = = E[i +1].W) the             { -                 if(del[len-1] = i) del[len++] =i; -del[len++] = i +1; the             } the          theMinroad =0; theFirst =true; - Kruskal (); theFirst =false; the  the         BOOLUnique =true;94          for(inti =0; i < Len; i++) the         { the             if(!e[del[i]].used)Continue;//used to delete theE[del[i]].del =true;//Delete98             if(!Kruskal ()) About             { -printf"Not unique!\n");101Unique =false; Break;102             }103E[del[i]].del =false;//Recovery104         } the 106         if(unique)107printf"%d\n", minroad);108     }109  the 111  the     return 0;113}

The-kruskal solution of ACM/ICPC's distinguishing MST uniqueness (POJ1679)