UVA1349 (with weighted binary graph maximum match-km algorithm template)

Source: Internet
Author: User

UVA1349

Test instructions: Given some weighted edges, it is found that these edges are constructed into rings and the total weights are minimized.

Solution:

The matching problem of weighted binary graphs can be solved by using km algorithm.

The requirement of maximum right matching is initialization g[i][j] is 0, can run directly;

The minimum right to match is the initialization g[i][j] is-inf, the edge is negative, and the inverse number of the final output answer.

Because each point is required to belong to a circle, it means that each point has a unique successor. Conversely, as long as each point has a unique successor, each point must belong to a certain circle.

The only thing we think about is the concept of a two-point graph, where we create a binary graph from u to V for each of the points, and then the problem is converted to the least-weight perfect match problem on the two-minute graph.

1#include <bits/stdc++.h>2 #defineREP (I, A, b) for (int i = (a); I < (b); i++)3 #defineMEM (a,x) memset (A,x,sizeof (a))4 #defineINF 0x3f3f3f3f5 #defineMAXN 100+106 using namespacestd;7 8 structKM {9     intN;Ten     intG[MAXN][MAXN]; One     intLX[MAXN], LY[MAXN]; A     intSLACK[MAXN];//How much weight is required to record the match from X to Y? -     intMATCH[MAXN];//records the points in the Y-set that each X-point matches to -     BOOLS[MAXN], T[MAXN]; the  -     voidInitintN) { -          This->n =N; -          for(inti =0; I < n; i++)  +              for(intj =0; J < N; J + +)  -G[I][J] =-INF; +         //Note that if this is the maximum weight value match and the assignment is 0 A         //minimum weights matching and is-inf at     } -  -     voidAdd_edge (intUintVintval) { -G[U][V] =Max (G[u][v], Val); -     } -  in     BOOLDfsinti) { -S[i] =true; to          for(intj =0; J < N; J + +) { +             if(T[j])Continue; -             intTMP = Lx[i] + ly[j]-G[i][j]; the             if(!tmp) { *T[J] =true; $                 if(Match[j] = =-1||DFS (Match[j])) {Panax NotoginsengMATCH[J] =i; -                     return true; the                 } +             } A             ElseSLACK[J] =min (slack[j], TMP); the         } +         return false; -     } $  $     voidUpdate () { -         intA =INF; -          for(inti =0; I < n; i++) the             if(! T[i]) A =min (A, slack[i]); -          for(inti =0; I < n; i++) {Wuyi             if(S[i]) Lx[i]-=A; the             if(T[i]) Ly[i] + =A; -         } Wu     } -  About     voidkm () { $          for(inti =0; I < n; i++) { -Match[i] =-1; -Lx[i] =-inf; Ly[i] =0; -              for(intj =0; J < N; J + +) ALx[i] =Max (Lx[i], g[i][j]); +         } the          for(inti =0; I < n; i++) { -              for(intj =0; J < N; J + +) Slack[j] =INF; $              while(1) { the                  for(intj =0; J < N; J + +) S[j] = t[j] =false; the                 if(Dfs (i)) Break; the                 Elseupdate (); the             } -         } in     } the }men; the  About intMain () { the     intN; the      while(SCANF ("%d", &n) = =1&&N) { the men.init (n); +REP (U,0, N) { -             intv; the              while(SCANF ("%d", &v) &&v) {Bayi                 intW scanf"%d", &W); thev--; theMen.add_edge (U, V,-W); -             } -         } the  the men.km (); the         intAns =0, flag =1; theREP (I,0, N) { -             if(Men.g[men.match[i]][i] = =-INF) { the                 //There is no match to, is not successful, because the title of the request is a perfect match theFlag =0; the                  Break;94             } theAns + = men.g[men.match[i]][i];//Cumulative Weight value the         } the         if(!flag) printf ("n\n");98         Elseprintf"%d\n",-ans);//Finally, the output is negative. About     } -     return 0;101}

UVA1349 (with weighted binary graph maximum match-km algorithm template)

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.