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

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)