HDU 1956 POJ 1637 Sightseeing Tour

Euler circuit determination method for mixed graphs:

1. First to determine whether the base diagram is connected, the non-connected words are impossible, otherwise enter the next step.

2. For the non-directional side, determine a direction arbitrarily

3. After the determination is made, the whole graph becomes a graph of graphs, calculating the degree of penetration and the degree of each node

4. If there is a node in the degree-out is an odd number, then it is not possible, otherwise enter the next step

5. Set up a network, add a new Origin s, and a meeting point T, and then set up a network

 for (i=1; i<=m; i++)     if (ff[i]==0) // If there is a forward edge         Addedge (U[i],v[i],1);  for (i=1; i<=n; i++) {    if(ru[i]>chu[i])        Addedge (I,t, (ru[i) -chu[i])/2);     Else          Addedge (S,i, (Chu[i]++-ru[i])/2);}            

6. Calculate the maximum network flow.

7. If the edge from S is full-flow, it means that it exists, otherwise it does not exist.

8. Find the edges in the network stream that are not associated with s,t, and if there is an edge with traffic equal to 1, then reverse these edges and finally get a Eulerian graph.

AC code (dinic continuous shortest augmented path algorithm for maximum network flow):

#include <cstdio>#include<cstring>#include<string>#include<cmath>#include<vector>#include<queue>#include<algorithm>using namespacestd;Const intmaxn= -+Ten;Const intinf=0x7FFFFFFF;structedge{int  from, To,cap,flow;}; Vector<Edge>Edges;vector<int>G[MAXN];BOOLVIS[MAXN];intD[MAXN];intCUR[MAXN];intRU[MAXN];intCHU[MAXN];intU[MAXN],V[MAXN],FF[MAXN];intFATHER[MAXN];intM,s,t,tot;intn,m;//finding a hierarchical networkBOOLBFS () {memset (Vis,0,sizeof(VIS)); Queue<int>Q;    Q.push (s); D[s]=0; Vis[s]=1;  while(!Q.empty ()) {        intx=Q.front ();        Q.pop ();  for(intI=0; I<g[x].size (); i++) {Edge& e=Edges[g[x][i]]; if(!vis[e.to]&&e.cap>e.flow) {vis[e.to]=1; D[e.to]=d[x]+1;            Q.push (e.to); }        }    }    returnvis[t];}//Add EdgevoidAddedge (int  from,intTo,intcap)    {Edge R; R. from= from; R.to=to ; R.cap=cap; R.flow=0;    Edges.push_back (R);    Edge D; D. from=to ; D.to= from; D.cap=0; D.flow=0;    Edges.push_back (d); M=edges.size (); g[ from].push_back (M-2); G[to].push_back (M-1);}//Each phase comes with a DFS augmentationintDFS (intXinta) {    if(x==t| | a==0)returnA; intflow=0, F;  for(intI=CUR[X]; I<g[x].size (); i++) {Edge& e=Edges[g[x][i]]; if(d[x]+1==d[e.to]&& (F=dfs (E.to,min (a,e.cap-e.flow)) >0) {E.flow+=F; Edges[g[x][i]^1].flow-=F; Flow+=F; A-=F; if(a==0) Break; }    }    returnflow;}//multiple stages, several times to establish a hierarchical network. intMaxflow (intSsintTT) {    intflow=0;  while(BFS ()) {memset (cur,0,sizeof(cur)); Flow+=DFS (Ss,inf); }    returnflow;}intFind (intx) {    if(X!=father[x]) father[x]=Find (father[x]); returnfather[x];}intMain () {intT,flag,i; scanf ("%d",&T);  while(t--) {scanf ("%d%d",&n,&M);        Edges.clear ();  for(i=0; i<maxn; i++) g[i].clear (); Flag=1; S=0, t=n+1;//set up super-origin and super-sink pointsmemset (Ru,0,sizeof(Ru)); memset (Chu,0,sizeof(Chu));  for(i=0; i<=n;i++) father[i]=i; Tot=N;  for(i=1; i<=m; i++) {scanf ("%d%d%d",&u[i],&v[i],&Ff[i]); intfx=Find (U[i]); intfy=Find (V[i]); if(fx!=FY) {FATHER[FX]=fy; Tot--; } Ru[v[i]]++; Chu[u[i]]++; }        if(tot!=1) flag=0; if(flag) { for(i=1; i<=n; i++)                if(ABS (Ru[i]-chu[i])%2==1) {flag=0;  Break; }        }        if(flag) { for(i=1; i<=m; i++)                if(ff[i]==0)//If there is a forward edgeAddedge (U[i],v[i],1);  for(i=1; i<=n; i++)            {                if(ru[i]>Chu[i]) Addedge (I,t, (Ru[i]-chu[i])/2); ElseAddedge (S,i, (Chu[i]++-ru[i])/2);            } maxflow (S,t);  for(i=0; I<edges.size (); i++)                if(Edges[i]. from==s&&edges[i].cap!=Edges[i].flow) {Flag=0;  Break; }        }        if(flag) printf ("possible\n"); Elseprintf"impossible\n"); }    return 0;}

HDU 1956 POJ 1637 Sightseeing Tour