【poj1637】【最大流】Sightseeing tour

这道题是一个混合图欧拉回路问题。

建图方法:将无向图随意定向，计算每个点的入度和出度，令calc[i] =abs(in[i] - out[i])/2。如果calc[i]为奇数，那么肯定不存在欧拉回路；如果所有点calc[i]都为偶数，那么先将有向边删去，然后按照一开始的定向方法构图，并且对于每个入度小于出度的点则添加一条源点到该点的边，容量为calc[i];反之则连一条该点到汇点的边，容量为calc[i]，最后再做一次最大流，如果为满流，则存在欧拉回路，否则不存在。

ps:这道题会有重边，所以用邻接矩阵不太好，最好写成邻接表的形式。

代码:

#include<cstdio>#include<cstring>using namespace std;const int inf = 0x3f3f3f3f;const int maxn = 500;const int maxm = 5000;struct Node{int c,pos,next;}E[maxm];struct Edge{int x,y,op;}edge[maxm];int T,n,m;int head[maxn];int id1[maxn],id2[maxn],tmp[maxn];int cur[maxn],dis[maxn],gap[maxn],pre[maxn];int s,t,NE,NV;void init(){freopen("poj1637.in","r",stdin);freopen("poj1637.out","w",stdout);}inline void checkmin(int &a,int b){if(a == -1 || a > b)a = b;}int abs(int x){if(x >= 0)return x;else return -x;}int sap(){memset(dis,0,sizeof(dis));memset(gap,0,sizeof(gap));for(int i = 0;i < NV;i++)cur[i] = head[i];int u = pre[s] = s,maxflow = 0,aug = -1;gap[0] = NV;while(dis[s] < NV){loop:for(int &i = cur[u];i != -1;i = E[i].next){int v = E[i].pos;if(E[i].c && dis[u] == dis[v] + 1){checkmin(aug,E[i].c);pre[v] = u;u = v;if(v == t){maxflow += aug;for(u = pre[u];v != s;v = u,u = pre[u]){E[cur[u]].c -= aug;E[cur[u]^1].c += aug;}aug = -1;}goto loop;}}int mind = NV;for(int i = head[u];i != -1;i = E[i].next){int v = E[i].pos;if(E[i].c && (mind > dis[v])){cur[u] = i;mind = dis[v];}}if((--gap[dis[u]]) == 0)break;gap[dis[u] = mind + 1]++;u = pre[u];}return maxflow;}void Insert(int u,int v,int c){E[NE].c = c;         E[NE].pos = v;E[NE].next = head[u];head[u] = NE++;E[NE].c = 0;         E[NE].pos = u;E[NE].next = head[v];head[v] = NE++;}void solve(){memset(E,0,sizeof(E));memset(head,-1,sizeof(head));s = 0;t = n + 1;NE = 0;NV = n + 2;for(int i = 1;i <= n;i++){tmp[i] = abs(id1[i] - id2[i]);if(tmp[i] & 1){printf("impossible\n");return;}tmp[i] >>= 1;}for(int i = 1;i <= m;i++){if(edge[i].op == 0){Insert(edge[i].x,edge[i].y,1);}}int comp = 0;for(int i = 1;i <= n;i++){if(id1[i] > id2[i])Insert(s,i,tmp[i]),comp += tmp[i];else if(id1[i] < id2[i])Insert(i,t,tmp[i]);}if(comp == sap())printf("possible\n");else printf("impossible\n");}void readdata(){scanf("%d",&T);for(int i = 1;i <= T;i++){memset(edge,0,sizeof(edge));memset(id1,0,sizeof(id1));memset(id2,0,sizeof(id2));memset(tmp,0,sizeof(tmp));scanf("%d%d",&n,&m);for(int j = 1;j <= m;j++){scanf("%d%d%d",&edge[j].x,&edge[j].y,&edge[j].op);id1[edge[j].x]++,id2[edge[j].y]++;}solve();}}int main(){init();readdata();return 0;}