题目传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=2095
这个题目啊!瞄一眼就知道是二分吧?
接下来就是给你一些有向边&无向边,让你判断是否存在欧拉回路
对于有向边,没有悬念,直接记录对于出度入度的贡献
只与有向边嘛,不妨先随便定一个向,然后考虑使用网络流进行调整
具体细节可以参见:http://blog.csdn.net/wzq_qwq/article/details/48651379
#include<bits/stdc++.h> #define LL long long #define abs(x) ((x)>0?(x):-(x)) using namespace std; const int N = 2000+9; const int M = 10000+9; const int INF = 1e9; struct Edge{int u,v,w1,w2;}edge[M]; int n,m,MX,MN=INF,in[N],out[N],cur[M]; int S,T,dis[N],flow[M],head[N],nxt[M],to[M],TT; queue<int> que; inline int read(){ char c=getchar(); int ret=0,f=1; while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();} while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();} return ret*f; } inline void Add_Edge(int u, int v, int f) { to[++TT] = v; nxt[TT] = head[u]; head[u] = TT; flow[TT] = f; to[++TT] = u; nxt[TT] = head[v]; head[v] = TT; flow[TT] = 0; } inline bool BFS(){ memset(dis,-1,sizeof(dis)); dis[S] = 0; que.push(0); while (!que.empty()) { int w = que.front(); que.pop(); for (int i=head[w];i;i=nxt[i]) if (flow[i] && !~dis[to[i]]) { dis[to[i]] = dis[w] + 1; que.push(to[i]); } } return ~dis[T]; } int DFS(int w, int f) { if (w == T) { return f; } else { int ret = 0; for (int &i=cur[w],tmp;i && f;i=nxt[i]) { if (dis[to[i]] == dis[w] + 1) { tmp = DFS(to[i], min(f, flow[i])); ret += tmp; f -= tmp; flow[i] -= tmp; flow[i^1] += tmp; } } return ret; } } inline int Dinic(){ int ret = 0; while (BFS()) { memcpy(cur,head,sizeof(head)); ret += DFS(S,INF); } return ret; } inline bool judge(int lim){ memset(in,0,sizeof(in)); memset(out,0,sizeof(out)); memset(head,0,sizeof(head)); S = 0; T = N - 1; TT = 1; int tot = 0; for (int i=1;i<=m;i++) { if (lim < edge[i].w1) { continue; } else if (lim < edge[i].w2) { in[edge[i].v]++; out[edge[i].u]++; } else { in[edge[i].v]++; out[edge[i].u]++; Add_Edge(edge[i].u, edge[i].v, 2); } } for (int i=1;i<=n;i++) { if (abs(in[i]-out[i]) & 1) { return false; } else if (in[i] < out[i]) { Add_Edge(S,i,out[i]-in[i]); tot += out[i] - in[i]; } else if (in[i] > out[i]) { Add_Edge(i,T,in[i]-out[i]); } } return Dinic() == tot; } int main(){ n = read(); m = read(); for (int i=1;i<=m;i++) { edge[i].u = read(); edge[i].v = read(); edge[i].w1 = read(); edge[i].w2 = read(); if (edge[i].w1 > edge[i].w2) { swap(edge[i].w1, edge[i].w2); swap(edge[i].u, edge[i].v); } MX = max(MX, edge[i].w2); MN = min(MN, edge[i].w1); } int l = MN, r = MX, mid, ret = -1; while (l <= r) { mid = l + r >> 1; if (judge(mid)) ret = mid, r = mid - 1; else l = mid + 1; } if (~ret) printf("%d\n",ret); else puts("NIE"); return 0; }
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