题意:给出一张有向图,每次你可以从图中的任意一点出发,经过若干条边后停止,然后问你最少走几次可以将图中的每条边都走过至少一次,并且要输出方案,这个转化为网络流的话,就相当于 求一个最小流,并且存在下界,即每条边至少走一次。
析:转载:http://blog.csdn.net/sdj222555/article/details/40380423
这上面说的很清楚了,就是先求一遍是正向的,然后再求逆向的,这个逆向就是为了求可以减少的边。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <cmath> #include <stack> #include <sstream> #include <list> #include <assert.h> #include <bitset> #include <numeric> #define debug() puts("++++") #define gcd(a, b) __gcd(a, b) #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define fi first #define se second #define pb push_back #define sqr(x) ((x)*(x)) #define ms(a,b) memset(a, b, sizeof a) #define sz size() #define pu push_up #define pd push_down #define cl clear() #define all 1,n,1 #define FOR(i,x,n) for(int i = (x); i < (n); ++i) #define freopenr freopen("in.txt", "r", stdin) #define freopenw freopen("out.txt", "w", stdout) using namespace std; typedef long long LL; typedef unsigned long long ULL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const LL LNF = 1e17; const double inf = 1e20; const double PI = acos(-1.0); const double eps = 1e-3; const int maxn = 100 + 40; const int maxm = (100000 << 8) + 10; const int mod = 1000000007; const int dr[] = {-1, 0, 1, 0}; const int dc[] = {0, -1, 0, 1}; const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"}; int n, m; const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; inline bool is_in(int r, int c) { return r >= 0 && r < n && c >= 0 && c < m; } struct Edge{ int from, to, cap, flow; }; struct Dinic{ int n, m, s, t; vector<Edge> edges; vector<int> G[maxn]; int d[maxn]; bool vis[maxn]; int cur[maxn]; void init(int n){ this-> n = n; FOR(i, 0, n) G[i].cl; edges.cl; } void addEdge(int from, int to, int cap){ edges.pb((Edge){from, to, cap, 0}); edges.pb((Edge){to, from, 0, 0}); m = edges.sz; G[from].pb(m - 2); G[to].pb(m - 1); } bool bfs(){ ms(vis, 0); vis[s] = 1; d[s] = 0; queue<int> q; q.push(s); while(!q.empty()){ int u = q.front(); q.pop(); for(int i = 0; i < G[u].sz; ++i){ Edge &e = edges[G[u][i]]; if(!vis[e.to] && e.cap > e.flow){ d[e.to] = d[u] + 1; vis[e.to] = 1; q.push(e.to); } } } return vis[t]; } int dfs(int u, int a){ if(u == t || a == 0) return a; int flow = 0, f; for(int &i = cur[u]; i < G[u].sz; ++i){ Edge &e = edges[G[u][i]]; if(d[e.to] == d[u] + 1 && (f = dfs(e.to, min(a, e.cap - e.flow))) > 0){ e.flow += f; edges[G[u][i]^1].flow -= f; flow += f; a -= f; if(a == 0) break; } } return flow; } int maxflow(int s, int t){ this-> s = s; this-> t = t; int flow = 0; while(bfs()){ ms(cur, 0); flow += dfs(s, INF); } return flow; } }; Dinic dinic; int in[maxn]; vector<P> edges[maxn]; int main(){ while(scanf("%d", &n) == 1){ ms(in, 0); int s = 0, t = n + 1; dinic.init(t + 4); int ans = 0; for(int i = 1; i <= n; ++i){ int x; scanf("%d", &x); while(x--){ int y; scanf("%d", &y); ++in[y]; --in[i]; dinic.addEdge(i, y, INF); } edges[i].cl; } int sum = 0; for(int i = 1; i <= n; ++i) if(in[i] > 0) dinic.addEdge(s, i, in[i]), ans += in[i]; else dinic.addEdge(i, t, -in[i]); printf("%d\n", ans -= dinic.maxflow(s, t)); for(int i = 1; i <= n; ++i){ for(int j = 0; j < dinic.G[i].sz; ++j){ Edge &e = dinic.edges[dinic.G[i][j]]; if(e.from != i || e.to == t || e.cap == 0) continue; edges[i].pb(P(e.to, e.flow + 1)); in[e.to] += e.flow; } } for(int i = 1; i <= n; ++i) while(in[i] < 0){ ++in[i]; vector<int> ans; ans.push_back(i); int u = i; while(1){ bool ok = true; for(int j = 0; j < edges[u].sz; ++j){ if(edges[u][j].se == 0) continue; ok = false; --edges[u][j].se; u = edges[u][j].fi; ans.push_back(u); break; } if(ok) break; } for(auto &it : ans) printf("%d%c", it, " \n"[it == ans.back()]); } } return 0; }