POJ 3155 最大密度子图

  1 #include <map>
  2 #include <set>
  3 #include <cmath>
  4 #include <queue>
  5 #include <stack>
  6 #include <cstdio>
  7 #include <string>
  8 #include <vector>
  9 #include <cstdlib>
 10 #include <cstring>
 11 #include <sstream>
 12 #include <iostream>
 13 #include <algorithm>
 14 #include <functional>
 15 using namespace std;
 16 #define rep(i,a,n) for (int i=a;i<n;i++)
 17 #define per(i,a,n) for (int i=n-1;i>=a;i--)
 18 #define pb push_back
 19 #define mp make_pair
 20 #define all(x) (x).begin(),(x).end()
 21 #define SZ(x) ((int)(x).size())
 22 typedef vector<int> VI;
 23 typedef long long ll;
 24 typedef pair<int, int> PII;
 25 const ll mod = 1e9 + 7;
 26 const int inf = 0x3f3f3f3f;
 27 const double eps = 1e-10;
 28 const double pi = acos(-1.0);
 29 // head
 30 
 31 struct edge { int to; double cap; int rev; };
 32 const int MAX_V = 110;
 33 vector<edge> G[MAX_V];
 34 int level[MAX_V];
 35 int iter[MAX_V];
 36 
 37 void add_edge(int from, int to, double cap) {
 38     G[from].pb(edge{ to, cap, (int)G[to].size() });
 39     G[to].pb(edge{ from, 0, (int)G[from].size() - 1 });
 40 }
 41 
 42 void bfs(int s) {
 43     memset(level, -1, sizeof(level));
 44     queue<int> que;
 45     level[s] = 0;
 46     que.push(s);
 47     while (!que.empty()) {
 48         int v = que.front(); que.pop();
 49         rep(i, 0, G[v].size()) {
 50             edge &e = G[v][i];
 51             if (e.cap > 0 && level[e.to] < 0) {
 52                 level[e.to] = level[v] + 1;
 53                 que.push(e.to);
 54             }
 55         }
 56     }
 57 }
 58 
 59 double dfs(int v, int t, double f) {
 60     if (v == t) return f;
 61     for (int &i = iter[v]; i < G[v].size(); i++) {
 62         edge &e = G[v][i];
 63         if (e.cap > 0 && level[v] < level[e.to]) {
 64             double d = dfs(e.to, t, min(f, e.cap));
 65             if (d > 0) {
 66                 e.cap -= d;
 67                 G[e.to][e.rev].cap += d;
 68                 return d;
 69             }
 70         }
 71     }
 72     return 0;
 73 }
 74 
 75 double max_flow(int s, int t) {
 76     double flow = 0;
 77     while (1) {
 78         bfs(s);
 79         if (level[t] < 0) return flow;
 80         memset(iter, 0, sizeof(iter));
 81         double f;
 82         while ((f = dfs(s, t, inf)) > 0) flow += f;
 83     }
 84 }
 85 
 86 struct Rel { int x, y; }p[1010];
 87 int degree[MAX_V];
 88 int n, m, s, t;
 89 
 90 void construct_graph(double mid) {
 91     rep(i, 0, MAX_V) G[i].clear();
 92     rep(i, 1, n + 1) add_edge(s, i, m), add_edge(i, t, m + 2 * mid - degree[i]);
 93     rep(i, 0, m) add_edge(p[i].x, p[i].y, 1.0), add_edge(p[i].y, p[i].x, 1.0);
 94 }
 95 
 96 int vis[MAX_V], sum;
 97 void dfs_travel(int v) {
 98     sum++;
 99     vis[v] = 1;
100     rep(i, 0, G[v].size()){
101         edge &e = G[v][i];
102         if (e.cap > eps && !vis[e.to]) dfs_travel(e.to);
103     }
104 }
105 
106 int main() {
107     cin >> n >> m;
108     if (m == 0) return puts("1\n1"), 0;
109     s = 0, t = n + 1; 
110     rep(i, 0, m) {
111         scanf("%d%d", &p[i].x, &p[i].y);
112         degree[p[i].x]++;
113         degree[p[i].y]++;
114     }
115     double lb = 0, ub = m, precision = 1.0 / n / n;
116     while (ub - lb >= precision) {
117         double mid = (lb + ub) / 2;
118         construct_graph(mid);
119         double hg = (n*m - max_flow(s, t)) / 2;
120         if (hg > eps) lb = mid;
121         else ub = mid;
122     }
123     construct_graph(lb);
124     max_flow(s, t);
125     dfs_travel(0);
126     cout << sum - 1 << endl;
127     rep(i, 1, n + 1) if (vis[i]) cout << i << endl;
128     return 0;
129 }