POJ - 3155 Hard Life

Posted 2020-12-05 mingsd

POJ-3155

一道裸的最大密度子图的题目。

代码：

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<queue>
  4 using namespace std;
  5 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout);
  6 #define LL long long
  7 #define ULL unsigned LL
  8 #define fi first
  9 #define se second
 10 #define pb push_back
 11 #define lson l,m,rt<<1
 12 #define rson m+1,r,rt<<1|1
 13 #define max3(a,b,c) max(a,max(b,c))
 14 #define min3(a,b,c) min(a,min(b,c))
 15 typedef pair<int,int> pll;
 16 const LL INF = 0x3f3f3f3f3f3f3f3f;
 17 const int inf = 0x3f3f3f3f;
 18 const LL mod =  (int)1e9+7;
 19 const int N = 120;
 20 const int M = 10000;
 21 double eps = 1e-6;
 22 int head[N], deep[N], cur[N];
 23 int u[M], v[M];
 24 int vis[N], d[N];
 25 double w[M]; int to[M], nx[M];
 26 int n, m, tot;
 27 void add(int u, int v,double val){
 28     w[tot]  = val; to[tot] = v;
 29     nx[tot] = head[u]; head[u] = tot++;
 30     w[tot]  = 0; to[tot] = u;
 31     nx[tot] = head[v]; head[v] = tot++;
 32 }
 33 int bfs(int s, int t){
 34     queue<int> q;
 35     memset(deep, 0, sizeof(int)*(n+3));
 36     q.push(s);
 37     deep[s] = 1;
 38     while(!q.empty()){
 39         int u = q.front();
 40         q.pop();
 41         for(int i = head[u]; ~i; i = nx[i]){
 42             if(w[i] > 0 && deep[to[i]] == 0){
 43                 deep[to[i]] = deep[u] + 1;
 44                 q.push(to[i]);
 45             }
 46         }
 47     }
 48     if(deep[t] > 0) return 1;
 49     return 0;
 50 }
 51 double Dfs(int u, int t, double flow){
 52     if(u == t) return flow;
 53     for(int &i = cur[u]; ~i; i = nx[i]){
 54         if(deep[u] + 1 == deep[to[i]] && w[i] > 0){
 55             double di = Dfs(to[i], t, min(w[i], flow));
 56             if(di > 0){
 57                 w[i] -= di, w[i^1] += di;
 58                 return di;
 59             }
 60         }
 61     }
 62     return 0;
 63 }
 64 
 65 int Dinic(int s, int t){
 66     double ans = 0, tmp;
 67     while(bfs(s, t)){
 68         for(int i = 0; i <= n+1; i++) cur[i] = head[i];
 69         while(tmp = Dfs(s, t, INF)) ans += tmp;
 70     }
 71     return ans;
 72 }
 73 
 74 bool check(double x){
 75     memset(head, -1, sizeof(int) * (n+2));
 76     tot = 0;
 77     int s = 0, t = n + 1;
 78     for(int i = 1; i <= m; i++){
 79         add(u[i], v[i], 1);
 80         add(v[i], u[i], 1);
 81     }
 82     for(int i = 1; i <= n; i++){
 83         add(s, i, m);
 84         add(i, t, m+2*x-d[i]);
 85     }
 86     return (m*n-Dinic(s,t))/2.0 >= 1e-6;
 87 }
 88 
 89 void Find(int x){
 90     vis[x] = 1;
 91     for(int i = head[x]; ~i; i = nx[i])
 92         if(w[i] > 0 && !vis[to[i]])
 93             Find(to[i]);
 94 }
 95 
 96 int main(){
 97     while(~scanf("%d%d", &n, &m)){
 98         if(m == 0){
 99             printf("1
1
");
100             continue;
101         }
102         memset(d, 0, sizeof(int)*(n+1));
103         for(int i = 1; i <= m; i++){
104             scanf("%d%d", &u[i], &v[i]);
105             d[u[i]]++; d[v[i]]++;
106         }
107         double l = 0, r = m,  mid;
108         while(r - l >= 1.0/n/n){
109             mid = (l+r)/2;
110             if(check(mid)) l = mid;
111             else r = mid;
112         }
113         check(l);
114         memset(vis, 0, sizeof(vis));
115         Find(0);
116         int ans = 0;
117         for(int i = 1; i <= n; i++) ans += vis[i];
118         printf("%d
", ans);
119         for(int i = 1; i <= n; i++)
120             if(vis[i]) printf("%d
", i);
121     }
122     return 0;
123 }

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