codeforces 510E. Fox And Dinner 网络流

  1 #include<bits/stdc++.h>
  2 using namespace std;
  3 #define pb(x) push_back(x)
  4 #define ll long long
  5 #define mk(x, y) make_pair(x, y)
  6 #define lson l, m, rt<<1
  7 #define mem(a) memset(a, 0, sizeof(a))
  8 #define rson m+1, r, rt<<1|1
  9 #define mem1(a) memset(a, -1, sizeof(a))
 10 #define mem2(a) memset(a, 0x3f, sizeof(a))
 11 #define rep(i, a, n) for(int i = a; i<n; i++)
 12 #define ull unsigned long long
 13 typedef pair<int, int> pll;
 14 const double PI = acos(-1.0);
 15 const double eps = 1e-8;
 16 const int mod = 1e9+7;
 17 const int inf = 1061109567;
 18 const int dir[][2] = { {-1, 0}, {1, 0}, {0, -1}, {0, 1} };
 19 const int maxn = 2e5;
 20 int prime[20005];
 21 int q[maxn*2], head[maxn*2], dis[maxn/10], s, t, a[205], num, vis[205];
 22 struct node
 23 {
 24     int to, nextt, c;
 25     node(){}
 26     node(int to, int nextt, int c):to(to), nextt(nextt), c(c){}
 27 }e[maxn*2];
 28 void init() {
 29     num = 0;
 30     mem1(head);
 31 }
 32 void pre() {
 33     for(int i = 2; i<=20000; i++) {
 34         if(!prime[i])
 35             for(int j = i*i; j<=20000; j+=i) {
 36                 prime[j] = 1;
 37             }
 38     }
 39 }
 40 void add(int u, int v, int c) {
 41     e[num] = node(v, head[u], c); head[u] = num++;
 42     e[num] = node(u, head[v], 0); head[v] = num++;
 43 }
 44 int bfs() {
 45     mem(dis);
 46     dis[s] = 1;
 47     int st = 0, ed = 0;
 48     q[ed++] = s;
 49     while(st<ed) {
 50         int u = q[st++];
 51         for(int i = head[u]; ~i; i = e[i].nextt) {
 52             int v = e[i].to;
 53             if(!dis[v]&&e[i].c) {
 54                 dis[v] = dis[u]+1;
 55                 if(v == t)
 56                     return 1;
 57                 q[ed++] = v;
 58             }
 59         }
 60     }
 61     return 0;
 62 }
 63 int dfs(int u, int limit) {
 64     if(u == t) {
 65         return limit;
 66     }
 67     int cost = 0;
 68     for(int i = head[u]; ~i; i = e[i].nextt) {
 69         int v = e[i].to;
 70         if(e[i].c&&dis[v] == dis[u]+1) {
 71             int tmp = dfs(v, min(limit-cost, e[i].c));
 72             if(tmp>0) {
 73                 e[i].c -= tmp;
 74                 e[i^1].c += tmp;
 75                 cost += tmp;
 76                 if(cost == limit)
 77                     break;
 78             } else {
 79                 dis[v] = -1;
 80             }
 81         }
 82     }
 83     return cost;
 84 }
 85 int dinic() {
 86     int ans = 0;
 87     while(bfs()) {
 88         ans += dfs(s, inf);
 89     }
 90     return ans;
 91 }
 92 vector <int> ve[205];
 93 void dfs1(int u, int pos) {
 94     ve[pos].pb(u);
 95     vis[u] = 1;
 96     for(int i = head[u]; ~i; i = e[i].nextt) {
 97         int v = e[i].to;
 98         if(vis[v])
 99             continue;
100         if(v == t|| v == s)
101             continue;
102         if(i%2==0&&!e[i].c) {
103             dfs1(v, pos);
104         }
105         if(i%2==1&&!e[i^1].c)
106             dfs1(v, pos);
107     }
108 }
109 int main()
110 {
111     int n;
112     cin>>n;
113     init();
114     pre();
115     for(int i = 0; i<n; i++) {
116         scanf("%d", &a[i]);
117     }
118     if(n&1) {
119         cout<<"Impossible"<<endl;
120         return 0;
121     }
122     s = n+1, t = n+2;
123     for(int i = 0; i<n; i++) {
124         if(a[i]&1) {
125             add(s, i, 2);
126         } else {
127             add(i, t, 2);
128         }
129     }
130     for(int i = 0; i<n; i++) {
131         for(int j = i+1; j<n; j++) {
132             if((a[i]&1) != (a[j]&1)) {
133                 if(!prime[a[i]+a[j]]) {
134                     if(a[i]&1)
135                         add(i, j, 1);
136                     else
137                         add(j, i, 1);
138                 }
139             }
140         }
141     }
142     int ans = dinic();
143     if(ans != n) {
144         cout<<"Impossible"<<endl;
145         return 0;
146     }
147     int cnt = 0;
148     for(int i = 0; i<n; i++) {
149         if(!vis[i]) {
150             dfs1(i, cnt++);
151         }
152     }
153     cout<<cnt<<endl;
154     for(int i = 0; i<cnt; i++) {
155         cout<<ve[i].size()<<" ";
156         for(int j = 0; j<ve[i].size(); j++) {
157             cout<<ve[i][j]+1<<" ";
158         }
159         cout<<endl;
160     }
161     return 0;
162 }