POJ 3084 Panic Room 最小割

来源：互联网发布：天津市网络教研平台编辑：程序博客网时间：2024/05/18 01:57
根据题意要求锁一些门使得入侵者无法到达指定的房间这个是不是很像网络流当中的最小割即把图中所有点分成 S T 两个集合使得满流后不再连通而最小割是网络流当中容量最小的割这恰好又满足题目所求锁最少门的限定
#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <vector>using namespace std;const int maxn = 30;const int INF = 1e7;struct Edge{          int u, v, cap, flow;          Edge(){}          Edge(int u, int v, int cap, int flow):u(u), v(v), cap(cap), flow(flow){}};struct ISAP{          int n, s, t;          int cur[maxn], d[maxn], p[maxn], num[maxn];          vector<int> G[maxn];          vector<Edge> edges;          void init(int n){                    this -> n = n;                    for(int i= 0; i < n; i++) G[i].clear();                    edges.clear();          }          void add(int u, int v, int cap){                    edges.push_back(Edge(u, v, cap, 0));                    edges.push_back(Edge(v, u, 0, 0));                    int m = edges.size();                    G[u].push_back(m-2);                    G[v].push_back(m-1);          }          void bfs(){                    for(int i = 0; i< n; i++) d[i] = INF;                    d[t] = 0;                    queue<int> Q;                    Q.push(t);                    while(!Q.empty()){                              int x = Q.front(); Q.pop();                              for(int i = 0; i < G[x].size(); i++){                                        Edge &e = edges[G[x][i]];                                        if(e.cap > 0 || d[e.v] <= d[x] + 1) continue;                                        d[e.v] = d[x] + 1;                                        Q.push(e.v);                              }                    }          }          int augment(){                    int x = t, a = INF;                    while(x != s){                              Edge &e = edges[p[x]];                              a = min(a, e.cap - e.flow);                              x = e.u;                    }                    x = t;                    while(x != s){                              edges[p[x]].flow += a;                              edges[p[x]^1].flow -= a;                              x = edges[p[x]].u;                    }                    return a;          }          int maxflow(int s, int t){                    this -> s = s;                    this -> t = t;                    memset(cur, 0, sizeof(cur));                    memset(num, 0, sizeof(num));                    bfs();                    for(int i = 0; i< n; i++)if(d[i] != INF) num[d[i]]++;                    int x = s, flow = 0;                    while(d[s] < n){                              if(x == t){                                        flow += augment();                                        x = s;                              }                              int ok = 0;                              for(int i = cur[x]; i < G[x].size(); i++){                                        Edge &e = edges[G[x][i]];                                        if(e.cap > e.flow && d[e.v] + 1 == d[x]){                                                  ok = 1;                                                  cur[x] = i;                                                  p[e.v] = G[x][i];                                                  x = e.v;                                                  break;                                        }                              }                              if(!ok){                                        int m = n - 1;                                        for(int i = 0; i < G[x].size(); i++){                                                  Edge &e = edges[G[x][i]];                                                  if(e.cap > e.flow) m = min(m, d[e.v]);                                        }                                        if(--num[d[x]] == 0) break;                                        ++num[d[x] = m + 1];                                        cur[x] = 0;                                        if(x != s) x = edges[p[x]].u;                              }                    }                    return flow;          }}solver;void solve(){          int n, m, x, S, T;          char s[3];          scanf("%d%d", &n, &T);          S = n;          solver.init(n + 1);          for(int i = 0; i < n; i++){                    scanf("%s%d", s, &m);                    if(s[0] == 'I') solver.add(S, i, INF);                    for(int j = 0; j < m; j++){                              scanf("%d", &x);                              solver.add(i, x, INF);                              solver.add(x, i, 1);                    }          }          int ans = solver.maxflow(S, T);          if(ans < INF) printf("%d\n", ans);          else printf("PANIC ROOM BREACH\n");}int main(){          //freopen("in.txt", "r", stdin);          int T;          scanf("%d", &T);          while(T--){                    solve();          }          return 0;}
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