Panic Room

Description

You are the lead programmer for the Securitron 9042, the latest and greatest in home security software from Jellern Inc. (Motto: We secure your stuff so YOU can't even get to it). The software is designed to "secure" a room; it does this by determining the minimum number of locks it has to perform to prevent access to a given room from one or more other rooms. Each door connects two rooms and has a single control panel that will unlock it. This control panel is accessible from only one side of the door. So, for example, if the layout of a house looked like this:

with rooms numbered 0-6 and control panels marked with the letters "CP" (each next to the door it can unlock and in the room that it is accessible from), then one could say that the minimum number of locks to perform to secure room 2 from room 1 is two; one has to lock the door between room 2 and room 1 and the door between room 3 and room 1. Note that it is impossible to secure room 2 from room 3, since one would always be able to use the control panel in room 3 that unlocks the door between room 3 and room 2.

Input

Input to this problem will begin with a line containing a single integer x indicating the number of datasets. Each data set consists of two components:
  1. Start line – a single line "m n" (1 <=m<= 20; 0 <=n<= 19) where m indicates the number of rooms in the house and n indicates the room to secure (the panic room).
  2. Room list – a series of m lines. Each line lists, for a single room, whether there is an intruder in that room ("I" for intruder, "NI" for no intruder), a count of doors c (0 <= c <= 20) that lead to other rooms and have a control panel in this room, and a list of rooms that those doors lead to. For example, if room 3 had no intruder, and doors to rooms 1 and 2, and each of those doors' control panels were accessible from room 3 (as is the case in the above layout), the line for room 3 would read "NI 2 1 2". The first line in the list represents room 0. The second line represents room 1, and so on until the last line, which represents room m - 1. On each line, the rooms are always listed in ascending order. It is possible for rooms to be connected by multiple doors and for there to be more than one intruder!

Output

For each dataset, output the fewest number of locks to perform to secure the panic room from all the intruders. If it is impossible to secure the panic room from all the intruders, output "PANIC ROOM BREACH". Assume that all doors start out unlocked and there will not be an intruder in the panic room.

Sample Input

3
7 2
NI 0
I 3 0 4 5
NI 2 1 6
NI 2 1 2
NI 0
NI 0
NI 0
7 2
I 0
NI 3 0 4 5
NI 2 1 6
I 2 1 2
NI 0
NI 0
NI 0
4 3
I 0
NI 1 2
NI 1 0
NI 4 1 1 2 2

Sample Output

2
PANIC ROOM BREACH
1
题意：如果房间a的机关能打开b，则a->b.有些房间有盗贼，因为游戏开始时，房间的门都开的，为了防止盗贼能到达某个秘密性房间，必须将一些房间的门关掉。
求：最少要关掉多少门。
分析：图的边连通度。
从盗贼为起点：
#include <stdio.h>  
#include <string.h>  
#include <algorithm>
#include <iostream>
#define Min(a, b) (a) < (b) ? a : b  
#define Max(a, b) (a) > (b) ? a : b
using  namespace std;  
const  int MAXN = 1005;  
const  int MAXM = 210000;  
const  int INF = 1100000;  
struct  Edge  
{  
    int  st, ed;  
    int  next;  
    int  flow; 
    int cap; 
}edge[MAXM]; 
int  head[MAXN], level[MAXN], que[MAXN], E;
void  add(int u, int v, int w)  
{  
    //printf("add %d %d %d\n", u, v, w);
    edge[E].flow = 0;  
    edge[E].cap = w;
    edge[E].st = u;  
    edge[E].ed = v;  
    edge[E].next = head[u];  
    head[u] = E++;      
    edge[E].flow = 0; 
    edge[E].cap = 0; 
    edge[E].st = v;  
    edge[E].ed = u;  
    edge[E].next = head[v];  
    head[v] = E++;  
}
int  dinic_bfs(int src, int dest, int ver)        
{        
    int i, j;         
    for (i = 0; i <= ver; i++)
    {    
        level[i] = -1;
    }
    int rear = 1;        
    que[0] = src; level[src] = 0;        
    for(i = 0; i < rear; i++) 
    {        
          for(j = head[que[i]]; j != -1; j = edge[j].next)
         {        
            if(level[edge[j].ed] == -1 && edge[j].cap > edge[j].flow)        
            {        
              level[edge[j].ed] = level[que[i]]+1;        
              que[rear++] = edge[j].ed;        
            }
         }
    }
    return  level[dest] >= 0;        
}        
     
int dinic_dfs(int src, int dest, int ver)        
{        
    int stk[MAXN], top = 0;        
    int ret = 0, cur, ptr, pre[MAXN], minf, i;        
    int del[MAXN];        
    for (i = 0; i <= ver; i++) 
    {
        del[i] = 0;
    }
    stk[top++] = src;         
    pre[src] = src; 
    cur = src;        
    while(top)        
    {        
        while(cur != dest && top)        
        {        
            for(i = head[cur]; i != -1; i = edge[i].next)        
            {        
                if(level[edge[i].ed] == level[cur] + 1 && edge[i].cap > edge[i].flow  && !del[edge[i].ed])        
                {        
                    stk[top++] = edge[i].ed;      
                    cur = edge[i].ed;        
                    pre[edge[i].ed] = i;                       
                    break;     
                }        
            }     
            if(i == -1)       
            {        
                del[cur] = 1;        
                top--;        
                if(top) cur = stk[top-1];        
            }        
        }                
        if(cur == dest)        
        {       
            minf = INF;        
            while(cur != src)        
            {        
                cur = pre[cur];        
                if(edge[cur].cap - edge[cur].flow < minf) minf = edge[cur].cap - edge[cur].flow;        
                cur = edge[cur].st;        
            }
            cur = dest;        
            while(cur != src)        
            {        
                cur = pre[cur];        
                edge[cur].flow += minf;        
                edge[cur^1].flow -= minf;        
                if(edge[cur].cap - edge[cur].flow == 0)
                {
                     ptr = edge[cur].st;
                }
                cur = edge[cur].st;        
            }        
            while(top > 0&& stk[top-1] != ptr) top--;        
            if(top)  cur = stk[top-1];        
            ret += minf;      
        }        
    }        
    return ret;        
}        
int Dinic(int src, int dest, int ver)        
{        
    int  ret = 0, t;        
    while(dinic_bfs(src, dest, ver))        
    {        
        t = dinic_dfs(src, dest, ver);        
        if(t) ret += t;        
        else  break;        
    }        
    return ret;        
}
int main()
{
    int ca, n, m, s, t, ver, i, j, k, v;
    scanf("%d", &ca);
    char ch[3];
    while (ca--)
    {
        scanf("%d%d", &n, &m);
        E = 0;
        s = n, t = n + 1, ver = t + 1;
        for (i = 0; i <= ver; i++)
        {
            head[i] = -1;
        }
        for (i = 0; i < n; i++)
        {
            scanf("%s%d", ch, &k);
            if (strcmp(ch, "I") == 0)
            {
                add(s, i, INF);//从盗贼为出发点 
            }
            while (k--)
            {
                scanf("%d", &v);
                add(i, v, INF);//表示通过i能直接打开v 
                add(v, i, 1);
            }
        }
        add(m, t, INF);
        int ans;
        ans = Dinic(s, t, ver);
        if (ans >= INF)
        {
            printf("PANIC ROOM BREACH\n");
        }
        else
        {
            printf("%d\n", ans);
        }
    }
    return 0;
}
/*
100
4 2
I 0
NI 1 0
NI 1 1
NI 2 2 1

5 2
I 0
NI 1 0
NI 1 1
NI 3 2 1 4
I 0

5 2
I 0
I 1 0
I 1 1
I 3 2 1 4
I 0

1 0
NI 0

1 0
I 0

2 1
I 0
NI 1 0

2 1
I 0
NI 3 0 0 0

3 2
I 0
NI 2 0 2
NI 1 1

2 1
I 1 1
NI 1 0
*/
以秘密房间为起点，这比较麻烦，如果某个房间能到秘密房间。则也必须从源向它连个inf的容量。
#include <stdio.h>  
#include <string.h>  
#include <algorithm>
#include <iostream>
#define Min(a, b) (a) < (b) ? a : b  
#define Max(a, b) (a) > (b) ? a : b
using  namespace std;  
const  int MAXN = 1005;  
const  int MAXM = 210000;  
const  int INF = 1100000;  
struct  Edge  
{  
    int  st, ed;  
    int  next;  
    int  flow; 
    int cap; 
}edge[MAXM]; 
int  head[MAXN], level[MAXN], que[MAXN], E;
void  add(int u, int v, int w)  
{  
    //printf("add %d %d %d\n", u, v, w);
    edge[E].flow = 0;  
    edge[E].cap = w;
    edge[E].st = u;  
    edge[E].ed = v;  
    edge[E].next = head[u];  
    head[u] = E++;      
    edge[E].flow = 0; 
    edge[E].cap = 0; 
    edge[E].st = v;  
    edge[E].ed = u;  
    edge[E].next = head[v];  
    head[v] = E++;  
}
int  dinic_bfs(int src, int dest, int ver)        
{        
    int i, j;         
    for (i = 0; i <= ver; i++)
    {    
        level[i] = -1;
    }
    int rear = 1;        
    que[0] = src; level[src] = 0;        
    for(i = 0; i < rear; i++) 
    {        
          for(j = head[que[i]]; j != -1; j = edge[j].next)
         {        
            if(level[edge[j].ed] == -1 && edge[j].cap > edge[j].flow)        
            {        
              level[edge[j].ed] = level[que[i]]+1;        
              que[rear++] = edge[j].ed;        
            }
         }
    }
    return  level[dest] >= 0;        
}
int dinic_dfs(int src, int dest, int ver)        
{        
    int stk[MAXN], top = 0;        
    int ret = 0, cur, ptr, pre[MAXN], minf, i;        
    int del[MAXN];        
    for (i = 0; i <= ver; i++) 
    {
        del[i] = 0;
    }
    stk[top++] = src;         
    pre[src] = src; 
    cur = src;        
    while(top)        
    {        
        while(cur != dest && top)        
        {        
            for(i = head[cur]; i != -1; i = edge[i].next)        
            {        
                if(level[edge[i].ed] == level[cur] + 1 && edge[i].cap > edge[i].flow  && !del[edge[i].ed])        
                {        
                    stk[top++] = edge[i].ed;      
                    cur = edge[i].ed;        
                    pre[edge[i].ed] = i;                       
                    break;     
                }        
            }     
            if(i == -1)       
            {        
                del[cur] = 1;        
                top--;        
                if(top) cur = stk[top-1];        
            }        
        }                
        if(cur == dest)        
        {       
            minf = INF;        
            while(cur != src)        
            {        
                cur = pre[cur];        
                if(edge[cur].cap - edge[cur].flow < minf) minf = edge[cur].cap - edge[cur].flow;        
                cur = edge[cur].st;        
            }
            cur = dest;        
            while(cur != src)        
            {        
                cur = pre[cur];        
                edge[cur].flow += minf;        
                edge[cur^1].flow -= minf;        
                if(edge[cur].cap - edge[cur].flow == 0)
                {
                     ptr = edge[cur].st;
                }
                cur = edge[cur].st;        
            }        
            while(top > 0&& stk[top-1] != ptr) top--;        
            if(top)  cur = stk[top-1];        
            ret += minf;      
        }        
    }        
    return ret;        
}        
int Dinic(int src, int dest, int ver)        
{        
    int  ret = 0, t;        
    while(dinic_bfs(src, dest, ver))        
    {        
        t = dinic_dfs(src, dest, ver);        
        if(t) ret += t;        
        else  break;        
    }        
    return ret;        
}
struct T
{
    int v, next;
}fn[1000];
int g[50], th, flag[50];
void insert(int u, int v)
{
    fn[th].v = v, fn[th].next = g[u], g[u] = th++;
}
void dfs(int u)
{
    flag[u] = 1;
    int i;
    for (i = g[u]; i != -1; i = fn[i].next)
    {
        if (!flag[fn[i].v])
        {
            dfs(fn[i].v);
        }
    }
}
int main()
{
    int ca, n, m, s, t, ver, i, j, k, v;
    scanf("%d", &ca);
    char ch[3];
    while (ca--)
    {
        scanf("%d%d", &n, &m);
        E = 0;
        th = 0;
        s = n, t = n + 1, ver = t + 1;
        for (i = 0; i < n; i++)
        {
            flag[i] = 0;
            g[i] = -1;
        }
        for (i = 0; i <= ver; i++)
        {
            head[i] = -1;
        }
        for (i = 0; i < n; i++)
        {
            scanf("%s%d", ch, &k);
            if (strcmp(ch, "I") == 0)
            {
                add(i, t, INF);
            }
            while (k--)
            {
                scanf("%d", &v);
                add(i, v, 1);
                add(v, i, INF);
                insert(v, i);
            }
        }
        dfs(m);
        for (i = 0; i < n; i++)
        {
            if (flag[i] == 1)
            {
                add(s, i, INF);
            }
        }
        int ans;
        ans = Dinic(s, t, ver);
        if (ans >= INF)
        {
            printf("PANIC ROOM BREACH\n");
        }
        else
        {
            printf("%d\n", ans);
        }
    }
    return 0;
}