Problemsetting
It's well-known that different programming contests require different kind of problems. For example, maximal array size for TopCoder problem is only 50, and you definitely can not give a Suffix Tree problem to IOI because children will not have a chance to solve it (except of some touristic-inclined ones). Thus not every problem is acceptable for every contest.
You are preparing problemsets for N different contests. These contests require different number of problems, depending of type. For example, ACM ICPC style problemset usually has 10 problems, TopCoder SRM - 5 and so on.
Luckily you have already prepared M different problems. For each problem you have determined a set of contests you can give that problem to. Also you know the required number of problems for each contest.
Find out the maximal number of different contests for which you can simultaneously compose complete problemsets from the given set of problems. All problems in the problemsets must be unique, i.e. no problem can be used twice in different problemsets.
Input
The input file contains several test cases.
The first line of each test case contains 2 integers N and M (1 < N < 15, 0 < M < 50) - the number of different contests and the number of prepared problems. Each of the followingN lines contains the name of contest, followed by the required number of problems for that contest. The name of a contest consists of lower - and uppercase Latin letters and/or digits, is not empty and does not exceed 100 characters. Contest names are case-sensitive. It's guaranteed that all contest names will be pairwise different. The required number of problems does not exceed 100.
Each of the following M lines contains a (possibly empty) list of acceptable contest names for each problem, separated by a single space. It's guaranteed that all contest names will be correct (i.e., noted in the previous section of the current test case) and unique.
The line containing two zeroes indicates the end of the input file.
For each test case print an answer for that case on a new line, as shown in the sample output.
Sample Input
4 5 IOI 3 IPSC 2 TopCoder 2 SEERC 10 IOI IPSC TopCoder IOI IPSC IOI IPSC TopCoder SEERC 1 1 SampleContest 1 SampleContest 0 0
Sample Output
Case #1: 2 Case #2: 1
Source
#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<math.h>
#include<string>
#include<iostream>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#include<set>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
#define mid (L+R)/2
#define lson rt*2,L,mid
#define rson rt*2+1,mid+1,R
const int mod = 1e9+7;
const int maxn = 100;
const int INF = 0x3f3f3f3f;
int Map[55][55];
int need[55];
struct Edge{
int from, to, next, cap, flow;
Edge(){}
Edge(int _from, int _to, int _cap, int _flow):from(_from), to(_to), cap(_cap),flow(_flow){}
};
int contest_table[20];
vector<Edge>edges;
vector<int>G[maxn];
void AddEdge(int from, int to, int cap){
edges.push_back(Edge(from, to, cap, 0));
edges.push_back(Edge(to, from, 0, 0));
int m = edges.size();
G[from].push_back(m - 2);
G[to].push_back(m - 1);
}
int capacity[maxn];
struct Dinic{
int s, t; //
bool vis[maxn];
int d[maxn];
int cur[maxn];
bool BFS(){
memset(vis,0,sizeof(vis));
queue<int>Q;
Q.push(s);
d[s] = 0;
vis[s] = 1;
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(!vis[e.to] && e.cap > e.flow){
vis[e.to] = 1;
d[e.to] = d[x] + 1;
Q.push(e.to);
}
}
}
return vis[t];
}
int DFS(int x,int a){
if(x == t || a == 0) return a;
int flow = 0, f;
for(int &i = cur[x]; i < G[x].size(); i++){
Edge &e = edges[G[x][i]];
if(d[x] + 1 == d[e.to]&&(f = DFS(e.to, min(a,e.cap - e.flow))) > 0){
e.flow += f;
edges[G[x][i]^1].flow -= f;
flow += f;
a -= f;
if(a == 0) break;
}
}
return flow;
}
int Maxflow(int s,int t){
this->s = s; this->t = t;
int flow = 0;
while(BFS()){
memset(cur,0,sizeof(cur));
flow += DFS(s, INF);
}
return flow;
}
};
int n, m;
int constructG(int enumc){
for(int i = 0; i <= n+m+10; i++){
G[i].clear();
}
edges.clear();
for(int i = 1; i <= n; i++){
for(int j = 1; j <= m; j++){
if(Map[i][j]){
AddEdge(i, n+j, 1);
}
}
}
for(int i = 1; i <= m; i++){
AddEdge(n+i,n+m+1,1);
}
int ret = 0;
for(int i = 1; i <= n; i++){
if(enumc&1){
AddEdge(0, i, capacity[i]);
ret += need[i];
}
enumc /= 2;
}
return ret;
}
int main(){
string str;
int cas = 0;
char s[100000];
while(scanf("%d%d",&n,&m)!=EOF&&(n+m) != 0){
map<string,int>mp;
int c;
for(int i = 1; i <= n; i++){
scanf("%s",s);
str = s;
mp[str] = i;
scanf("%d",&need[i]);
}
memset(Map,0,sizeof(Map));
memset(capacity,0,sizeof(capacity));
getchar(); getchar();
for(int i = 1; i <= m; i++){
str = "";
gets(s);
int len = strlen(s);
for(int j = 0; j < len-1; j++) {
if(s[j]==' '&&j!=0){
if(s[j-1]!=' '){
Map[mp[str]][i]=1;
capacity[mp[str]]++;
}
str="";
}else if(s[j]!=' ') str+=s[j];
}
if(str!="") {
Map[mp[str]][i]=1;
capacity[mp[str]]++;
}
}
int enumc = (int)pow((double)2,(double)n);
int ans = 0;
Dinic ansf;
for(int i = 0; i < enumc; i++){
int j = i, cnum = 0, c = 0;
while(j){
if(j&1)
cnum++;
j = j >> 1;
}
if(ans >= cnum) continue;
int needMaxf = constructG(i);
int Maxf = ansf.Maxflow(0,n+m+1);
if(Maxf >= needMaxf){
ans = cnum;
}
}
printf("Case #%d: ",++cas);
printf("%d
",ans);
}
return 0;
}