【HDOJ】1669 Jamie's Contact Groups

二分+二分图多重匹配。

 /* 1669 */
 #include <iostream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 const int maxn = ;
 const int maxm = ;
 bool M[maxn][maxm];
 bool visit[maxm];
 int can[maxm][maxm];
 int sz[maxm];
 int n, gn, bound;

 bool dfs(int u) {
     rep(i, , gn) {
         if (M[u][i] && !visit[i]) {
             visit[i] = true;
             if (sz[i] < bound) {
                 can[i][sz[i]++] = u;
                 return true;
             }
             rep(j, , sz[i]) {
                 if (dfs(can[i][j])) {
                     can[i][j] = u;
                     return true;
                 }
             }
         }
     }

     return false;
 }

 bool judge(int bound_) {
     bound = bound_;
     memset(sz, , sizeof(sz));
     rep(i, , n) {
         memset(visit, false, sizeof(visit));
         if (!dfs(i))
             return false;
     }

     return true;
 }

 void solve() {
     int l, r, mid;
     int ans;

     l = ;
     ans = r = n;
     while (l <= r) {
         mid = (l + r) >> ;
         if (judge(mid)) {
             ans = mid;
             r = mid - ;
         } else {
             l = mid + ;
         }
     }

     printf("%d\n", ans);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     char name[];
     int gid;
     char ch;

     while (scanf("%d %d", &n, &gn)!=EOF && (n||gn)) {
         memset(M, false, sizeof(M));
         rep(i, , n) {
             scanf("%s", name);
             while () {
                 scanf("%d%c", &gid, &ch);
                 M[i][gid] = true;
                 if (ch == '\n')
                     break;
             }
         }
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

二分+网络流Dinic也可以解。

 /* 1669 */
 #include <iostream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 typedef struct {
     int v, c, nxt;
 } Edge_t;

 const int INF = 0x3f3f3f3f;
 const int maxn = ;
 const int maxm = ;
 const int maxv = maxn + maxm;
 const int maxe = maxn*maxm*+;
 Edge_t E[maxe];
 int F[maxe];
 int head[maxv], head_[maxv];
 int id[maxm];
 int dis[maxv], Q[maxv];
 int m;
 int n, gn;
 int s, t;

 void init() {
     memset(head, -, sizeof(head));
     m = ;
     s = ;
     t = n + gn + ;
 }

 void addEdge(int u, int v, int c) {
     E[m].v = v;
     E[m].c = c;
     E[m].nxt = head[u];
     head[u] = m++;

     E[m].v = u;
     E[m].c = ;
     E[m].nxt = head[v];
     head[v] = m++;
 }

 bool bfs() {
     int l = , r = ;
     int u, v, k;

     Q[r++] = s;
     memset(dis, , sizeof(dis));
     dis[s] = ;

     while (l < r) {
         u = Q[l++];
         for (k=head[u]; k!=-; k=E[k].nxt) {
             v = E[k].v;
             if (!dis[v] && E[k].c>F[k]) {
                 dis[v] = dis[u] + ;
                 if (v == t)
                     return false;
                 Q[r++] = v;
             }
         }
     }

     return true;
 }

 int dfs(int u, int val) {
     if (u==t || val==)
         return val;

     int ret = ;
     int tmp, v;

     for (int& k=head_[u]; k!=-; k=E[k].nxt) {
         v = E[k].v;
         if (dis[v]==dis[u]+ && E[k].c>F[k] && (tmp=dfs(v, min(val, E[k].c-F[k])))>) {
             F[k] += tmp;
             F[k^] -= tmp;
             ret += tmp;
             val -= tmp;
             if (val == )
                 break;
         }
     }

     return ret;
 }

 int Dinic() {
     int ret = , tmp;

     while () {
         if (bfs())
             break;

         memcpy(head_, head, sizeof(head));
         while () {
             tmp = dfs(s, INF);
             if (tmp == )
                 break;
             ret += tmp;
         }
     }
     #ifndef ONLINE_JUDGE
         printf("Dinic = %d\n", ret);
     #endif
     return ret;
 }

 bool judge(int bound) {
     rep(i, , gn+)
         E[id[i]].c = bound;
     memset(F, , sizeof(F));

     return Dinic()>=n;
 }

 void solve() {
     int l = , r = n, mid;
     int ans = -;

     while (r >= l) {
         mid = (l + r) >> ;
         if (judge(mid)) {
             ans = mid;
             r = mid - ;
         } else {
             l = mid + ;
         }
     }

     printf("%d\n", ans);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     char name[];
     char ch;
     int gid;

     while (scanf("%d %d", &n, &gn)!=EOF && (n||gn)) {
         init();
         rep(i, , n+) {
             scanf("%s", name);
             while () {
                 scanf("%d%c", &gid, &ch);
                 addEdge(i, gid+n+, );
                 if (ch == '\n')
                     break;
             }
         }
         rep(i, , n+)
             addEdge(s, i, );
         rep(i, , gn+) {
             id[i] = m;
             addEdge(n+i, t, );
         }
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }