UVa1663 Purifying Machine (二分图最大匹配,最大流)

  1 #include <iostream>
  2 #include <string>
  3 #include <set>
  4 #include <queue>
  5 #include <cstring>
  6 #include <vector>
  7 using namespace std;
  8 
  9 const int maxn = 1000 + 5;
 10 const int INF = 0x3f3f3f3f;
 11 
 12 struct Edge {
 13     int from, to, cap, flow;
 14     Edge(int u, int v, int c, int f):from(u), to(v), cap(c), flow(f) {}
 15 };
 16 
 17 struct EdmondsKarp {
 18     int n, m;
 19     vector<Edge> edges;
 20     vector<int> G[maxn];
 21     int a[maxn];
 22     int p[maxn];
 23 
 24     void init(int n) {
 25         for (int i = 0; i < n; i++) G[i].clear();
 26         edges.clear();
 27     }
 28 
 29     void AddEdge(int from, int to, int cap) {
 30         edges.push_back(Edge(from, to, cap, 0));
 31         edges.push_back(Edge(to, from, 0, 0));
 32         m = edges.size();
 33         G[from].push_back(m - 2);
 34         G[to].push_back(m - 1);
 35     }
 36 
 37     int Maxflow(int s, int t) {
 38         int flow = 0;
 39         for (;;) {
 40             memset(a, 0, sizeof(a));
 41             queue<int> Q;
 42             Q.push(s);
 43             a[s] = INF;
 44             while (!Q.empty()) {
 45                 int x = Q.front(); Q.pop();
 46                 for (int i = 0; i < G[x].size(); i++) {
 47                     Edge& e = edges[G[x][i]];
 48                     if (!a[e.to] && e.cap > e.flow) {
 49                         p[e.to] = G[x][i];
 50                         a[e.to] = min(a[x], e.cap - e.flow);
 51                         Q.push(e.to);
 52                     }
 53                 }
 54                 if (a[t]) break;
 55             }
 56             if (!a[t]) break;
 57             for (int u = t; u != s; u = edges[p[u]].from) {
 58                 edges[p[u]].flow += a[t];
 59                 edges[p[u] ^ 1].flow -= a[t];
 60             }
 61             flow += a[t];
 62         }
 63         return flow;
 64     }
 65 };
 66 
 67 EdmondsKarp g;
 68 
 69 int n, m;
 70 string s[maxn];
 71 set<string> st;
 72 vector<int> e[maxn * 2];
 73 int color[maxn];
 74 
 75 bool ismatch(string& a, string& b) {
 76     int cnt = 0;
 77     for (int i = 0; i < n; i++)
 78         if (a[i] != b[i]) cnt++;
 79     if (cnt == 1) return true;
 80     else return false;
 81 }
 82 
 83 void AddColor(int s, int c) {
 84     color[s] = c;
 85     for (int i = 0; i < e[s].size(); i++) {
 86         int t = e[s][i];
 87         if (!color[t]) AddColor(t, 3 - c);
 88     }
 89 }
 90 
 91 int main() {
 92     while (cin >> n >> m && (n || m)) {
 93         for (int i = 0; i < m; i++) cin >> s[i];
 94         // for (int i = 0; i < m; i++) cout << s[i] << endl;
 95         st.clear();
 96         for (int i = 0; i < m; i++) {
 97             int j = 0;
 98             while (j < n) {
 99                 if (s[i][j] == ‘*‘) {
100                     s[i][j] = ‘0‘;
101                     st.insert(s[i]);
102                     s[i][j] = ‘1‘;
103                     st.insert(s[i]);
104                     break;
105                 }
106                 j++;
107             }
108             if (j == n) st.insert(s[i]);
109         }
110         // cout << "ok" << endl;
111         int cnt = 0;
112         for (set<string>:: iterator it = st.begin(); it != st.end(); it++)
113             s[++cnt] = *it;
114        // for (int i = 1; i <= cnt; i++) cout << s[i] << endl;
115         for (int i = 1; i <= cnt; i++) e[i].clear();
116         for (int i = 1; i <= cnt; i++)
117             for (int j = i + 1; j <= cnt; j++)
118                 if (ismatch(s[i], s[j])) {
119                     e[i].push_back(j);
120                     e[j].push_back(i);
121                 }
122         memset(color, 0, sizeof(color));
123         for (int i = 1; i <= cnt; i++) if (!color[i]) AddColor(i, 1);
124         // for (int i = 1; i <= cnt; i++) cout << color[i] << endl;
125         g.init(cnt + 2);
126         for (int i = 1; i <= cnt; i++) {
127             if (color[i] == 1) {
128                 g.AddEdge(0, i, 1);
129                // g.AddEdge(i, 0, 0);
130                 for (int j = 0; j < e[i].size(); j++) {
131                     int v = e[i][j];
132                     g.AddEdge(i, v, 1);
133                   //  g.AddEdge(v, i, 0);
134                 }
135             }
136             if (color[i] == 2) {
137                 g.AddEdge(i, cnt + 1, 1);
138                // g.AddEdge(cnt + 1, i, 0);
139             }
140         }
141         // cout << g.Maxflow(0, cnt + 1) << endl;
142         cout << cnt - g.Maxflow(0, cnt + 1) << endl;
143     }
144     return 0;
145 }