HLG1407Leyni的游戏【最小点权覆盖集】

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 using namespace std;
 5 
 6 const int maxn = 205;
 7 const int INF = 1000000000;
 8 int n;
 9 
10 int W[maxn][maxn];
11 int Lx[maxn], Ly[maxn];
12 int Left[maxn];
13 bool S[maxn], T[maxn];
14 
15 bool match(int i) {
16     S[i] = true;
17     for(int j = 1; j <= n; j++) if(Lx[i] + Ly[j] == W[i][j] && !T[j]) {
18         T[j] = true;
19         if(!Left[j] || match(Left[j])) {
20             Left[j] = i;
21             return true;
22         }
23     }
24     return false;
25 }
26 
27 void update() {
28     int a = INF;
29     for(int i = 1; i <= n; i++) if(S[i])
30         for(int j= 1; j <= n; j++) if(!T[j])
31             a = min(a, Lx[i] + Ly[j] - W[i][j]);
32     for(int i = 1; i <= n; i++) {
33         if(S[i]) Lx[i] -= a;
34         if(T[i]) Ly[i] += a;
35     }
36 }
37 
38 void KM() {
39     for(int i = 1; i <= n; i++) {
40         Left[i] = Lx[i] = Ly[i] = 0;
41         for(int j = 1; j <= n; j++)
42             Lx[i] = max(Lx[i], W[i][j]);
43     }
44     for(int i = 1; i<= n; i++) {
45         for(;;) {
46             for(int j = 1; j <= n; j++) S[j] = T[j] = 0;
47             if(match(i)) break; else update();
48         }
49     }
50 }
51 
52 int main() {
53     int num;
54     int m;
55     while(EOF != scanf("%d %d",&n, &m)) {
56         memset(W, 0, sizeof(W));
57         for(int i = 1; i <= n; i++) {
58             for(int j = 1; j <= m; j++) {
59                 scanf("%d",&num);
60                 W[i][j] = num;
61             }
62         }
63         n = max(n, m);
64         KM();
65         int ans = 0;
66         for(int i = 1; i <= n; i++) {
67             ans += Lx[i] + Ly[i];
68         }
69         printf("%d\n",ans);
70     }
71     return 0;
72 }

  1 #include <iostream>
  2 #include <queue>
  3 #include <cstdio>
  4 #include <cstring>
  5 #include <vector>
  6 using namespace std;
  7 
  8 const int maxn = 200 * 200 + 10;
  9 const int INF = 1000000000;
 10 
 11 struct Edge {
 12     int from, to, cap, flow, cost;
 13 };
 14 
 15 struct MCMF
 16 {
 17     int n, m, s, t;
 18     vector<Edge> edges;
 19     vector<int> G[maxn];
 20 
 21     int inq[maxn];
 22     int d[maxn];
 23     int p[maxn];
 24     int a[maxn];
 25 
 26     void init(int n) {
 27         this -> n = n;
 28         for(int i = 0; i < n; i++) G[i].clear();
 29         edges.clear();
 30     }
 31 
 32     void AddEdge(int from, int to, int cap, int cost) {
 33         edges.push_back((Edge) { from, to, cap, 0, cost } );
 34         edges.push_back((Edge) { to, from, 0, 0, -cost } );
 35         m = edges.size();
 36         G[from].push_back(m - 2);
 37         G[to].push_back(m - 1);
 38     }
 39 
 40     bool BellmanFord(int s, int t, int &flow, int &cost) {
 41         for(int i = 0; i < n; i++) d[i] = INF;
 42         memset(inq, 0, sizeof(inq) );
 43         d[s] = 0; inq[s] = 1; p[s] = 0; a[s] = INF;
 44         queue<int> Q;
 45         Q.push(s);
 46         while(!Q.empty()) {
 47             int u = Q.front(); Q.pop();
 48             inq[u] = 0;
 49             for(int i = 0; i < G[u].size(); i++) {
 50                 Edge &e = edges[G[u][i]];
 51                 if(e.cap > e.flow && d[e.to] > d[u] + e.cost) {
 52                     d[e.to] = d[u] + e.cost;
 53                     p[e.to] = G[u][i];
 54                     a[e.to] = min(a[u], e.cap - e.flow);
 55                     if(!inq[e.to]) { Q.push(e.to); inq[e.to] = 1; }
 56                 }
 57             }
 58         }
 59 
 60         if(d[t] == INF) return false;
 61         flow += a[t];
 62         cost += d[t] * a[t];
 63         int u = t;
 64         while(u != s) {
 65             edges[p[u]].flow += a[t];
 66             edges[p[u] ^ 1].flow -= a[t];
 67             u = edges[p[u]].from;
 68         }
 69         return true;
 70     }
 71 
 72     int MinCost(int s, int t) {
 73         //this -> s = s; this -> t = t;
 74         int flow = 0, cost = 0;
 75         while(BellmanFord(s, t, flow, cost)){};
 76         return cost;
 77     }
 78 };
 79 
 80 MCMF g;
 81 
 82 int main() {
 83     int n, m;
 84     int num;
 85     while(EOF != scanf("%d %d",&n, &m)) {
 86         int s = 0; int t = n + m + 1;
 87         g.init(n * m + 10);
 88         for(int i = 1; i <= n; i++) {
 89             for(int j = 1; j <= m; j++) {
 90                 scanf("%d",&num);
 91                 g.AddEdge(i, j + n, 1,-num);
 92             }
 93         }
 94         for(int i = 1; i <= n; i++) {
 95             g.AddEdge(s, i, 1, 0);
 96         }
 97         for(int j = 1; j <= m; j++) {
 98             g.AddEdge(j + m, t, 1, 0);
 99         }
100         printf("%d\n",-g.MinCost(s, t));
101     }
102     return 0;
103 }