hdu 2489 Minimal Ratio Tree (DFS枚举+MST)

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstdlib>
 4 #include<cstring>
 5 #include<string>
 6 #include<queue>
 7 #include<algorithm>
 8 #include<map>
 9 #include<iomanip>
10 #define INF 99999999
11 using namespace std;
12 
13 const int MAX = 15 + 5;
14 int edge[MAX][MAX], dist[MAX], node[MAX];//node记录最终选的点 
15 int vale[MAX], temp[MAX], n, m;//temp记录选的m个点
16 double minratio;
17 bool mark[MAX];
18 
19 int Prim(int s){
20     int sum = 0;
21     for (int i = 1; i <= m; ++i)mark[temp[i]] = false, dist[temp[i]] = edge[s][temp[i]];
22     mark[s] = true;
23     dist[s] = 0;
24     for (int i = 1; i<m; ++i){
25         int point = s;
26         for (int j = 1; j <= m; ++j){
27             if (point == s && !mark[temp[j]])point = temp[j];
28             if (!mark[temp[j]] && dist[point]>dist[temp[j]])point = temp[j];
29         }
30         mark[point] = true;
31         sum += dist[point];
32         for (int j = 1; j <= m; ++j){
33             if (!mark[temp[j]] && edge[point][temp[j]]<dist[temp[j]])dist[temp[j]] = edge[point][temp[j]];
34         }
35     }
36     return sum;
37 }
38 
39 void dfs(int u, int num){
40     if (num == m){
41         int ans = 0;
42         for (int i = 1; i <= m; ++i)ans += vale[temp[i]];
43         double sum = Prim(u)*1.0 / ans;
44         if (sum - minratio < -(1e-9)){
45             minratio = sum;
46             for (int i = 1; i <= m; ++i) node[i] = temp[i];
47         }
48         return;
49     }
50     if (n - u + num<m)return;
51     for (int i = u + 1; i <= n; ++i){
52         temp[num + 1] = i;
53         dfs(i, num + 1);
54     }
55 }
56 
57 int main(){
58     while (cin >> n >> m, n + m){
59         minratio = INF*1.0;
60         for (int i = 1; i <= n; ++i)cin >> vale[i];
61         for (int i = 1; i <= n; ++i){
62             for (int j = 1; j <= n; ++j){
63                 cin >> edge[i][j];
64             }
65         }
66         for (int i = 1; i <= n; ++i){
67             temp[1] = i;
68             dfs(i, 1);
69         }
70         for (int i = 1; i<m; ++i)cout << node[i] << ‘ ‘;
71         cout << node[m] << endl;
72     }
73     return 0;
74 }

 1 //调用时：dfs(1,0,0);
 2 
 3 //dep表示点的编号，cnt表示选取的点的个数，sum_pw表示目前选取了cnt个点后总的点权值
 4 void dfs(int dep, int cnt, int sum_pw) {
 5     if(cnt == m) {
 6         ...;
 7         return ;
 8     }
 9     if(dep == n + 1) return ;
10     use[dep] = true;  //选取点dep，这里use[i]=true表示选取点i，在用prim求最小生成树的时候有用
11     dfs(dep + 1, cnt + 1, sum_pw + weight[dep]);
12     use[dep] = false; //不选取点dep
13     dfs(dep + 1, cnt, sum_pw);
14 }