hdu 2489 Minimal Ratio Tree (DFS枚举+MST)

参考链接：http://blog.csdn.net/xingyeyongheng/article/details/9373271

　　　　　http://www.cnblogs.com/chenxiwenruo/p/3294668.html

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<string>
#include<queue>
#include<algorithm>
#include<map>
#include<iomanip>
#define INF 99999999
using namespace std;

const int MAX = 15 + 5;
int edge[MAX][MAX], dist[MAX], node[MAX];//node记录最终选的点 
int vale[MAX], temp[MAX], n, m;//temp记录选的m个点
double minratio;
bool mark[MAX];

int Prim(int s){
    int sum = 0;
    for (int i = 1; i <= m; ++i)mark[temp[i]] = false, dist[temp[i]] = edge[s][temp[i]];
    mark[s] = true;
    dist[s] = 0;
    for (int i = 1; i<m; ++i){
        int point = s;
        for (int j = 1; j <= m; ++j){
            if (point == s && !mark[temp[j]])point = temp[j];
            if (!mark[temp[j]] && dist[point]>dist[temp[j]])point = temp[j];
        }
        mark[point] = true;
        sum += dist[point];
        for (int j = 1; j <= m; ++j){
            if (!mark[temp[j]] && edge[point][temp[j]]<dist[temp[j]])dist[temp[j]] = edge[point][temp[j]];
        }
    }
    return sum;
}
/*
dfs枚举m个点，num代表目前选取了多少个点，k代表第num个点为k。
表示前num个点选自1~k，剩余的点从k+1~n中选。
*/
void dfs(int u, int num){
    if (num == m){
        int ans = 0;
        for (int i = 1; i <= m; ++i)ans += vale[temp[i]];
        double sum = Prim(u)*1.0 / ans;
        if (sum - minratio < -(1e-9)){
            minratio = sum;
            for (int i = 1; i <= m; ++i) node[i] = temp[i];
        }
        return;
    }
 //若剩余的点的个数(n-k)加上目前选取的个数num小于m的话，说明即使接下来n-k个点都选取，也选不足m个点，直接return
    if (n - u + num<m)return;
    for (int i = u + 1; i <= n; ++i){
        temp[num + 1] = i;
        dfs(i, num + 1);
    }
}

int main(){
    while (cin >> n >> m, n + m){
        minratio = INF*1.0;
        for (int i = 1; i <= n; ++i)cin >> vale[i];
        for (int i = 1; i <= n; ++i){
            for (int j = 1; j <= n; ++j){
                cin >> edge[i][j];
            }
        }
        for (int i = 1; i <= n; ++i){
            temp[1] = i;
            dfs(i, 1);
        }
        for (int i = 1; i<m; ++i)cout << node[i] << ' ';
        cout << node[m] << endl;
    }
    return 0;
}

别的大牛DFS写法

//调用时：dfs(1,0,0);

//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
void dfs(int dep, int cnt, int sum_pw) {
    if(cnt == m) {
        ...;
        return ;
    }
    if(dep == n + 1) return ;
    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
    dfs(dep + 1, cnt + 1, sum_pw + weight[dep]);
    use[dep] = false; //不选取点dep
    dfs(dep + 1, cnt, sum_pw);
}