HDU 1561 The more, The Better (treeDP 背包) #by Plato

http://acm.hdu.edu.cn/showproblem.php?pid=1561

 

题意：一棵树，每个结点有个价值，从中取M个结点使得价值最大。（必须先取前置）

 

Idea:

之前也做过类似的题了。

f[i][k][j] = max{ f[i][k-1][j] , f[i][k-1][j-m] + f[第k个儿子][…][m] }

方程比较简单，treeDP上加个背包就是了。边界比较麻烦：

f[i][0][1] = w[i],else 全赋值为-INF

i:treeDp

k:1àsize

j:1àmcap，mcap是以此结点为根的子树所含的结点总数

m:1àmcap &&(j – m > 0)

然后还要去压缩状态，把第二维给压缩了。

 

#include <cstdio>#include <iostream>#include <fstream>#include <cstring>#include <vector>using namespace std;#define MAX(x,y) ((x)>(y)?(x):(y))const int INF = (1<<31)-1;struct edge{    int ev,w;    edge(){}    edge(int a,int b):ev(a),w(b){}};vector <edge> elist[209];int w[209];int f[209][209];int mcap[209];void DFS(int fv){    int size = elist[fv].size();    f[fv][1] = w[fv];    int ev;    for (int k = 0;k < size;k++)  //for (int k = 1;k <= size;k++) 使用vector注意下标是从0开始的~~~    {        ev = elist[fv][k].ev;        DFS(ev);        mcap[fv] += mcap[ev];        for (int j = mcap[fv];j >= 1;j--)        {            for (int m = 1;m <= mcap[fv];m++) if (j - m > 0)//特别注意j - m > 0 这个边界            {                f[fv][j] = MAX(f[fv][j],f[fv][j - m] + f[ev][m]);            }        }    }}int main(){    freopen("test.txt","r",stdin);    int N,M;    while(scanf("%d%d",&N,&M),N+M)    {        for (int i = 0; i <= N; i++)            elist[i].clear();        memset(w,0,sizeof(w));        int fv;        for (int i = 1; i <= N; i++)        {            scanf("%d%d",&fv,&w[i]);            elist[fv].push_back(edge(i,w[i]));        }        for (int i = 0;i < 209;i++) for (int j = 0;j < 209;j++) f[i][j] = -INF;        for (int i = 0;i < 209;i++) mcap[i] = 1;        DFS(0);        printf("%d\n",f[0][M+1]);//printf("%d\n",f[N][M]);    }    return 0;}