Ural 1018 (tree DP + backpack + optimization)

Question Link: Http://acm.hust.edu.cn/vjudge/problem/viewProblem.action? Id = 17662

Theme: The branches are connected with a lump of Apples (don't care about 'lump '). Given that M branches are left, ask the maximum number of apples left at the end.

Solutions:

In fact, the meaning is similar to that of vijos 1180 (Course Selection. Only the right is on the edge.

First, create an undirected graph DFS.

For (F + 1... j... cost)

For (1... k... j-cost)

F indicates the number of DFS subnodes. The reason for the addition of 1 is that the current vertex also needs to be allocated a branch to get the apple of This vertex.

F + = DFS (t), DFS (t) returns the F + 1 of the Child vertex T.

In fact, F + 1 can be directly written as m + 1, but it takes many unnecessary loops.

The final result is DP [1] [M + 1]. Note that because of the tree structure, the apple on 1 can be obtained by default, but in this DP mode, the apple on 1 should be obtained, you also need to add a virtual branch, that is, Why m + 1.

 

#include "cstdio"#include "queue"#include "iostream"#include "cstring"using namespace std;#define maxn 105int n,m,dp[maxn][maxn],head[maxn],tol;struct Edge{    int next,to,w;}e[maxn*2];void addedge(int u,int v,int w){    e[tol].to=v;    e[tol].next=head[u];    e[tol].w=w;    head[u]=tol++;}int dfs(int root,int pre){    int cost=1,i=root,f=0;    for(int a=head[root];a!=-1;a=e[a].next)    {        int t=e[a].to;        if(t==pre) continue;        f+=dfs(t,root);        for(int j=f+1;j>=1;j--)            for(int k=1;k<=j-cost;k++)                dp[i][j]=max(dp[i][j],dp[i][j-k]+dp[t][k]+e[a].w);    }    return f+cost;}int main(){    //freopen("in.txt","r",stdin);    int u,v,w;    scanf("%d%d",&n,&m);    memset(head,-1,sizeof(head));    for(int i=1;i<n;i++)    {        scanf("%d%d%d",&u,&v,&w);        addedge(u,v,w);        addedge(v,u,w);    }    dfs(1,1);    printf("%d\n",dp[1][m+1]);}

 

2867777

Neopenx

Ural

1018

Accepted

418

31

G ++ 4.9

917

2014-10-20 16:15:45

Ural 1018 (tree DP + backpack + optimization)