HDU 4616 Game tree DP

There are n knots in a tree, each of which has several valuable gifts. Some may have stuffing traps, and m chances of dropping them into the stuffing trap.

After the first m point drops into the stuffing trap, it cannot go any more, and each point can only go through once at most. Q: You can use any vertex as the starting point.

To the total value of a gift.

Analysis:

There are two situations:

I. Starting Point with filling points

Ii. Starting Point with non-stuffing points

Code:

1. Search from bottom up (self-written code)

 

 

#include<iostream>  #include<cstdio>  #include<cstring>  #include<vector>  using namespace std; typedef long long LL; const int maxn=55555; vector<int>Tree[maxn]; LL val[maxn],dp[2][maxn][5],ans; int vid[maxn],par[maxn]; int n,m; LL max(LL a,LL b){     return a>b?a:b; } void DFS(int cnt){     int len=Tree[cnt].size(),q=0;     for(int i=0;i<len;++i){         int son=Tree[cnt][i];         if(par[son]==son&&son){             par[son]=cnt; q=1;             DFS(son);             if(!vid[cnt]&&!vid[son])                 dp[0][cnt][0]=max(dp[0][cnt][0],dp[0][son][0]+val[cnt]);             for(int i=1; i<=m; ++i){                 if(vid[son])                     dp[0][cnt][i]=max(dp[0][cnt][i], dp[0][son][i-1]+val[cnt]);                 else                      dp[0][cnt][i]=max(dp[0][cnt][i], dp[0][son][i]+val[cnt]);             }             if(vid[cnt]){                 for(int i=1;i<=m;++i)                     dp[1][cnt][i]=max(dp[1][cnt][i],dp[1][son][i-1]+val[cnt]);             }else {                 for(int i=1;i<=m;++i){                     if(dp[1][son][i])                         dp[1][cnt][i]=max(dp[1][cnt][i],dp[1][son][i]+val[cnt]);                 }             }         }     }     ans=max(ans,max(dp[0][cnt][m],dp[1][cnt][m])); }  void comp1(int cnt,int a,int b){  // vid[cnt]=1      if(vid[a]){         for(int i=1;i<m;++i){             LL k=dp[1][b][m-i-1];             if(m-i-1) k=max(k,dp[0][b][m-i-2]);             ans=max(ans,dp[0][a][i]+val[cnt]+k);         }     }     else {         for(int i=1;i<=m;++i){             LL k=dp[1][b][m-i];             if(m-i) k=max(k,dp[0][b][m-i-1]);             ans=max(ans,dp[0][a][i]+val[cnt]+k);         }     } } void comp2(int cnt,int a,int b){  // vid[cnt]=0      if(vid[a]){         for(int i=1;i<=m;++i){             LL k=dp[1][b][m-i];             if(m-i) k=max(k,dp[0][b][m-i-1]);             ans=max(ans,dp[0][a][i]+val[cnt]+k);         }     }     else {         for(int i=1;i<=m;++i){             LL k=dp[1][b][m-i+1];             if(m-i+1) k=max(k,dp[0][b][m-i]);             ans=max(ans,dp[0][a][i]+val[cnt]+k);         }     } } void DFS_DP(int cnt){     int len=Tree[cnt].size();     for(int i=0;i<len;++i){         int a=Tree[cnt][i];         if(par[a]!=cnt) continue;         for(int j=i+1;j<len;++j){             int b=Tree[cnt][j];             if(par[b]!=cnt)continue;             if(vid[cnt]) {                 comp1(cnt,a,b);                 comp1(cnt,b,a);             } else {                 comp2(cnt,a,b); comp2(cnt,b,a);             }         }     }     for(int i=0;i<len;++i){         int son=Tree[cnt][i];         if(par[son]!=cnt) continue;         DFS_DP(son);     } } void print(); int main(){     int T; scanf("%d",&T);     while(T--){         memset(dp,0,sizeof(dp));         scanf("%d%d",&n,&m);         for(int i=0;i<n;++i){             Tree[i].clear();             scanf("%I64d%d",val+i,vid+i);             par[i]=i;             if(vid[i])                  for(int j=1; j<=m; ++j)                      dp[0][i][j]=dp[1][i][j]=val[i];             else                  for(int j=0; j<=m; ++j)                      dp[0][i][j]=val[i];         }          for(int i=1;i<n;++i){             int a,b; scanf("%d%d",&a,&b);             Tree[a].push_back(b);             Tree[b].push_back(a);         }         ans=0LL;         DFS(0);         DFS_DP(0);         printf("%I64d\n",ans);     }     return 0; } #include<iostream>#include<cstdio>#include<cstring>#include<vector>using namespace std;typedef long long LL;const int maxn=55555;vector<int>Tree[maxn];LL val[maxn],dp[2][maxn][5],ans;int vid[maxn],par[maxn];int n,m;LL max(LL a,LL b){    return a>b?a:b;}void DFS(int cnt){    int len=Tree[cnt].size(),q=0;    for(int i=0;i<len;++i){        int son=Tree[cnt][i];        if(par[son]==son&&son){            par[son]=cnt; q=1;            DFS(son);            if(!vid[cnt]&&!vid[son])                dp[0][cnt][0]=max(dp[0][cnt][0],dp[0][son][0]+val[cnt]);            for(int i=1; i<=m; ++i){                if(vid[son])                    dp[0][cnt][i]=max(dp[0][cnt][i], dp[0][son][i-1]+val[cnt]);                else                    dp[0][cnt][i]=max(dp[0][cnt][i], dp[0][son][i]+val[cnt]);            }            if(vid[cnt]){                for(int i=1;i<=m;++i)                    dp[1][cnt][i]=max(dp[1][cnt][i],dp[1][son][i-1]+val[cnt]);            }else {                for(int i=1;i<=m;++i){                    if(dp[1][son][i])                        dp[1][cnt][i]=max(dp[1][cnt][i],dp[1][son][i]+val[cnt]);                }            }        }    }    ans=max(ans,max(dp[0][cnt][m],dp[1][cnt][m]));}void comp1(int cnt,int a,int b){  // vid[cnt]=1    if(vid[a]){        for(int i=1;i<m;++i){            LL k=dp[1][b][m-i-1];            if(m-i-1) k=max(k,dp[0][b][m-i-2]);            ans=max(ans,dp[0][a][i]+val[cnt]+k);        }    }    else {        for(int i=1;i<=m;++i){            LL k=dp[1][b][m-i];            if(m-i) k=max(k,dp[0][b][m-i-1]);            ans=max(ans,dp[0][a][i]+val[cnt]+k);        }    }}void comp2(int cnt,int a,int b){  // vid[cnt]=0    if(vid[a]){        for(int i=1;i<=m;++i){            LL k=dp[1][b][m-i];            if(m-i) k=max(k,dp[0][b][m-i-1]);            ans=max(ans,dp[0][a][i]+val[cnt]+k);        }    }    else {        for(int i=1;i<=m;++i){            LL k=dp[1][b][m-i+1];            if(m-i+1) k=max(k,dp[0][b][m-i]);            ans=max(ans,dp[0][a][i]+val[cnt]+k);        }    }}void DFS_DP(int cnt){    int len=Tree[cnt].size();    for(int i=0;i<len;++i){        int a=Tree[cnt][i];        if(par[a]!=cnt) continue;        for(int j=i+1;j<len;++j){            int b=Tree[cnt][j];            if(par[b]!=cnt)continue;            if(vid[cnt]) {                comp1(cnt,a,b);                comp1(cnt,b,a);            } else {                comp2(cnt,a,b); comp2(cnt,b,a);            }        }    }    for(int i=0;i<len;++i){        int son=Tree[cnt][i];        if(par[son]!=cnt) continue;        DFS_DP(son);    }}void print();int main(){    int T; scanf("%d",&T);    while(T--){        memset(dp,0,sizeof(dp));        scanf("%d%d",&n,&m);        for(int i=0;i<n;++i){            Tree[i].clear();            scanf("%I64d%d",val+i,vid+i);            par[i]=i;            if(vid[i])                for(int j=1; j<=m; ++j)                    dp[0][i][j]=dp[1][i][j]=val[i];            else                for(int j=0; j<=m; ++j)                    dp[0][i][j]=val[i];        }        for(int i=1;i<n;++i){            int a,b; scanf("%d%d",&a,&b);            Tree[a].push_back(b);            Tree[b].push_back(a);        }        ans=0LL;        DFS(0);        DFS_DP(0);        printf("%I64d\n",ans);    }    return 0;}

2. Search from top to bottom (refer to the code written by shenniu)

 

#include<iostream>  #include<cstdio>  #include<cstring>  #include<vector>  using namespace std; const int maxn=55555; int n,m; int val[maxn],vid[maxn]; int up[2][maxn][4]; int dp[2][maxn][4]; vector<int>G[maxn]; void DFS(int cnt,int fa){     up[0][cnt][0]=dp[0][cnt][0]=val[cnt];     if(val[cnt]) up[1][cnt][1]=dp[1][cnt][1]=val[cnt];     if(fa!=-1){         for(int i=0;i<=m;++i){             if(i!=m&&(up[0][fa][i]||dp[0][fa][i]))                 dp[0][cnt][i+vid[cnt]]=max(dp[0][fa][i],up[0][fa][i])+val[cnt];             if(i==m&&vid[cnt]) continue;             if(dp[1][fa][i]||up[1][fa][i])                 dp[1][cnt][i+vid[cnt]]=max(dp[1][fa][i],up[1][fa][i])+val[cnt];         }     }     int len=G[cnt].size();     for(int i=0;i<len;++i){         int son=G[cnt][i];         if(son==fa) continue;         DFS(son,cnt);         for(int j=0;j<=m;++j){             if(j!=m&&up[0][son][j])                 up[0][cnt][j+vid[cnt]]=max(up[0][cnt][j+vid[cnt]],up[0][son][j]+val[cnt]);             if(j==m&&vid[cnt]) continue;             if(up[1][son][j])                 up[1][cnt][j+vid[cnt]]=max(up[1][cnt][j+vid[cnt]],up[1][son][j]+val[cnt]);         }     } } int main(){     int T; scanf("%d",&T);     while(T--){         memset(dp,0,sizeof(dp));         memset(up,0,sizeof(up));         scanf("%d%d",&n,&m);         for(int i=0;i<n;++i)             scanf("%d%d",val+i,vid+i), G[i].clear();         for(int i=1;i<n;++i){             int a,b; scanf("%d%d",&a,&b);             G[a].push_back(b);             G[b].push_back(a);         }         DFS(0,-1);         int ans=0;         for(int i=0;i<n;++i)             for(int j=0;j<=m;++j)                 ans=max(ans,max(dp[0][i][j],dp[1][i][j]));         printf("%d\n",ans);     }     return 0; } #include<iostream>#include<cstdio>#include<cstring>#include<vector>using namespace std;const int maxn=55555;int n,m;int val[maxn],vid[maxn];int up[2][maxn][4];int dp[2][maxn][4];vector<int>G[maxn];void DFS(int cnt,int fa){    up[0][cnt][0]=dp[0][cnt][0]=val[cnt];    if(val[cnt]) up[1][cnt][1]=dp[1][cnt][1]=val[cnt];    if(fa!=-1){        for(int i=0;i<=m;++i){            if(i!=m&&(up[0][fa][i]||dp[0][fa][i]))                dp[0][cnt][i+vid[cnt]]=max(dp[0][fa][i],up[0][fa][i])+val[cnt];            if(i==m&&vid[cnt]) continue;            if(dp[1][fa][i]||up[1][fa][i])                dp[1][cnt][i+vid[cnt]]=max(dp[1][fa][i],up[1][fa][i])+val[cnt];        }    }    int len=G[cnt].size();    for(int i=0;i<len;++i){        int son=G[cnt][i];        if(son==fa) continue;        DFS(son,cnt);        for(int j=0;j<=m;++j){            if(j!=m&&up[0][son][j])                up[0][cnt][j+vid[cnt]]=max(up[0][cnt][j+vid[cnt]],up[0][son][j]+val[cnt]);            if(j==m&&vid[cnt]) continue;            if(up[1][son][j])                up[1][cnt][j+vid[cnt]]=max(up[1][cnt][j+vid[cnt]],up[1][son][j]+val[cnt]);        }    }}int main(){    int T; scanf("%d",&T);    while(T--){        memset(dp,0,sizeof(dp));        memset(up,0,sizeof(up));        scanf("%d%d",&n,&m);        for(int i=0;i<n;++i)            scanf("%d%d",val+i,vid+i), G[i].clear();        for(int i=1;i<n;++i){            int a,b; scanf("%d%d",&a,&b);            G[a].push_back(b);            G[b].push_back(a);        }        DFS(0,-1);        int ans=0;        for(int i=0;i<n;++i)            for(int j=0;j<=m;++j)                ans=max(ans,max(dp[0][i][j],dp[1][i][j]));        printf("%d\n",ans);    }    return 0;}