【CF1244D】Paint the Tree（树形DP，树）

题意：

n<=1e5，1<=a[i][j]<=1e9

思路：

不是很懂INF为什么要开到1e15，我觉得只要1e14就好

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef pair<ll,ll> Pll;
 typedef vector<int> VI;
 typedef vector<PII> VII;
 //typedef pair<ll,ll>P;
 #define N  200010
 #define M  200010
 #define fi first
 #define se second
 #define MP make_pair
 #define pb push_back
 #define pi acos(-1)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
 #define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
 #define lowbit(x) x&(-x)
 #define Rand (rand()*(1<<16)+rand())
 #define id(x) ((x)<=B?(x):m-n/(x)+1)
 #define ls p<<1
 #define rs p<<1|1

 struct node
 {
     int x,y;
 }pre[N][][];

 ll dp[N][][];
 ll a[N][];
 int head[N],vet[N],nxt[N],d[N],c[N],son[N],f[N],tot,n;

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 void add(int a,int b)
 {
     nxt[++tot]=head[a];
     vet[tot]=b;
     head[a]=tot;
 }

 void dfs(int u,int fa)
 {
     //printf("dfs u=%d fa=%d\n",u,fa);
     int e=head[u],s=;
     rep(i,,)
      rep(j,,) dp[u][i][j]=1e15;
     while(e)
     {
         int v=vet[e];
         if(v!=fa)
         {
             s++;
             son[u]=v;
             f[v]=u;
             dfs(v,u);
         }
         e=nxt[e];
     }
     if(u==&&d[]==)
     {
         //printf("case 2\n");
         return;
     }

     if(s==)
     {
         rep(i,,)
          rep(j,,)
           if(i!=j) dp[u][i][j]=a[u][i];
     }
      else
      {
          int v=son[u];
          //printf("u=%d v=%d\n",u,v);
          rep(i,,)
           rep(j,,)
            rep(k,,)
             if(i!=j&&j!=k&&i!=k)
             {
                 if(dp[u][i][j]>dp[v][j][k]+a[u][i])
                 {
                     dp[u][i][j]=dp[v][j][k]+a[u][i];
                     pre[u][i][j].x=j;
                     pre[u][i][j].y=k;
                 }
             }

      }

 }

 void print()
 {
     /*rep(i,1,n)
      rep(j,0,2)
       rep(k,0,2)
        if(j!=k) printf("i=%d j=%d k=%d dp[i][j][k]=%I64d\n",i,j,k,dp[i][j][k]);*/
     if(d[]==)
     {
         ll ans=1e15;
         int x=,y=;
         rep(i,,)
          rep(j,,)
           if(i!=j&&dp[][i][j]<ans)
           {
                 ans=dp[][i][j];
                 x=i; y=j;
           }
         int u=;
         while(u)
         {
             c[u]=x;
             int x1=pre[u][x][y].x;
             int y1=pre[u][x][y].y;
             u=son[u];
             x=x1,y=y1;
         }
         printf("%I64d\n",ans);
         rep(i,,n) printf("%d ",c[i]+);
     }
      else
      {
          int k1=,k2=;
          rep(i,,n)
           if(f[i]==){k1=i; break;}
          per(i,n,)
           if(f[i]==){k2=i; break;}
          int x1,y1,x2,y2,z;
          ll ans=1e15;
          rep(i,,)
           rep(j,,)
            rep(k,,)
             rep(p,,)
              rep(q,,)
               if(i!=j&&i!=k&&j!=k&&j!=p&&p!=i&&i!=q&&k!=q&&dp[k1][j][p]+dp[k2][k][q]+a[][i]<ans)
               {
                   ans=dp[k1][j][p]+dp[k2][k][q]+a[][i];
                   z=i;
                   x1=j; y1=p;
                   x2=k; y2=q;
               }
          c[]=z;
          int u=k1,x=x1,y=y1;
          while(u)
          {
              c[u]=x;
              int x1=pre[u][x][y].x;
              int y1=pre[u][x][y].y;
              u=son[u];
              x=x1,y=y1;
          }
          u=k2,x=x2,y=y2;
          while(u)
          {
              c[u]=x;
              int x1=pre[u][x][y].x;
              int y1=pre[u][x][y].y;
              u=son[u];
              x=x1,y=y1;
          }
          printf("%I64d\n",ans);
          rep(i,,n) printf("%d ",c[i]+);
      }

 }

 int main()
 {
     //freopen("1.in","r",stdin);
     n=read();
     rep(j,,)
      rep(i,,n) scanf("%I64d",&a[i][j]);
     rep(i,,n) head[i]=d[i]=;
     tot=;
     rep(i,,n-)
     {
         int x=read(),y=read();
         add(x,y);
         add(y,x);
         d[x]++; d[y]++;
     }
     int flag=;
     rep(i,,n)
      if(d[i]>=) flag=;
     if(!flag)
     {
         printf("-1\n");
         return ;
     }
     dfs(,);
     print();
     return ;
 }

实际上只有1条或者2条从1下来的链，枚举1和与1相邻的颜色然后就能推出整条链

 #include<bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 typedef unsigned int uint;
 typedef unsigned long long ull;
 typedef pair<int,int> PII;
 typedef pair<ll,ll> Pll;
 typedef vector<int> VI;
 typedef vector<PII> VII;
 //typedef pair<ll,ll>P;
 #define N  200010
 #define M  200010
 #define fi first
 #define se second
 #define MP make_pair
 #define pb push_back
 #define pi acos(-1)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
 #define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
 #define lowbit(x) x&(-x)
 #define Rand (rand()*(1<<16)+rand())
 #define id(x) ((x)<=B?(x):m-n/(x)+1)
 #define ls p<<1
 #define rs p<<1|1

 const ll MOD=1e9+,inv2=(MOD+)/;
       double eps=1e-;
       ll INF=1e15;
       int da[]={-,,,};
       int db[]={,,-,};

 struct node
 {
     int x,y;
 }pre[N][][];

 ll a[N][];
 int head[N],vet[N],nxt[N],f[N],g[N],b[N],c[N],d[N],p[N],tot,son;

 int read()
 {
    int v=,f=;
    char c=getchar();
    while(c<||<c) {if(c=='-') f=-; c=getchar();}
    while(<=c&&c<=) v=(v<<)+v+v+c-,c=getchar();
    return v*f;
 }

 void add(int a,int b)
 {
     nxt[++tot]=head[a];
     vet[tot]=b;
     head[a]=tot;
 }

 void dfs(int u,int fa)
 {
     int e=head[u];
     while(e)
     {
         int v=vet[e];
         if(v!=fa)
         {
             f[v]=u;
             g[u]=v;
             if(u==)
             {
                 son++;
                 p[son]=v;
             }
             dfs(v,u);
         }
         e=nxt[e];
     }
 }

 int main()
 {
     //freopen("1.in","r",stdin);
     int n=read();
     rep(j,,)
      rep(i,,n) scanf("%I64d",&a[i][j]);
     rep(i,,n) head[i]=d[i]=;
     tot=;
     rep(i,,n-)
     {
         int x=read(),y=read();
         add(x,y);
         add(y,x);
         d[x]++; d[y]++;
     }
     int flag=;
     rep(i,,n)
      if(d[i]>=) flag=;
     if(!flag)
     {
         printf("-1\n");
         return ;
     }
     son=;
     dfs(,);
     ll ans=INF;
     if(son==)
     {
         rep(x,,)
         {
             int u=p[];
             rep(y,,)
              if(x!=y)
              {
                 b[]=x; b[u]=y;
                 int k=u;
                 while(k)
                 {
                     k=g[k];
                     if(!k) break;
                     b[k]=-b[f[k]]-b[f[f[k]]];
                 }
                  ll s=;
                  rep(i,,n) s+=a[i][b[i]];
                  if(s<ans)
                  {
                     ans=s;
                     rep(i,,n) c[i]=b[i];
                  }
              }
         }
     }
      else
      {
          int u1=p[],u2=p[];
          rep(x,,)
          rep(y,,)
           rep(z,,)
            if(x!=y&&x!=z&&y!=z)
            {
                 b[]=x; b[u1]=y;
                 int k=u1;
                 while(k)
                 {
                     k=g[k];
                     if(!k) break;
                     b[k]=-b[f[k]]-b[f[f[k]]];
                 }
                 b[u2]=z;
                 k=u2;
                 while(k)
                 {
                     k=g[k];
                     if(!k) break;
                     b[k]=-b[f[k]]-b[f[f[k]]];
                 }
                 ll s=;
                 rep(i,,n) s+=a[i][b[i]];
                 if(s<ans)
                 {
                     ans=s;
                     rep(i,,n) c[i]=b[i];
                 }
            }
      }

     printf("%I64d\n",ans);
     rep(i,,n) printf("%d ",c[i]+);
     return ;
 }