Poj1741[Tree]题解--点分治||Treap

【链接】

poj1741

【题目大意】

给你一棵树，对于这课树有n个顶点，定义dist(u,v)= 节点u和v之间的最小距离。再给你一个数k，使dist(u,v)<=k为一个有效对数，计算对于给定树有效的对数

【解题报告】

此题就是Treap的启发式合并和点分治的裸题，不用多说贴代码。

Treap:

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
using namespace std;
const int maxn=10005,maxm=20005;
int n,m,tot,ans,lnk[maxn],w[maxm],son[maxm],nxt[maxm];
struct Treap
{
Treap* son[2];
int x,s,w,ran;
int Cmp(int k) {if (k<x) return 0; if (k>x) return 1; return -1;}
void Updata() {s=son[0]->s+son[1]->s+w;}
}a[maxn*6],*Null=a,*ro[maxn];
void Add(int x,int y,int z)
{
w[++tot]=z; son[tot]=y; nxt[tot]=lnk[x]; lnk[x]=tot;
}
inline int Read()
{
int res=0;
char ch=getchar();
while (ch<'0'||ch>'9') ch=getchar();
while (ch>='0'&&ch<='9') res=res*10+ch-48,ch=getchar();
return res;
}
void Turn(Treap* &k,int d)
{
Treap* t=k->son[d]; k->son[d]=t->son[d^1]; t->son[d^1]=k;
t->s=k->s; k->Updata(); k=t;
}
void New(Treap* &k,int x,int p)
{
++tot; k=&a[tot]; k->s=k->w=p; k->x=x; k->ran=rand(); k->son[0]=k->son[1]=Null;
}
void Insert(Treap* &k,int x,int p)
{
if (k==Null) {New(k,x,p); return;}
int d=k->Cmp(x); k->s+=p;
if (d<0) k->w+=p;
else
{
Insert(k->son[d],x,p);
if (k->son[d]->ran<k->ran) Turn(k,d);
}
}
int Ask(Treap* k,int x)
{
if (k==Null) return 0;
int d=k->Cmp(x);
if (d<0) return k->son[0]->s+k->w;
else if (d) return k->son[0]->s+k->w+Ask(k->son[1],x);
return Ask(k->son[0],x);
}
void Join(Treap* &k1,Treap* k2)
{
if (k2==Null) return;
Insert(k1,k2->x,k2->w);
Join(k1,k2->son[0]); Join(k1,k2->son[1]);
}
int Count(Treap* k1,Treap* k2,int x)
{
if (k2==Null) return 0;
return k2->w*Ask(k1,x-k2->x)+Count(k1,k2->son[0],x)+Count(k1,k2->son[1],x);
}
void Dfs(int x,int dep,int fa)
{
for (int j=lnk[x]; j; j=nxt[j])
if (son[j]!=fa)
{
Dfs(son[j],dep+w[j],x);
if (ro[x]->s<ro[son[j]]->s) swap(ro[x],ro[son[j]]);
ans+=Count(ro[x],ro[son[j]],2*dep+m); Join(ro[x],ro[son[j]]);
}
ans+=Ask(ro[x],dep+m);
Insert(ro[x],dep,1);
}
void Work()
{
memset(lnk,0,sizeof(lnk)); tot=0;
for (int i=1; i<=n; i++) ro[i]=Null;
for (int i=1,x,y,z; i<n; i++) {x=Read();y=Read();z=Read(); Add(x,y,z); Add(y,x,z);}
tot=ans=0; Dfs(1,0,0);
printf("%d\n",ans);
n=Read(); m=Read();
}
int main()
{
n=Read(); m=Read();
while (n||m) Work();
return 0;
}

点分治：

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn=10005,maxm=20005,INF=((1<<30)-1)*2+1;
int n,m,tot,rot,ans,nn,p[maxn],f[maxn],f_son[maxn],dep[maxn],lnk[maxn],son[maxm],nxt[maxm],w[maxm];
bool vis[maxn];
inline int read_()
{
int sum=0;
char ch=getchar();
while (ch<'0'||ch>'9') ch=getchar();
while (ch>='0'&&ch<='9') sum=sum*10+ch-48,ch=getchar();
return sum;
}
void add_(int x,int y,int z)
{
w[++tot]=z; son[tot]=y; nxt[tot]=lnk[x]; lnk[x]=tot;
}
void getrot(int x,int fa)
{
f_son[x]=1; f[x]=0;
for (int j=lnk[x]; j; j=nxt[j])
if (!vis[son[j]]&&son[j]!=fa)
{
getrot(son[j],x);
f_son[x]+=f_son[son[j]];
f[x]=max(f[x],f_son[son[j]]);
}
f[x]=max(f[x],nn-f_son[x]);
if (f[x]<f[rot]) rot=x;
}
void getdep(int x,int fa)
{
dep[++dep[0]]=p[x];
for (int j=lnk[x]; j; j=nxt[j])
if (!vis[son[j]]&&son[j]!=fa)
{
p[son[j]]=p[x]+w[j];
getdep(son[j],x);
}
}
int cal(int x,int v)
{
p[x]=v; dep[0]=0;
getdep(x,0);
sort(dep+1,dep+1+dep[0]);
int L=1,R=dep[0],sum=0;
while (L<R)
if (dep[L]+dep[R]<=m) {sum+=R-L; L++;}  else R--;
return sum;
}
void solve(int x)
{
vis[x]=1; ans+=cal(x,0);
for (int j=lnk[x]; j; j=nxt[j])
if (!vis[son[j]])
{
ans-=cal(son[j],w[j]);
nn=f_son[son[j]]; rot=0;
getrot(son[j],0);
solve(rot);
}
}
void work_()
{
memset(vis,0,sizeof(vis));
memset(lnk,0,sizeof(lnk));
tot=0;
for (int i=1; i<n; i++)
{
int x=read_(),y=read_(),z=read_();
add_(x,y,z); add_(y,x,z);
}
nn=n; f[0]=INF; rot=ans=0;
getrot(1,0);
solve(rot);
printf("%d\n",ans);
n=read_(); m=read_();
}
int main()
{
n=read_(); m=read_();
while (n||m) work_();
return 0;
}