[Bzoj 1468]Tree

Posted 2021-01-31 wolfycz

Description
给你一棵TREE,以及这棵树上边的距离.问有多少对点它们两者间的距离小于等于K

Input
N（n<=40000） 接下来n-1行边描述管道，按照题目中写的输入 接下来是k

Output
一行，有多少对点之间的距离小于等于k

Sample Input
7
1 6 13
6 3 9
3 5 7
4 1 3
2 4 20
4 7 2
10

Sample Output
5

前置知识：点分治

后置知识：还能有啥后置知识，处理过程中sort+two point扫描即可

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
#define sqr(x) ((x)*(x))
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
    static char buf[1000000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
inline int frd(){
    int x=0,f=1;char ch=gc();
    for (;ch<'0'||ch>'9';ch=gc())   if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=gc()) x=(x<<1)+(x<<3)+ch-'0';
    return x*f;
}
inline int read(){
    int x=0,f=1;char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar())  if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar())    x=(x<<1)+(x<<3)+ch-'0';
    return x*f;
}
inline void print(int x){
    if (x<0)    putchar('-'),x=-x;
    if (x>9)    print(x/10);
    putchar(x%10+'0');
}
const int N=4e4;
int pre[(N<<1)+10],now[N+10],child[(N<<1)+10],val[(N<<1)+10];
int size[N+10],dis[N+10],h[N+10];
bool vis[N+10];
int tot,Max,root,K,top;
ll Ans;
void join(int x,int y,int z){pre[++tot]=now[x],now[x]=tot,child[tot]=y,val[tot]=z;}
void insert(int x,int y,int z){join(x,y,z),join(y,x,z);}
void Get_root(int x,int fa,int sz){
    int res=0; size[x]=1;
    for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
        if (son==fa||vis[son])  continue;
        Get_root(son,x,sz);
        size[x]+=size[son];
        res=max(res,size[son]);
    }
    res=max(res,sz-size[x]);
    if (res<Max)    Max=res,root=x;
}
void get_dis(int x,int fa){
    h[++top]=dis[x];
    for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
        if (son==fa||vis[son])  continue;
        dis[son]=dis[x]+val[p];
        get_dis(son,x);
    }
}
int solve(int x,int v){
    top=0,dis[x]=v;
    get_dis(x,0);
    sort(h+1,h+1+top);
    int l=1,r=top; ll res=0;
    for (;l<=r;l++){
        while (l<=r&&h[l]+h[r]>K)   r--;
        res+=r-l+1;
    }
    return res;
}
void divide(int x){
    vis[x]=1,Ans+=solve(x,0);
    for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
        if (vis[son])   continue;
        Ans-=solve(son,val[p]);
        Max=inf,root=0;
        Get_root(son,0,size[son]);
        divide(root);
    }
}
int main(){
    int n=read();
    for (int i=1;i<n;i++){
        int x=read(),y=read(),z=read();
        insert(x,y,z);
    }K=read();
    Max=inf,root=0;
    Get_root(1,0,n);
    divide(root);
    printf("%lld
",Ans-n);
    return 0;
}