【CF293E. Close Vertices】点分治 + 树状数组

CF293E
现在有一棵树，每条边的长度都为1，然后有一个权值，求存在多少个(u,v)点对，他们的路径长度 <= l, 总权重 <= w.

观察到边权长度都是 1 所以我们可以对路径的长度建立树状数组每次查询区间内满足的w即可

//现在有一棵树，每条边的长度都为1，然后有一个权值，求存在多少个(u,v)点对，他们的路劲长度 <= l, 总权重 <= w.
/*
    if you can't see the repay
    Why not just work step by step
    rubbish is relaxed
    to ljq
*/
#include <cstdio>
#include <cstring>
#include <iostream>
#include <queue>
#include <cmath>
#include <map>
#include <stack>
#include <set>
#include <sstream>
#include <vector>
#include <stdlib.h>
#include <algorithm>
//#pragma comment(linker, "/STACK:10240000,10240000")
using namespace std;

#define dbg(x) cout<<#x<<" = "<< (x)<< endl
#define dbg2(x1,x2) cout<<#x1<<" = "<<x1<<" "<<#x2<<" = "<<x2<<endl
#define dbg3(x1,x2,x3) cout<<#x1<<" = "<<x1<<" "<<#x2<<" = "<<x2<<" "<<#x3<<" = "<<x3<<endl
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))

typedef pair<int,int> pll;
typedef long long ll;
typedef unsigned long long ull;
const ull hash1 = 201326611;
const int inf = 0x3f3f3f3f;
const int _inf = 0xc0c0c0c0;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const ll _INF = 0xc0c0c0c0c0c0c0c0;
const ll mod =  (int)1e9+7;

ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll ksm(ll a,ll b,ll mod){int ans=1;while(b){if(b&1) ans=(ans*a)%mod;a=(a*a)%mod;b>>=1;}return ans;}
ll inv2(ll a,ll mod){return ksm(a,mod-2,mod);}
void exgcd(ll a,ll b,ll &x,ll &y,ll &d){if(!b) {d = a;x = 1;y=0;}else{exgcd(b,a%b,y,x,d);y-=x*(a/b);}}//printf("%lld*a + %lld*b = %lld\n", x, y, d);
//ull ha[MAX_N],pp[MAX_N];

inline int read()
{
    int date = 0,m = 1; char ch = 0;
    while(ch!='-'&&(ch<'0'|ch>'9'))ch = getchar();
    if(ch=='-'){m = -1; ch = getchar();}
    while(ch>='0' && ch<='9')
    {
        date = date*10+ch-'0';
        ch = getchar();
    }return date*m;
}

/*namespace sgt
{
    #define mid ((l+r)>>1)

    #undef mid
}*/

/*int root[MAX_N],cnt,sz;
namespace hjt
{
    #define mid ((l+r)>>1)
    struct node{int l,r,maxx;}T[MAX_N*40];

    #undef mid
}*/
const int MAX_N = 100025;
int C[MAX_N<<1];
void ADD(int x,int v)
{
    for(;x<MAX_N;x+=x&(-x))
        C[x]+=v;
}
int getsum(int x)
{
    int res = 0;
    if(x<=0) return 0;
    for(;x;x-=x&(-x))
        res+=C[x];
    return res;
}
int n,l,W,p[MAX_N],eid,Size[MAX_N],SIZE,ms,root,maxson[MAX_N],dep[MAX_N],weight[MAX_N];
ll ans;
bool vis[MAX_N];
void init()
{
    memset(p,-1,sizeof(p));
    eid = 0;
}
struct edge
{
    int v,next,dis,w;
}e[MAX_N<<1];
struct node
{
    int a,b;
    bool operator < (const node other) const
    {
        return b < other.b;
    }
}now[MAX_N];
void add(int u,int v,int dis,int w)
{
    e[eid].v = v;
    e[eid].next = p[u];
    e[eid].dis = dis;
    e[eid].w = w;
    p[u] = eid++;
}
void getroot(int x,int fa)
{
    Size[x] = 1;maxson[x] = 0;
    for(int i = p[x];i+1;i=e[i].next)
    {
        int v = e[i].v;
        if(vis[v]||v==fa) continue;
        getroot(v,x);
        Size[x]+=Size[v];
        if(Size[v]>maxson[x]) maxson[x] = Size[v];
    }
    if(SIZE-Size[x]>maxson[x]) maxson[x] = SIZE - Size[x];
    if(ms>maxson[x]) ms = maxson[x],root = x;
}
void getdis(int x,int fa)
{
    now[++now[0].a].a = dep[x];now[now[0].a].b = weight[x];
    for(int i = p[x];i+1;i=e[i].next)
    {
        int v = e[i].v;
        if(v==fa||vis[v]) continue;
        dep[v] = dep[x] + 1;
        weight[v] = weight[x] + e[i].w;
        getdis(v,x);
    }
}
ll solve(int x,int dis,int w)
{
    dep[x] = dis;weight[x] = w;now[0].a = 0;getdis(x,-1);
    sort(now+1,now+1+now[0].a);
    int L = 1,R = now[0].a;
    ll sum = 0;
    for(int i = 1;i<=now[0].a;++i) ADD(now[i].a+1,1);
    for(;L<=R;L++)
    {
        ADD(now[L].a+1,-1);
        while(L<R&&now[L].b+now[R].b>W)
        {
            ADD(now[R].a+1,-1);
            R--;
        }
        if(L>=R) break;
        if(l-now[L].a>=0)
        {
        sum+=1ll*getsum(l-now[L].a+1);
        }
    }
    if(getsum(now[R].a+1)) ADD(now[R].a+1,-1);
    return sum;
}
void fenzhi(int x,int ssize)
{
    vis[x] = true;
    ans+=solve(x,0,0);
    for(int i = p[x];i+1;i=e[i].next)
    {
        int v = e[i].v;
        if(vis[v]) continue;
        ans-=solve(v,e[i].dis,e[i].w);
        ms = inf;root = 0;
        SIZE = Size[v]<Size[x]?Size[v]:(ssize-Size[x]);
        getroot(v,0);
        fenzhi(root,(Size[v]<Size[x]?Size[v]:(ssize-Size[x])));
    }
}

int main()
{
    //ios::sync_with_stdio(false);
    //freopen("a.txt","r",stdin);
    //freopen("b.txt","w",stdout);
    int a,b;
    scanf("%d%d%d",&n,&l,&W);
    init();
    for(int i = 2;i<=n;++i)
    {
        scanf("%d%d",&a,&b);
        add(a,i,1,b);add(i,a,1,b);
    }
    ms = inf;root = 0;SIZE = n;
    getroot(1,-1);
    fenzhi(root,SIZE);
    printf("%lld\n",ans);
    //fclose(stdin);
    //fclose(stdout);
    //cout << "time: " << (long long)clock() * 1000 / CLOCKS_PER_SEC << " ms" << endl;
    return 0;
}