[Luogu] 【模板】点分治1

// 模板题
#include <bits/stdc++.h>

const int N = 2e4 + 10;

int n, now = 1, head[N], dis[N];
struct Node {int v, w, nxt;} G[N << 1];
int size[N], maxson[N], Root;
bool vis[N];
int js[N];
int Answer;
int Size;

#define gc getchar()

inline int read() {
    int x = 0; char c = gc;
    while(c < ‘0‘ || c > ‘9‘) c = gc;
    while(c >= ‘0‘ && c <= ‘9‘) x = x * 10 + c - ‘0‘, c = gc;
    return x;
} 

inline void Add(int u, int v, int w) {G[now].v = v; G[now].w = w; G[now].nxt = head[u]; head[u] = now ++;}

void Getroot(int u, int fa) {
    size[u] = 1;
    maxson[u] = 0;
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(vis[v] || v == fa) continue ;
        Getroot(v, u);
        size[u] += size[v];
        maxson[u] = std:: max(maxson[u], size[v]); 
    }
    maxson[u] = std:: max(maxson[u], Size - size[u]);
    if(maxson[u] < maxson[Root]) Root = u;
}

void Getdis(int u, int fa, int len) {
    dis[u] = len; js[dis[u]] ++;
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(vis[v] || v == fa) continue ;
        Getdis(v, u, (len + G[i].w) % 3);
    }
}

int Calc(int u, int len) {
    js[0] = js[1] = js[2] = 0;
    Getdis(u, 0, len % 3);
    return js[1] * js[2] * 2 + js[0] * js[0];
}

void Getans(int u) {
    vis[u] = 1;
    Answer += Calc(u, 0);
//    std:: cout << "#";
//    for(int i = 1; i <= n; i ++) std:: cout << dis[i] << " ";
//    std:: cout << "\n";
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(vis[v]) continue ;
        Answer -= Calc(v, G[i].w);
        Root = 0;
        Size = size[v];
        Getroot(v, u);
        Getans(Root);
    }
}

int Gcd(int a, int b) {
    return b == 0 ? a : Gcd(b, a % b);
}

int main() {
//    freopen("gg.in", "r", stdin); 
    n = read();
    for(int i = 1; i <= n; i ++) head[i] = -1;
    for(int i = 1; i < n; i ++) {
        int u = read(), v = read(), w = read();
        Add(u, v, w), Add(v, u, w);
    }
    maxson[Root] = n;
    Size = n;
    Getroot(1, 0);
//    std:: cout << Root << "\n";
    Getans(Root);
    int gcd = Gcd(Answer, n * n);
    std:: cout << Answer / gcd << "/" << n * n / gcd << "\n";
    return 0;
}