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| #include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <ctime>
#define MAXN 101000
#define LOG 20
struct Treap {
int v, dat, num;
int cnt, siz, maxx, maxid;
int l, r;
}a[MAXN * LOG << 2];
struct Edge {
int v, nx;
}e[MAXN << 1];
int tot, rt[MAXN], head[MAXN], ecnt, anc[MAXN][LOG + 1], dep[MAXN], ans[MAXN], fa[MAXN];
void add(int f, int t) {
e[++ecnt] = (Edge) {t, head[f]};
head[f] = ecnt;
}
int New(int val, int num) {
tot++;
a[tot].v = val;
a[tot].num = num;
a[tot].dat = rand();
a[tot].cnt = a[tot].siz = 1;
a[tot].maxx = num;
a[tot].maxid = val;
return tot;
}
void update(int p) {
a[p].siz = a[p].cnt + a[a[p].l].siz + a[a[p].r].siz;
a[p].maxx = a[p].num;
a[p].maxid = a[p].v;
int maxx = a[p].maxx, maxid = a[p].maxid;
if (a[a[p].l].maxx > maxx || (a[a[p].l].maxx == maxx && a[a[p].l].maxid < maxid)) {
maxx = a[a[p].l].maxx;
maxid = a[a[p].l].maxid;
}
if (a[a[p].r].maxx > maxx || (a[a[p].r].maxx == maxx && a[a[p].r].maxid < maxid)) {
maxx = a[a[p].r].maxx;
maxid = a[a[p].r].maxid;
}
a[p].maxx = maxx;
a[p].maxid = maxid;
}
void zig(int &p) {
int q = a[p].l;
a[p].l = a[q].r, a[q].r = p, p = q;
update(a[p].r), update(p);
}
void zag(int &p) {
int q = a[p].r;
a[p].r = a[q].l, a[q].l = p, p = q;
update(a[p].l), update(p);
}
void insert(int &p, int val, int num) {
if (!p) {
p = New(val, num);
return;
}
if (val == a[p].v) {
a[p].num += num;
update(p);
return;
}
if (val < a[p].v) {
insert(a[p].l, val, num);
if (a[p].dat < a[a[p].l].dat) zig(p);
}
else {
insert(a[p].r, val, num);
if (a[p].dat < a[a[p].r].dat) zag(p);
}
update(p);
}
int find(int x) {
if (x == fa[x]) return x;
else return fa[x] = find(fa[x]);
}
void merge(int x, int y) {
if (!y) return;
insert(rt[x], a[y].v, a[y].num);
merge(x, a[y].l);
merge(x, a[y].r);
}
void dfs(int f, int u, int d) {
dep[u] = d;
for (int i = head[u]; i; i = e[i].nx) {
int to = e[i].v;
if (to == f) continue;
anc[to][0] = u;
dfs(u, to, d + 1);
}
}
void swim(int &x, int h) {
for (int i = 0; h; i++) {
if (h & 1) x = anc[x][i];
h >>= 1;
}
}
int LCA(int x, int y) {
if (dep[x] < dep[y]) std::swap(x, y);
swim(x, dep[x] - dep[y]);
if (x == y) return x;
for (int i = LOG; i >= 0; i--) {
if (anc[x][i] != anc[y][i]) {
x = anc[x][i];
y = anc[y][i];
}
}
return anc[x][0];
}
void dfs1(int f, int u) {
for (int i = head[u]; i; i = e[i].nx) {
int to = e[i].v;
if (to == f) continue;
dfs1(u, to);
int x = find(u);
int y = find(to);
if (a[rt[x]].siz < a[rt[y]].siz) std::swap(x, y);
fa[y] = x;
merge(x, rt[y]);
}
int q = find(u);
ans[u] = a[rt[q]].maxid;
}
int n, m, x, y, z;
int main() {
srand(time(NULL));
scanf("%d%d", &n, &m);
for (int i = 1; i < n; i++) {
scanf("%d%d", &x, &y);
add(x, y);
add(y, x);
}
for (int i = 1; i <= n; i++) {
fa[i] = i;
}
dfs(1, 1, 1);
for (int i = 1; i <= LOG; i++) {
for (int j = 1; j <= n; j++) {
anc[j][i] = anc[anc[j][i - 1]][i - 1];
}
}
while (m--) {
scanf("%d%d%d", &x, &y, &z);
insert(rt[x], z, 1);
insert(rt[y], z, 1);
int lc = LCA(x, y);
insert(rt[lc], z, -1);
insert(rt[anc[lc][0]], z, -1);
}
dfs1(1, 1);
for (int i = 1; i <= n; i++) {
printf("%d\n", ans[i]);
}
return 0;
}
|
