// compile: make data
// run: time ./data < big.in > big.out && diff big.out big.ans
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#define Debug(x...) _debug_print_format(#x, x);
#else
#define debug(x...)
#define Debug(x...)
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define VI vector<int>
#define VII vector<vector<int>>
#define VIII vector<vector<vector<int>>>
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0)
#define cmin(x,...) x=min({(x), __VA_ARGS__})
#define cmax(x,...) x=max({(x), __VA_ARGS__})
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define NaN (int)(0x8b88e1d0595d51d1)
#define double long double
#define int long long
#define MAXN 200010
struct tree {
int n;
vector<vector<int>> e;
struct node {
vector<node*> ch;
node *parent = nullptr;
int size, depth, val, dfn;
node *heavy = nullptr, *top = nullptr;
};
vector<node> vertex;
node *root;
tree(int V) {
n = V;
e.resize(n);
vertex.resize(n);
}
void add_edge(int u, int v) {
e[u].push_back(v), e[v].push_back(u);
}
int ind(node *x) {return x - &vertex[0]; }
void build(int rt = 0) {
function<void(int, int)> dfs = [&](int u, int pre) {
node *x = &vertex[u];
x->size = 1;
x->depth = x==root ? 0 : x->parent->depth + 1;
for (int v: e[u]) {
if (v == pre) continue;
node *y = &vertex[v];
x->ch.push_back(y);
y->parent = x;
dfs(v, u);
x->size += y->size;
}
};
root = &vertex[rt];
dfs(rt, -1);
}
vector<int> rank;
void decomposition() {
rank.resize(n);
function<void(node*)> dfs1 = [&](node *x) {
for (auto y: x->ch) {
dfs1(y);
if (!x->heavy || y->size > x->heavy->size) x->heavy = y;
}
};
int total = 0;
function<void(node*, node*)> dfs2 = [&](node *x, node *top) {
vertex[ind(x)].dfn = total, rank[total++] = ind(x);
x->top = top;
if (x->heavy) dfs2(x->heavy, top);
for (auto y: x->ch) {
if (y == x->heavy) continue;
dfs2(y, y);
if (!x->heavy || y->size > x->heavy->size) x->heavy = y;
}
};
dfs1(root);
dfs2(root, root);
}
vector<pair<int, int>> path(int u, int v) {
vector<pair<int, int>> res;
node *x = &vertex[u], *y = &vertex[v];
while (x->top != y->top) {
if (x->top->depth < y->top->depth) swap(x, y);
res.push_back({x->top->dfn, x->dfn});
x = x->top->parent;
}
res.push_back({min(x->dfn, y->dfn), max(x->dfn, y->dfn)});
return res;
}
int solve(int u, int v, auto func) {
node *x = &vertex[u], *y = &vertex[v];
int ans = -INF;
while (x->top != y->top) {
if (x->top->depth < y->top->depth) swap(x, y);
cmax(ans, func(x->top->dfn, x->dfn));
// res.push_back({x->top->dfn, x->dfn});
x = x->top->parent;
}
cmax(ans, func(min(x->dfn, y->dfn), max(x->dfn, y->dfn)));
return ans;
}
void graphviz_dump(int plus = 0, string filename = "graph.dot") {
string vlabel = "", elabel = "";
// vlabel = " color=\"red\"";
elabel = " color=\"red\"";
set<int> vset; set<pair<int, int>> eset;
rep(i, 0, n) if (vertex[i].heavy) vset.insert(ind(vertex[i].heavy)), eset.insert({i, ind(vertex[i].heavy)});
FILE *f = fopen(filename.c_str(), "w");
fprintf(f, "digraph Tree {\n");
rep(i, 0, n) {
node *x = &vertex[i];
fprintf(f, " %lld;\n", vset.count(i) ? vlabel.c_str() : "");
}
rep(i, 0, n) {
node *x = &vertex[i];
for (auto y: x->ch) {
fprintf(f, " %ld -> %ld[arrowhead=\"none\"%s];\n", x - &vertex[0], y - &vertex[0], eset.count({i, ind(y)}) ? elabel.c_str() : "");
}
}
fprintf(f, "}\n");
}
};
template <class T> struct segtree {
struct node {
int l, r;
T val;
node *ch[2];
};
int cnt = 0;
T DEFAULT_VALUE;
node *newnode(int l, int r) {
node *x = (l==r) ? &datalist[l] : &datalist[cnt++];
// node *x = &datalist[cnt++];
x->l = l, x->r = r;
x->ch[0] = x->ch[1] = nullptr;
return x;
}
vector<int> a;
vector<node> datalist;
node *root;
segtree(vector<int> arr) {
cnt = sz(arr);
a = arr, build();
}
void pushup(node *x) {
if (!x) return;
if (!x->ch[0] && !x->ch[1]) return;
if (x->ch[0] && x->ch[1]) x->val = x->ch[0]->val + x->ch[1]->val;
else x->val = x->ch[!x->ch[0]]->val;
}
T query(int ql, int qr) {
if (qr - ql < 10) {
T res = DEFAULT_VALUE;
rep(i, ql, qr+1) res = res + datalist[i].val;
return res;
}
function<T(node*)> dfs = [&](node *x) -> T {
if (ql > x->r || qr < x->l) return DEFAULT_VALUE;
if (x->l >= ql && x->r <= qr) return x->val;
return dfs(x->ch[0]) + dfs(x->ch[1]);
};
return dfs(root);
}
template <typename U> void modify(int q, U val) {
function<void(node*)> dfs = [&](node *x) -> void {
if (q > x->r || q < x->l) return;
if (x->l >= q && x->r <= q) {
x->val.update(val);
return;
}
dfs(x->ch[0]), dfs(x->ch[1]);
pushup(x);
};
dfs(root);
}
void build() {
datalist.resize(sz(a) * 2);
function<node*(int, int)> dfs = [&](int l, int r) {
node *x = newnode(l, r);
if (r > l) x->ch[0] = dfs(l, (l+r) >> 1), x->ch[1] = dfs(((l+r)>>1) + 1, r);
else x->val.set(a[l]);
pushup(x);
return x;
};
root = dfs(0, sz(a)-1);
}
void graphviz_dump(string filename = "graph.dot") {
FILE *f = fopen(filename.c_str(), "w");
fprintf(f, "digraph {\n");
rep(i, 0, cnt) {
node *x = &datalist[i];
fprintf(f, " %lld;\n");
}
rep(i, 0, cnt) {
node *x = &datalist[i];
if (x->ch[0]) fprintf(f, " %lld -> %ld;\n", i, x->ch[0] - &datalist[0]);
if (x->ch[1]) fprintf(f, " %lld -> %ld;\n", i, x->ch[1] - &datalist[0]);
}
fprintf(f, "}\n");
}
};
int32_t main() {
ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
struct value {
int maxv = -INF;
value operator+(const value &other) const {
return {max(maxv, other.maxv)};
}
void set(int rhs) {
maxv = rhs;
}
void update(int val) {
maxv = val;
}
};
int n, q; cin >> n >> q;
tree g(n);
rep(i, 0, n) {
int x; cin >> x;
g.vertex[i].val = x;
}
rep(i, 0, n-1) {
int u, v; cin >> u >> v;
g.add_edge(u-1, v-1);
}
g.build(0);
g.decomposition();
vector<int> a(n);
rep(i, 0, n) a[i] = g.vertex[g.rank[i]].val;
segtree<value> t(a);
while (q--) {
int op; cin >> op;
if (op == 1) {
int u, k; cin >> u >> k;
t.modify(g.vertex[u-1].dfn, k);
}
else if (op == 2) {
int u, v; cin >> u >> v;
int ans = -INF;
auto ps = g.path(u-1, v-1);
for (auto [l, r]: ps) cmax(ans, t.query(l, r).maxv);
printf("%lld ", ans);
}
}
printf("\n");
return 0;
}
No Comments