Cod sursa(job #3293940)

Utilizator MagicantPlusIuoras Andrei MagicantPlus Data 13 aprilie 2025 21:42:34
Problema Heavy Path Decomposition Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 8.3 kb
#include <bits/stdc++.h>

using namespace std;

#define ll int
#define ull unsigned ll
#define vec vector
#define flist forward_list
#define um unordered_map
#define us unordered_set
#define prioq priority_queue
#define all(x) x.begin(), x.end()
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ld long double
#define cd complex<ld>
#define pll pair<ll, ll>
#define tll tuple<ll, ll, ll>
#define ass assign
#define fun function

#define LL_MAX LLONG_MAX
#define LL_MIN LLONG_MIN
#define ULL_MAX ULLONG_MAX
#define LD_MAX LDBL_MAX
#define LD_MIN LDBL_MIN

#define nl '\n'

#define vv(type, name, n, ...) vector<vector<type>> name(n, vector<type>(__VA_ARGS__))
#define vvv(type, name, n, m, ...) \
    vector<vector<vector<type>>> name(n, vector<vector<type>>(m, vector<type>(__VA_ARGS__)))

// https://trap.jp/post/1224/
#define rep1(n) for(ll i=0; i<(ll)(n); ++i)
#define rep2(i,n) for(ll i=0; i<(ll)(n); ++i)
#define rep3(i,a,b) for(ll i=(ll)(a); i<(ll)(b); ++i)
#define rep4(i,a,b,c) for(ll i=(ll)(a); i<(ll)(b); i+=(ll)(c))
#define cut4(a,b,c,d,e,...) e
#define rep(...) cut4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rep1e(n) for(ll i=1; i<=(ll)(n); ++i)
#define rep2e(i,n) for(ll i=1; i<=(ll)(n); ++i)
#define rep3e(i,a,b) for(ll i=(ll)(a); i<=(ll)(b); ++i)
#define rep4e(i,a,b,c) for(ll i=(ll)(a); i<=(ll)(b); i+=(ll)(c))
#define repe(...) cut4(__VA_ARGS__,rep4e,rep3e,rep2e,rep1e)(__VA_ARGS__)
#define per1(n) for(ll i=(ll)(n)-1; i>=0; --i)
#define per2(i,n) for(ll i=(ll)(n)-1; i>=0; --i)
#define per3(i,a,b) for(ll i=(ll)(a)-1; i>=(ll)(b); --i)
#define per4(i,a,b,c) for(ll i=(ll)(a)-1; i>=(ll)(b); i-=(ll)(c))
#define per(...) cut4(__VA_ARGS__,per4,per3,per2,per1)(__VA_ARGS__)
#define per1e(n) for(ll i=(ll)(n); i>=1; --i)
#define per2e(i,n) for(ll i=(ll)(n); i>=1; --i)
#define per3e(i,a,b) for(ll i=(ll)(a); i>=(ll)(b); --i)
#define per4e(i,a,b,c) for(ll i=(ll)(a); i>=(ll)(b); i-=(ll)(c))
#define pere(...) cut4(__VA_ARGS__,per4e,per3e,per2e,per1e)(__VA_ARGS__)
#define rep_subset(i,s) for(ll i=0;i!=-1;i=i==(s)?-1:(i|~(s))+1&(s))
#define per_subset(i,s) for(ll i=(s);i!=-1;i=i==0?-1:i-1&(s))
// #define forit(v) for (auto it = v.begin(); it != v.end(); it++)
// #define forit2(it, v) for (auto it = v.begin(); it != v.end(); it++)
// #define forrit(v) for (auto it = v.rbegin(); it != v.rend(); it++)
// #define forrit2(it, v) for (auto it = v.rbegin(); it != v.rend(); it++)

// #ifdef i_am_noob
#define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__)
template<typename T> void _do(vector<vector<T>> x){cerr << "\n"; for(auto i: x) {for(auto j : i) {cerr << j << ' ';} cerr << "\n";}}
template<typename T> void _do(vector<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(unordered_set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(T && x) {cerr << x << endl;}
template<typename T, typename ...S> void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);}
// #else
// #define bug(...) 777771449
// #endif
template<class T, class S> bool mkmin(T& a, const initializer_list<S>& b)
{S m = *min_element(all(b)); if(m<a){a=m;return 1;}return 0;}
template<class T, class S> bool mkmax(T& a, const initializer_list<S>& b)
{S m = *max_element(all(b)); if(m>a){a=m;return 1;}return 0;}
template<class T, class S> bool mkmin(T& a, const S& b){if(b<a){a=b;return 1;}return 0;}
template<class T, class S> bool mkmax(T& a, const S& b){if(b>a){a=b;return 1;}return 0;}

const ll MOD = 1e9 + 7;
const ll INF = (1ll << 27);

const string FILENAME = "heavypath";
ifstream fin(FILENAME + ".in");
ofstream fout(FILENAME + ".out");

#define cin fin
#define cout fout

// class Dst;
// class Lca;
// 
// class Dst
// {
// public:
// 
	// ll n, exp;
	// vec<vec<ll>> dst;
	// vec<ll> v;
// 	
	// ll minInd(ll i, ll j){return v[i]<v[j]?i:j;}
	// void build(vec<ll>& nums)
	// {
		// v=nums;
		// n=v.size();
		// exp=0;
		// while((1ll<<exp)<n)exp++;
		// dst.ass(exp, vec<ll>(n));
// 		
		// fun<void(ll,ll,ll)>build_([&](ll level, ll l, ll r)
		// {
			// if(r-l<1 || l >= n) return;
			// ll mid=(l+r)/2, ls=min(mid,n-1);
// 			
			// dst[level][ls] = ls;
			// pere(i, ls-1, l) dst[level][i] = minInd(i, dst[level][i+1]);
// 			
			// if(mid+1 < n)
			// {
				// dst[level][mid+1] = mid+1;
				// repe(i, mid+2, min(r,n-1)) dst[level][i] = minInd(dst[level][i-1], i);
			// }
// 			
			// if(level+1<exp)
			// {
				// build_(level+1,l,mid);
				// build_(level+1,mid+1,r);
			// }
		// });
		// build_(0,0,(1ll<<exp)-1);
	// }
	// ll query(ll x, ll y)
	// {
		// if(x==y) return x;
		// ll lev = exp - (32 - __builtin_clz(x^y));
		// return minInd(dst[lev][x], dst[lev][y]);
	// }
// };
// 
// class Tree
// {
// public:
// 
	// ll n;
	// vec<flist<ll>> adj;
	// Lca *lca;
// };
// 
// class Lca
// {
// public:
// 
	// vec<ll> appear, level, etour;
	// Dst dst;
// 	
	// void build(Tree *g)
	// {
		// appear.resize(g->n);
		// level.reserve(2*g->n+1);
		// etour.reserve(2*g->n+1);
// 		
		// fun<void(ll,ll,ll)>dfs([&](ll o, ll p, ll l)
		// {
			// etour.pb(o);
			// level.pb(l);
			// appear[o] = etour.size()-1;
// 			
			// for(auto u : g->adj[o])if(u!=p)
			// {
				// dfs(u, o, l+1);
				// etour.pb(o);
				// level.pb(l);
			// }
		// });
		// dfs(0,-1,0);
// 		
		// dst.build(level);
	// }
	// ll query(ll a, ll b)
	// {
		// return etour[dst.query(min(appear[a],appear[b]),max(appear[a],appear[b]))];
	// }
// };

class HLD;
class Hoshino
{
public:

	ll n;
	vec<ll> ai;
	
	pll calc(ll i, ll l, ll r){return{(l+r)/2, i+2*((l+r)/2-l+1)};}
	void build(vec<ll>& nums)
	{
		n=nums.size();
		ai.resize(2*n-1);
		
		fun<void(ll,ll,ll)>build_([&](ll i, ll l, ll r)
		{
			if(l==r)
			{
				ai[i] = nums[l];
				return;
			}
			
			ll mid,rc;tie(mid,rc)=calc(i,l,r);
			build_(i+1,l,mid);
			build_(rc,mid+1,r);
			
			ai[i] = max(ai[i+1],ai[rc]);
		});
		build_(0,0,n-1);
	}
	void update(ll x, ll val)
	{
		fun<void(ll,ll,ll)>update_([&](ll i, ll l, ll r)
		{
			if(l==r)
			{
				ai[i] = val;
				return;
			}
			
			ll mid,rc;tie(mid,rc)=calc(i,l,r);
			if(x<=mid)update_(i+1,l,mid);
			else update_(rc,mid+1,r);
			
			ai[i] = max(ai[i+1],ai[rc]);
		});
		update_(0,0,n-1);
	}
	ll query(ll x, ll y)
	{
		ll ans = -INF;
		
		fun<void(ll,ll,ll)>query_([&](ll i, ll l, ll r)
		{
			if(x<=l&&r<=y)
			{
				mkmax(ans,ai[i]);
				return;
			}
			
			ll mid,rc;tie(mid,rc)=calc(i,l,r);
			if(x<=mid)query_(i+1,l,mid);
			if(mid<y)query_(rc,mid+1,r);
		});
		query_(0,0,n-1);
		
		return ans;
	}
};

class Tree
{
public:

	ll n;
	vec<flist<ll>> adj;
	vec<ll> cost;
	HLD *hld;
	
	void read();
};

class HLD
{
public:

	vec<ll> parent, depth, heavy, head, pos, v;
	ll n;
	Hoshino ai;
	
	void build(Tree *t)
	{
		n = t->n;
		parent.resize(n);
		depth.resize(n);
		heavy.resize(n);
		head.resize(n);
		pos.resize(n);
		v.reserve(n);
		
		fun<ll(ll)>dfs1([&](ll o)->ll
		{
			ll maxval = -1, maxu = -1;
			ll size = 1;
			
			for(auto u : t->adj[o])if(u!=parent[o])
			{
				parent[u] = o;
				depth[u] = depth[o]+1;
				ll usize = dfs1(u);
				size += usize;
				if(mkmax(maxval, usize)) maxu = u;
			}
			
			heavy[o] = maxu;
			
			return size;
		});
		depth[0] = 0;
		parent[0] = -1;
		dfs1(0);
		
		fun<void(ll,ll)>dfs2([&](ll o, ll h)
		{
			head[o] = h;
			v.pb(t->cost[o]);
			pos[o] = v.size()-1;
			
			if(heavy[o] != -1)
			{
				dfs2(heavy[o], h);
			}
			
			for(auto u : t->adj[o])if(u!=parent[o])
			{
				if(u != heavy[o])
				{
					dfs2(u, u);
				}
			}
		});
		dfs2(0,0);
		
		ai.build(v);
	}
	void update(ll o, ll val)
	{
		ai.update(pos[o], val);
	}
	ll query(ll a, ll b)
	{
		ll ans = -INF;
		
		while(head[a] != head[b])
		{
			if(depth[head[a]] < depth[head[b]]) swap(a,b);
			// bug(a, b, head[a], head[b]);
			mkmax(ans, ai.query(pos[head[a]], pos[a]));
			a = parent[head[a]];
		}
		
		if(depth[a] < depth[b]) swap(a,b);
		
		mkmax(ans, ai.query(pos[b], pos[a]));
		
		return ans;
	}
};

void Tree::read()
{
	ll q;
	cin >> n >> q;
	adj.resize(n);
	cost.resize(n);
	rep(n) cin >> cost[i];
	rep(n-1)
	{
		ll a,b;
		cin >> a >> b;
		a--,b--;
		adj[a].pf(b);
		adj[b].pf(a);
	}
	
	hld = new HLD;
	hld->build(this);
	
	rep(q)
	{
		ll t, x, y;
		cin >> t >> x >> y;
		
		if(t==0)
		{
			x--;
			hld->update(x, y);
		}
		else
		{
			x--,y--;
			cout << hld->query(x,y) << nl;
		}
	}
}

int main()
{
	Tree t;
	t.read();
	
    return 0;
}