Cod sursa(job #3245930)

Utilizator MagicantPlusIuoras Andrei MagicantPlus Data 1 octombrie 2024 10:19:08
Problema Heavy Path Decomposition Scor 40
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 6.95 kb
#include <bits/stdc++.h>

using namespace std;

#define ll long long
#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 mp make_pair
#define mt make_tuple
#define ld long double
#define pll pair<ll, ll>

#define LL_MAX LLONG_MAX
#define LL_MIN LLONG_MIN
#define ULL_MAX ULLONG_MAX
#define ULL_MIN 0
#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+=(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+=(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-=(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-=(c))
#define pere(...) cut4(__VA_ARGS__,per4e,per3e,per2e,per1e)(__VA_ARGS__)
#define rep_subset(i,s) for(ll i=(s); i>=0; 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

const ll MOD = 1e9 + 7;

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

#define cin fin
#define cout fout

struct segTree
{
	ll n;
	vec<ll> st, *nums;
	
	void buildAux(ll i, ll l, ll r)
	{
		if(l == r)
		{
			st[i] = (*nums)[l];
			return;
		}
		
		ll mid = (l + r) / 2;
		buildAux(i * 2, l, mid);
		buildAux(i * 2 + 1, mid + 1, r);
		st[i] = max(st[2 * i], st[2 * i + 1]);
	}
	void build(vec<ll>& v)
	{
		n = v.size();
		st.resize(4*n + 10);
		nums = &v;
		buildAux(1, 0, n - 1);
	}
	void updateAux(ll i, ll l, ll r, ll pos)
	{
		if(l == r)
		{
			st[i] = (*nums)[pos];
			return;
		}
		
		ll mid = (l + r) / 2;
		
		if(pos <= mid)
		{
			updateAux(i * 2, l, mid, pos);
		}
		else
		{
			updateAux(i * 2 + 1, mid + 1, r, pos);
		}
		
		st[i] = max(st[2 * i], st[2 * i + 1]);
	}
	void update(ll pos, ll val)
	{
		(*nums)[pos] = val;
		updateAux(1, 0, n - 1, pos);
	}
	ll rmqAux(ll i, ll l, ll r, ll a, ll b)
	{
		if(r < a || l > b)
		{
			return -1;
		}
		else if(a <= l && r <= b)
		{
			return st[i];
		}
		
		ll mid = (l + r) / 2;
		return max(rmqAux(2 * i, l, mid, a, b), rmqAux(2 * i + 1, mid + 1, r, a, b));
	}
	ll rmq(ll l, ll r)
	{
		return rmqAux(1, 0, n - 1, l, r);
	}
};

vec<flist<ll>> adj;
vec<ll> log_2, tour, depth, posTour, parent, cost, heavy, posVals, vals, head;
vec<vec<ll>> st;
segTree segt;

void initLca();
ll dfsTour(ll v, ll d);
ll minByDepth(ll a, ll b);
ll lca(ll a, ll b);
void initDecomp();
void dfsDecomp(ll v, ll h);
ll maxPath(ll a, ll b);

int main()
{
	ll n, q;
	
	cin >> n >> q;
	
	adj.resize(n);
	tour.reserve(2*n + 10);
	log_2.resize(2*n + 10);
	depth.resize(n);
	posTour.resize(n);
	parent.assign(n, -1);
	cost.resize(n);
	vals.reserve(n);
	posVals.resize(n);
	heavy.assign(n, -1);
	head.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);
	}
	
	initLca();
	initDecomp();
	
	rep(q)
	{
		ll t, x, y;
		cin >> t >> x >> y;
		
		if(t == 0)
		{
			x--;
			segt.update(posVals[x], y);
		}
		else
		{
			x--;
			y--;
			ll asc = lca(x, y);
			cout << max(maxPath(asc, x), maxPath(asc, y)) << nl;
		}
	}
	
    return 0;
}

ll maxPath(ll asc, ll node)
{
	ll res = vals[posVals[node]];
	
	while(node != asc)
	{
		if(head[node] == node)
		{
			node = parent[node];
			res = max(res, vals[posVals[node]]);
		}
		else if(head[node] == head[asc])
		{
			res = max(res, segt.rmq(posVals[asc], posVals[node]));
			node = asc;
		}
		else if(head[node] != head[asc])
		{
			res = max(res, segt.rmq(posVals[head[node]], posVals[node]));
			node = head[node];
		}
	}
	
	return max(res, vals[posVals[asc]]);
}
void dfsDecomp(ll v, ll h)
{
	head[v] = h;
	vals.pb(cost[v]);
	posVals[v] = vals.size() - 1;
	
	if(heavy[v] != -1)
		dfsDecomp(heavy[v], h);
	
	for(auto u : adj[v])
	{
		if(u != parent[v] && u != heavy[v])
			dfsDecomp(u, u);
	}
}
void initDecomp()
{
	dfsDecomp(0, 0);
	segt.build(vals);
}
ll lca(ll a, ll b)
{
	ll ap = posTour[a], bp = posTour[b];
	if(ap > bp) swap(a, b), swap(ap, bp);
	
	ll exp = log_2[bp - ap + 1], pw2 = (1ll << exp);
	return tour[minByDepth(st[ap][exp], st[bp - pw2 + 1][exp])];
}
ll minByDepth(ll a, ll b)
{
	return depth[tour[a]] < depth[tour[b]] ? a : b;
}
void initLca()
{
	log_2[0] = -1;
	rep(i, 1, log_2.size()) log_2[i] = log_2[i / 2] + 1;
	
	dfsTour(0, 0);
	st.assign(tour.size(), vec<ll>(log_2[tour.size()] + 1));
	
	rep(st.size())
	{
		st[i][0] = i;
	}
	
	rep(i, 1, st[0].size())
	{
		ll pw2 = (1ll << i);
		
		for(ll j = 0; j + pw2 - 1 < st.size(); j++)
		{
			st[j][i] = minByDepth(st[j][i - 1], st[j + (pw2 >> 1ll)][i - 1]);
		}
	}
}
ll dfsTour(ll v, ll d)
{
	tour.pb(v);
	posTour[v] = tour.size() - 1;
	depth[v] = d;
	ll size = 1, maxUSize = 0, uSize;
	
	for(auto u : adj[v])
	{
		if(u == parent[v]) continue;
		
		parent[u] = v;
		uSize = dfsTour(u, d + 1);
		if(uSize > maxUSize)
		{
			maxUSize = uSize;
			heavy[v] = u;
		}
		size += uSize;
		tour.pb(v);
	}
	
	return size;
}