Cod sursa(job #3041706)

Utilizator lolismekAlex Jerpelea lolismek Data 1 aprilie 2023 11:43:18
Problema Heavy Path Decomposition Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.7 kb
#include <iostream>
#include <fstream>
#include <vector>

using namespace std;

ifstream fin("heavypath.in");
ofstream fout("heavypath.out");

const int NMAX = 1e5;

int n, q;
int v[NMAX + 1];
vector <int> adj[NMAX + 1];

int level[NMAX + 1];
int sz[NMAX + 1];

int parent[NMAX + 1];
int heavyChild[NMAX + 1];

void explore(int node, int Parent){
    sz[node] = 1;
    level[node] = level[Parent] + 1;
    
    parent[node] = Parent;

    for(int child : adj[node]){
        if(child != Parent){
            explore(child, node);
            sz[node] += sz[child];

            if(sz[child] > sz[heavyChild[node]]){
                heavyChild[node] = child;
            }
        }
    } 
}

int head[NMAX + 1];
int id[NMAX + 1];

int lin[NMAX + 1];
int pos[NMAX + 1];

int Id = 0;
int dfsTime = 0;

void heavyFirstLin(int node, int Parent){
    ++dfsTime;
    lin[dfsTime] = node;
    pos[node] = dfsTime;

    
    if(heavyChild[Parent] == node){
        id[node] = id[Parent];
    }else{
        ++Id;
        id[node] = Id;
        head[Id] = node;
    }

    if(heavyChild[node] != 0){
        heavyFirstLin(heavyChild[node], node);
    }

    for(int child : adj[node]){
        if(child != Parent && child != heavyChild[node]){
            heavyFirstLin(child, node);
        }
    }
}

namespace AINT{
    int aint[4 * NMAX + 1];

    void build(int node, int left, int right){
        if(left == right){
            aint[node] = v[lin[left]];
            return;
        }

        int mid = (left + right) / 2;
        build(2 * node, left, mid);
        build(2 * node + 1, mid + 1, right);

        aint[node] = max(aint[2 * node], aint[2 * node + 1]);
    }

    void update(int node, int left, int right, int pos, int val){
        if(left == right){
            aint[node] = val;
            return;
        }

        int mid = (left + right) / 2;
        if(pos <= mid){
            update(2 * node, left, mid, pos, val);
        }else{
            update(2 * node + 1, mid + 1, right, pos, val);
        }

        aint[node] = max(aint[2 * node], aint[2 * node + 1]);
    }   

    int query(int node, int left, int right, int qLeft, int qRight){
        if(qLeft <= left && right <= qRight){
            return aint[node];
        }

        int mid = (left + right) / 2, ans = 0;
        if(qLeft <= mid){
            ans = max(ans, query(2 * node, left, mid, qLeft, qRight));
        }
        if(mid + 1 <= qRight){
            ans = max(ans, query(2 * node + 1, mid + 1, right, qLeft, qRight));
        }

        return ans;
    }
}

int query(int a, int b){
    int ans = 0;
    
    while(id[a] != id[b]){
        if(level[head[id[a]]] > level[head[id[b]]]){
            ans = max(ans, AINT::query(1, 1, n, pos[head[id[a]]], pos[a]));
            a = parent[head[id[a]]];
        }else{
            ans = max(ans, AINT::query(1, 1, n, pos[head[id[b]]], pos[b]));
            b = parent[head[id[b]]];
        }
    }

    ans = max(ans, AINT::query(1, 1, n, min(pos[a], pos[b]), max(pos[a], pos[b])));

    return ans;
}

int main(){
    
    fin >> n >> q;

    for(int i = 1; i <= n; i++){
        fin >> v[i];
    }

    for(int i = 1; i <= n - 1; i++){
        int a, b;
        fin >> a >> b;
        adj[a].push_back(b);
        adj[b].push_back(a);
    }

    explore(1, 0);
    heavyFirstLin(1, 0);

    AINT::build(1, 1, n);

    while(q--){
        int type, x, y;
        fin >> type >> x >> y;

        if(type == 0){
            v[x] = y;
            AINT::update(1, 1, n, pos[x], v[x]);
        }else{
            fout << query(x, y) << '\n';
        }
    }

    return 0;
}