Cod sursa(job #3303641)

Utilizator paulihno15Ciumandru Paul paulihno15 Data 16 iulie 2025 18:59:24
Problema Heavy Path Decomposition Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 2.9 kb
#include <bits/stdc++.h>
#define NMAX 100000

using namespace std;

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

int n, q, op, x, y, ord;
int val[NMAX + 3], val_dfs[NMAX + 3];
vector<int> arb[NMAX + 3];
int par[NMAX + 3], niv[NMAX + 3], sz[NMAX + 3], heavy[NMAX + 3], head[NMAX + 3], poz[NMAX + 3];
int tree[NMAX * 4 + 3];

void dfs(int nod, int p) {
    par[nod] = p;
    sz[nod] = 1;
    int sz_max = 0;

    for (int vec : arb[nod]) {
        if (vec == p) {
            continue;
        }
        niv[vec] = niv[nod] + 1;
        dfs(vec, nod);
        sz[nod] += sz[vec];
        if (sz[vec] > sz_max) {
            sz_max = sz[vec];
            heavy[nod] = vec;
        }
    }
}

void decompose(int nod, int p) {
    head[nod] = p;
    poz[nod] = ++ord;
    val_dfs[ord] = val[nod];

    if (heavy[nod]) {
        decompose(heavy[nod], p);
    }
    for (int vec : arb[nod]) {
        if (vec != par[nod] && vec != heavy[nod]) {
            decompose(vec, vec);
        }
    }
}

void build_tree(int st, int dr, int node) {
    if (st == dr) {
        tree[node] = val_dfs[st];
        return;
    }

    int mij = (st + dr) >> 1;
    build_tree(st, mij, (node << 1));
    build_tree(mij + 1, dr, (node << 1) + 1);

    tree[node] = max(tree[(node << 1)], tree[(node << 1) + 1]);
}

void update(int st, int dr, int node, int poz, int val) {
    if (st == dr) {
        tree[node] = val;
        return;
    }

    int mij = (st + dr) >> 1;
    if (poz <= mij) {
        update(st, mij, (node << 1), poz, val);
    }
    else {
        update(mij + 1, dr, (node << 1) + 1, poz, val);
    }

    tree[node] = max(tree[(node << 1)], tree[(node << 1) + 1]);
}

int max_query(int st, int dr, int node, int a, int b) {
    if (dr < a || st > b) {
        return INT_MIN;
    }
    if (a <= st && dr <= b) {
        return tree[node];
    }

    int mij = (st + dr) >> 1;
    return max(max_query(st, mij, (node << 1), a, b),
        max_query(mij + 1, dr, (node << 1) + 1, a, b));
}

int hld_query(int a, int b) {
    int ans = INT_MIN;
    while (head[a] != head[b]) {
        if (niv[head[a]] < niv[head[b]]) {
            swap(a, b);
        }
        ans = max(ans, max_query(1, n, 1, poz[head[a]], poz[a]));
        a = par[head[a]];
    }
    if (niv[a] > niv[b]) {
        swap(a, b);
    }
    ans = max(ans, max_query(1, n, 1, poz[a], poz[b]));
    return ans;
}

int main() {
    ios_base::sync_with_stdio(false);
    fin.tie(NULL);
    fout.tie(NULL);

    fin >> n >> q;
    for (int i = 1; i <= n; i++) {
        fin >> val[i];
    }
    for (int i = 1; i <= n - 1; i++) {
        fin >> x >> y;
        arb[x].push_back(y);
        arb[y].push_back(x);
    }

    dfs(1, 0);
    decompose(1, 1);
    build_tree(1, n, 1);

    while (q--) {
        fin >> op >> x >> y;
        if (op == 0) {
            update(1, n, 1, poz[x], y);
        }
        else {
            fout << hld_query(x, y) << '\n';
        }
    }
    return 0;
}