Cod sursa(job #3122384)

Utilizator HandoMihnea-Vicentiu Hando Data 18 aprilie 2023 20:31:48
Problema Heavy Path Decomposition Scor 40
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 7.42 kb
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define ar array
#define vt vector
#define pq priority_queue
#define pu push
#define pub push_back
#define em emplace
#define emb emplace_back
#define mt make_tuple

#define all(x) x.begin(), x.end()
#define allr(x) x.rbegin(), x.rend()
#define allp(x, l, r) x.begin() + l, x.begin() + r
#define len(x) (int)x.size()
#define uniq(x) unique(all(x)), x.end()

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template <class T, size_t N>
void re(array <T, N>& x);
template <class T> 
void re(vt <T>& x);

template <class T> 
void re(T& x) {
    cin >> x;
}

template <class T, class... M> 
void re(T& x, M&... args) {
    re(x); re(args...);
}

template <class T> 
void re(vt <T>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void re(array <T, N>& x) {
    for(auto& it : x)
        re(it);
}

template <class T, size_t N>
void wr(array <T, N> x);
template <class T> 
void wr(vt <T> x);

template <class T> 
void wr(T x) {
    cout << x;
}

template <class T, class ...M>  void wr(T x, M... args) {
    wr(x), wr(args...);
}

template <class T> 
void wr(vt <T> x) {
    for(auto it : x)
        wr(it, ' ');
}

template <class T, size_t N>
void wr(array <T, N> x) {
    for(auto it : x)
        wr(it, ' ');
}

template<class T, class... M>
auto mvt(size_t n, M&&... args) {
    if constexpr(sizeof...(args) == 1)
        return vector<T>(n, args...);
    else
        return vector(n, mvt<T>(args...));
}

void set_fixed(int p = 0) {
    cout << fixed << setprecision(p);
}

void set_scientific() {
    cout << scientific;
}

inline void Open(const string Name) {
    #ifndef ONLINE_JUDGE
        (void)!freopen((Name + ".in").c_str(), "r", stdin);
        (void)!freopen((Name + ".out").c_str(), "w", stdout);
    #endif
}

struct ST {
    #define vl v * 2 + 1
    #define vr v * 2 + 2

    const int inf = 1e9 + 1;

    int n;
    vt <int> t;

    ST() {}
    ST(int _n) {
        n = _n;
        t.resize(4 * n + 10);
    }

    void init(int _n) {
        n = _n;
        t.resize(4 * n + 10);
    }

    void build(const vt <int>& a, int v, int tl, int tr) {
        if (tl == tr) {
            t[v] = a[tl];
            return;
        }

        int tm = (tl + tr) / 2;
        build(a, vl, tl, tm);
        build(a, vr, tm + 1, tr);
        t[v] = max(t[vl], t[vr]);
    }

    void build(const vt <int>&a) {
        build(a, 0, 0, n - 1);
    }

    void upd(int v, int tl, int tr, int pos, int val) {
        if (tl > pos or tr < pos) {
            return;
        }

        if (tl == pos and pos == tr) {
            t[v] = val;
            return;
        }

        int tm = (tl + tr) / 2;
        upd(vl, tl, tm, pos, val);
        upd(vr, tm + 1, tr, pos, val);
        t[v] = max(t[vl], t[vr]);
    }

    void upd(int pos, int val) {
        upd(0, 0, n - 1, pos, val);
    }

    int query(int v, int tl, int tr, int l, int r) {
        if (tl > r or tr < l) {
            return -inf;
        }

        if (l <= tl and tr <= r) {
            return t[v];
        }

        int tm = (tl + tr) / 2;
        int L = query(vl, tl, tm, l, r);
        int R = query(vr, tm + 1, tr, l, r);
        return max(L, R);
    }

    int query(int l, int r) {
        return query(0, 0, n - 1, l, r);
    }
};

struct LCA {
    const int LMX = 18;
    vt <vt <int>> adj, up;
    vt <int> tin, tout;
    int n, timer = 0;

    void init(int _n, vt <vt <int>> _adj) {
        n = _n;
        adj = _adj;
        up.assign(LMX, vt <int>(n + 10));
        tin.assign(n, 0), tout.assign(n, 0);

        dfs(0);
        for (int i = 1; i < LMX; ++i)
            for (int j = 0; j < n; ++j)
                up[i][j] = up[i - 1][up[i - 1][j]];
    }

    void dfs(int u, int p = 0) {
        up[0][u] = p;
        tin[u] = ++timer;
        for (auto& v : adj[u])
            if (v != p) {
                dfs(v, u);
            }
        tout[u] = ++timer;
    }

    bool is_ancestor(int u, int v) {
        return tin[u] <= tin[v] and tout[u] >= tout[v];
    }

    int getLCA(int u, int v) {
        if (is_ancestor(u, v))
            return u;
        if (is_ancestor(v, u))
            return v;

        for (int i = LMX - 1; i >= 0; --i)
            if (!is_ancestor(up[i][u], v))
                u = up[i][u];

        return up[0][u];
    }
};

struct HPD {
    vt <int> heavyChild, STpos, chain, par, sz, v;
    vt <vt <int>> adj;
    ST T; LCA L;
    int n, timer = 0;

    void init(int _n, vt <vt <int>> _adj, vt <int> _v) {
        n = _n;
        v = _v;
        adj = _adj;

        heavyChild.assign(n, 0);
        STpos.assign(n, 0);
        chain.assign(n, 0);
        par.assign(n, 0);
        sz.assign(n, 0);

        L.init(n, adj);
        T.init(n);

        for (int u = 0; u < n; ++u) {
            chain[u] = u;
            heavyChild[u] = -1;
        }

        makeSZ(0);
        makeHeavy(0);
        setHeavy(0);

        for (int i = 0; i < n; ++i) {
            T.upd(STpos[i], v[i]);
        }
    }

    void makeSZ(int u, int p = 0) {
        sz[u] = 1;
        par[u] = p;
        int bestV = -1, Vmx = -1;
        for (auto& v : adj[u]) {
            if (v == p)
                continue;

            makeSZ(v, u);
            sz[u] += sz[v];
            if (sz[v] > Vmx) {
                Vmx = sz[v];
                bestV = v;
            }
        }

        heavyChild[u] = bestV;
    }

    void makeHeavy(int u, int p = 0) {
        if (heavyChild[u] != -1) {
            chain[heavyChild[u]] = chain[u];
        }

        for (auto& v : adj[u]) {
            if (v == p)
                continue;
            makeHeavy(v, u);
        }
    }

    void setHeavy(int u, int p = 0) {
        STpos[u] = timer++;
        if (heavyChild[u] != -1) {
            setHeavy(heavyChild[u], u);
        }

        for (auto& v : adj[u])
            if (v != p and v != heavyChild[u]) {
                setHeavy(v, u);
            }
    }

    void upd(int u, int val) {
        T.upd(STpos[u], val);
    }

    int queryPath(int u, int p) {
        int res = -1;
        while (chain[u] != chain[p]) {
            res = max(res, T.query(STpos[chain[u]], STpos[u]));
            u = par[chain[u]];
        }
        res = max(res, T.query(STpos[p], STpos[u]));
        return res;
    }

    int query(int u, int v) {
        int lca = L.getLCA(u, v);
        return max(queryPath(u, lca), queryPath(v, lca));
    }
};

void solve() {
    int n, q; re(n, q);
    vt <int> v(n); re(v);
    vt <vt <int>> adj(n);
    for (int i = 0; i < n - 1; ++i) {
        int u, v; re(u, v);
        --u, --v;
        adj[u].emb(v);
        adj[v].emb(u);
    }

    HPD T;
    T.init(n, adj, v);

    for (int i = 0; i < q; ++i) {
        int task, u, v; re(task, u, v);
        if (task == 0) {
            --u;
            T.upd(u, v);
            continue;
        }
        --u, --v;
        wr(T.query(u, v), '\n');
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    Open("heavypath");

    int t = 1;
    for(;t;t--) {
        solve();
    }
    
    return 0;
}