CSES-solutions/CSES Problem Set/Path Queries.cpp

/* Problem URL: https://cses.fi/problemset/task/1138/ */

#include <bits/stdc++.h>

using namespace std;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (size_t i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (size_t i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

vvi graph;
vi sizes;
vi parent;
vi head;
vl v;
vi pos;
vl seg;
int t = 0;

void dfs(int i, int p)
{
    parent[i] = p;

    sizes[i] = 1;
    for (auto &u : graph[i]) {
        if (u == p)  {
            continue;
        }

        dfs(u, i);
        if (sizes[graph[i][0]] < sizes[u]) {
            swap(graph[i][0], u);
        }

        sizes[i] += sizes[u];
    }
}

void f(int i, int p, vl &values)
{
    pos[i] = t;
    v[t] = values[i];
    t++;

    for (auto u : graph[i]) {
        if (u == p) {
            continue;
        }

        if (u == graph[i][0]) {
            head[u] = head[i];
        } else {
            head[u] = u;
        }

        f(u, i, values);
    }
}

ll seg_query(int i, int l, int r, int la, int ra)
{
    if (l > ra || r < la) {
        return 0;
    }

    if (l >= la && r <= ra) {
        return seg[i];
    }

    int mid = (l + r) / 2;
    return seg_query(i * 2, l, mid, la, ra) + seg_query(i * 2 + 1, mid + 1, r, la, ra);
}

ll query(int a, int b)
{
    if (pos[a] > pos[b]) {
        swap(a, b);
    }

    if (head[a] == head[b]) {
        return seg_query(1, 0, v.size() - 1, pos[a], pos[b]);
    }

    return seg_query(1, 0, v.size() - 1, pos[head[b]], pos[b]) + query(parent[head[b]], a);
}

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

    int n, q;
    cin >> n >> q;

    vl values(n);
    cin >> values;

    graph.resize(n);
    sizes.resize(n);
    parent.resize(n);
    head.resize(n);
    v.resize(n);
    pos.resize(n);

    rep(i, n - 1) {
        int a, b;
        cin >> a >> b;
        a--, b--;

        graph[a].push_back(b);
        graph[b].push_back(a);
    }

    dfs(0, -1);
    f(0, -1, values);

    while (__builtin_popcountll(v.size()) != 1) {
        v.push_back(0);
    }

    size_t sz = v.size();
    seg.resize(sz * 2);

    for (size_t i = sz; i < sz * 2; i++) {
        seg[i] = v[i - sz];
    }
    for (size_t i = sz - 1; i > 0; i--) {
        seg[i] = seg[i * 2] + seg[i * 2 + 1];
    }

    while (q--) {
        int op;
        cin >> op;

        if (op == 1) {
            ll a, v;
            cin >> a >> v;
            a--;

            seg[sz + pos[a]] = v;
            for (size_t i = (sz + pos[a]) / 2; i > 0; i /= 2) {
                seg[i] = seg[i * 2] + seg[i * 2 + 1];
            }
            continue;
        }

        int num;
        cin >> num;
        cout << query(0, num - 1) << '\n';
    }
}