test/data_structure/pck2022y11.test.cpp

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• Last update: 2023-06-20 22:32:45+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/0489

Depends on

• segtree (data_structure/segtree.hpp)
• テンプレート (template/template.hpp)
• Lowest Common Ancestor (tree/LowestCommonAncestor.hpp)

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0489"

#include"../../template/template.hpp"

#include"../../data_structure/segtree.hpp"
#include"../../tree/LowestCommonAncestor.hpp"

using namespace lib;

using P = pair<int,int>;
const int geta = 1'000'000;
const int mx = geta*2+10;

int op(int a, int b){
    return a + b;
}
int e(){
    return 0;
}

int main(){
    int n, m; cin >> n >> m;
    vector<int> a(n);
    rep(i,0,n) cin >> a[i];
    vector<vector<int>> querys;
    vector<P> es(n-1);
    rep(i,0,n-1) cin >> es[i].first >> es[i].second;
    {   
        int pre = n+1;
        while (m--){
            int t; cin >> t;
            if (t == 1){
                int u, w; cin >> u >> w;
                es.emplace_back(u,pre++);
                a.emplace_back(w);
            }
            if (t == 2){
                int u, v, k; cin >> u >> v >> k; u--, v--;
                querys.push_back({u,v,k});
            }
        }
        n = es.size()+1;
        m = querys.size();
    }
    vector<vector<int>> g(n);
    for (auto &[u, v] : es){
        u--, v--;
        g[u].emplace_back(v);
        g[v].emplace_back(u);
    }
    LowestCommonAncestor lca(g);
    vector<int> lcas(m);
    rep(i,0,m) lcas[i] = lca.lca(querys[i][0],querys[i][1]);
    vector<int> les(m,0), ris(m,mx);
    int test = 22;
    while (test--){
        vector<int> mds(m);
        vector<vector<P>> ask(n);
        rep(i,0,m){
            mds[i] = (les[i] + ris[i]) / 2;
            ask[querys[i][0]].emplace_back(i,1);
            ask[querys[i][1]].emplace_back(i,1);
            ask[lcas[i]].emplace_back(i,-2);
        }
        vector<int> cur(m,0);
        segtree<int,op,e> seg(mx);
        auto add = [&](int val, int cnt){
            val += geta;
            seg.set(val,seg.get(val)+cnt);
        };
        auto dfs = [&](auto dfs, int v, int f) -> void {
            add(a[v],1);
            for (auto &[id, type] : ask[v]){
                cur[id] += seg.prod(0,mds[id]) * type;
                if (type == -2 && a[v]+geta < mds[id]) cur[id]++; 
            }
            for (int u : g[v]){
                if (u == f) continue;
                dfs(dfs,u,v);
            }
            add(a[v],-1);
        };
        dfs(dfs,0,-1);
        rep(i,0,m){
            if (cur[i] < querys[i][2]) les[i] = mds[i];
            else ris[i] = mds[i];
        }
    }
    rep(i,0,m) cout << les[i]-geta << endl;
}

#line 1 "test/data_structure/pck2022y11.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0489"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

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

template <typename T> bool chmin(T &a, const T &b) {
    if (a <= b) return false;
    a = b;
    return true;
}
template <typename T> bool chmax(T &a, const T &b) {
    if (a >= b) return false;
    a = b;
    return true;
}

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 4 "test/data_structure/pck2022y11.test.cpp"

#line 2 "data_structure/segtree.hpp"

#line 4 "data_structure/segtree.hpp"

namespace lib {

using namespace std;

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  private:
    int n;
    int sz;
    vector<S> data;

    void update(int i) {
        data[i] = op(data[2 * i], data[2 * i + 1]);
    }

  public:
    segtree(int n) : segtree(vector<S>(n, e())) {}
    segtree(const vector<S> &v) : n((int)v.size()), sz(1) {
        while (sz < n) sz *= 2;
        data = vector<S>(2 * sz, e());
        rep(i, 0, n) {
            data[sz + i] = v[i];
        }
        rrep(i, 1, sz) update(i);
    }

    void set(int p, S x) {
        assert(0 <= p && p < n);
        p += sz;
        data[p] = x;
        while (p > 1) {
            p >>= 1;
            update(p);
        }
    }

    S get(int p) {
        assert(0 <= p && p < n);
        return data[p + sz];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        S sml = e(), smr = e();
        l += sz;
        r += sz;
        while (l < r) {
            if (l & 1) sml = op(sml, data[l++]);
            if (r & 1) smr = op(data[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() {
        return data[1];
    }

    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= n);
        assert(f(e()));
        if (l == n) return n;
        l += sz;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, data[l]))) {
                while (l < sz) {
                    l = 2 * l;
                    if (f(op(sm, data[l]))) {
                        sm = op(sm, data[l]);
                        l++;
                    }
                }
                return l - sz;
            }
            sm = op(sm, data[l]);
            l++;
        } while ((l & -l) != l);
        return n;
    }

    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= n);
        assert(f(e()));
        if (r == 0) return 0;
        r += sz;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(data[r], sm))) {
                while (r < sz) {
                    r = 2 * r + 1;
                    if (f(op(data[r], sm))) {
                        sm = op(data[r], sm);
                        r--;
                    }
                }
                return r + 1 - sz;
            }
            sm = op(data[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
};

}  // namespace lib
#line 2 "tree/LowestCommonAncestor.hpp"

#line 4 "tree/LowestCommonAncestor.hpp"

namespace lib {

struct LowestCommonAncestor {
    int n;
    std::vector<std::vector<int>> table;
    std::vector<int> depth;
    int log = 25;

    LowestCommonAncestor(const std::vector<std::vector<int>> &gh, int root = 0)
        : n(gh.size()) {
        table = std::vector(log, std::vector<int>(n, -1));
        depth.assign(n, 0);
        auto dfs = [&](auto &&self, int v) -> void {
            for (auto nv : gh[v]) {
                if (table[0][v] == nv) continue;
                table[0][nv] = v;
                depth[nv] = depth[v] + 1;
                self(self, nv);
            }
        };
        dfs(dfs, root);
        table[0][root] = root;
        rep(i, 0, log - 1) {
            rep(v, 0, n) {
                table[i + 1][v] = table[i][table[i][v]];
            }
        }
    }

    int la(int u, int k) const {
        if (depth[u] < k) return -1;
        rrep(i, 0, log) {
            if ((k >> i) & 1) {
                u = table[i][u];
            }
        }
        return u;
    }

    int lca(int u, int v) const {
        if (depth[u] < depth[v]) std::swap(u, v);
        u = la(u, depth[u] - depth[v]);
        if (u == v) return u;
        rrep(i, 0, log) {
            if (table[i][u] != table[i][v]) {
                u = table[i][u];
                v = table[i][v];
            }
        }
        return table[0][u];
    }

    int distance(int u, int v) const {
        int l = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[l];
    };
};

}  // namespace lib
#line 7 "test/data_structure/pck2022y11.test.cpp"

using namespace lib;

using P = pair<int,int>;
const int geta = 1'000'000;
const int mx = geta*2+10;

int op(int a, int b){
    return a + b;
}
int e(){
    return 0;
}

int main(){
    int n, m; cin >> n >> m;
    vector<int> a(n);
    rep(i,0,n) cin >> a[i];
    vector<vector<int>> querys;
    vector<P> es(n-1);
    rep(i,0,n-1) cin >> es[i].first >> es[i].second;
    {   
        int pre = n+1;
        while (m--){
            int t; cin >> t;
            if (t == 1){
                int u, w; cin >> u >> w;
                es.emplace_back(u,pre++);
                a.emplace_back(w);
            }
            if (t == 2){
                int u, v, k; cin >> u >> v >> k; u--, v--;
                querys.push_back({u,v,k});
            }
        }
        n = es.size()+1;
        m = querys.size();
    }
    vector<vector<int>> g(n);
    for (auto &[u, v] : es){
        u--, v--;
        g[u].emplace_back(v);
        g[v].emplace_back(u);
    }
    LowestCommonAncestor lca(g);
    vector<int> lcas(m);
    rep(i,0,m) lcas[i] = lca.lca(querys[i][0],querys[i][1]);
    vector<int> les(m,0), ris(m,mx);
    int test = 22;
    while (test--){
        vector<int> mds(m);
        vector<vector<P>> ask(n);
        rep(i,0,m){
            mds[i] = (les[i] + ris[i]) / 2;
            ask[querys[i][0]].emplace_back(i,1);
            ask[querys[i][1]].emplace_back(i,1);
            ask[lcas[i]].emplace_back(i,-2);
        }
        vector<int> cur(m,0);
        segtree<int,op,e> seg(mx);
        auto add = [&](int val, int cnt){
            val += geta;
            seg.set(val,seg.get(val)+cnt);
        };
        auto dfs = [&](auto dfs, int v, int f) -> void {
            add(a[v],1);
            for (auto &[id, type] : ask[v]){
                cur[id] += seg.prod(0,mds[id]) * type;
                if (type == -2 && a[v]+geta < mds[id]) cur[id]++; 
            }
            for (int u : g[v]){
                if (u == f) continue;
                dfs(dfs,u,v);
            }
            add(a[v],-1);
        };
        dfs(dfs,0,-1);
        rep(i,0,m){
            if (cur[i] < querys[i][2]) les[i] = mds[i];
            else ris[i] = mds[i];
        }
    }
    rep(i,0,m) cout << les[i]-geta << endl;
}

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