test/tree/aoj_0489.test.cpp

• View this file on GitHub
• Last update: 2023-06-30 14:03:10+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/0489

Depends on

• segtree (data_structure/segtree.hpp)
• misc/mo_algorithm.hpp
• テンプレート (template/template.hpp)
• Lowest Common Ancestor (tree/LowestCommonAncestor.hpp)
• 木上の Mo (tree/Mo_on_Tree.hpp)

Code

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

#include"../../tree/Mo_on_Tree.hpp"
#include"../../tree/LowestCommonAncestor.hpp"
#include"../../data_structure/segtree.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;
}

using ar = array<int,3>;

int main(){
    int n, m; cin >> n >> m;
    vector<int> a(n);
    rep(i,0,n) cin >> a[i];
    vector<ar> 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--; k--;
                querys.push_back({u,v,k});
            }
        }
        n = es.size()+1;
        m = querys.size();
    }
    MoTree_vertex<int> mo(n,a);
    for (auto &[u, v] : es){
        u--, v--;
        mo.add_edge(u,v);
    }
    LowestCommonAncestor g(mo.es);
    mo.build(querys.size());
    for (auto [u, v, k] : querys){
        mo.insert(u,v,g.lca(u,v));
    }
    segtree<int,op,e> seg(mx);
    vector<int> ans(querys.size());
    auto get = [&](int k){
        auto f = [&](int cnt){
            return cnt <= k;
        };
        return seg.max_right(0,f) - geta;
    };
    auto add = [&](int v){
        v += geta;
        seg.set(v,seg.get(v)+1);
    };
    auto del = [&](int v){
        v += geta;
        seg.set(v,seg.get(v)-1);
    };
    auto ask = [&](int i){
        ans[i] = get(querys[i][2]);
    };
    mo.run(add,del,ask);
    for (auto z : ans) cout << z << '\n';
}

#line 1 "test/tree/aoj_0489.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0489"

#line 2 "tree/Mo_on_Tree.hpp"

#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 2 "misc/mo_algorithm.hpp"

#line 4 "misc/mo_algorithm.hpp"

namespace lib {

struct Mo {
    int width;
    vector<int> left, right, order;

    Mo(int N = 1, int Q = 1) : order(Q) {
        width = max<int>(1, 1.0 * N / max<double>(1.0, sqrt(Q * 2.0 / 3.0)));
        iota(begin(order), end(order), 0);
    }

    void insert(int l, int r) { /* [l, r) */
        left.emplace_back(l);
        right.emplace_back(r);
    }

    template <typename AL, typename AR, typename DL, typename DR, typename REM>
    void run(const AL &add_left, const AR &add_right, const DL &delete_left,
             const DR &delete_right, const REM &rem) {
        assert(left.size() == order.size());
        sort(begin(order), end(order), [&](int a, int b) {
            int ablock = left[a] / width, bblock = left[b] / width;
            if (ablock != bblock) return ablock < bblock;
            if (ablock & 1) return right[a] < right[b];
            return right[a] > right[b];
        });
        int nl = 0, nr = 0;
        for (auto idx : order) {
            while (nl > left[idx]) add_left(--nl);
            while (nr < right[idx]) add_right(nr++);
            while (nl < left[idx]) delete_left(nl++);
            while (nr > right[idx]) delete_right(--nr);
            rem(idx);
        }
    }
};

}  // namespace lib
#line 5 "tree/Mo_on_Tree.hpp"

/*

MoTree_edge is verified with : https://atcoder.jp/contests/pakencamp-2022-day1/submissions/43052952

*/

namespace lib{

template<class T>
struct MoTree_edge {
    int n;
    vector<vector<pair<int,T>>> es;
    MoTree_edge (int _n) : n(_n) {
        es.resize(n);
    }
    void add_edge(int u, int v, T w){
        es[u].emplace_back(v,w);
        es[v].emplace_back(u,w);
    }
    vector<int> in;
    vector<pair<int,T>> vals;
    Mo mo;
    void build(int q){
        int tnow = 0;
        auto dfs = [&](auto dfs, int v, int f) -> void {
            in[v] = tnow++;
            for (auto [u, w] : es[v]){
                if (u == f) continue;
                vals.emplace_back(u,w);
                dfs(dfs,u,v);
                vals.emplace_back(u,w);
                tnow++;
            }
        };
        in.resize(n);
        dfs(dfs,0,-1);
        mo = Mo(2*n-2,q);
    }
    void insert(int u, int v){
        u = in[u], v = in[v];
        if (u > v) swap(u,v);
        mo.insert(u,v);
    }
    template<typename ADD, typename DEL, typename REM>
    void run(const ADD &add, const DEL &del, const REM &rem){
        vector<bool> contain(n,false);
        auto change = [&](int i){
            int id = vals[i].first;
            if (contain[id]){
                del(vals[i].second);
                contain[id] = false;
            }
            else {
                add(vals[i].second);
                contain[id] = true;
            }
        };
        mo.run(change,change,change,change,rem);
    }
};


template<class T>
struct MoTree_vertex {
    int n;
    vector<vector<int>> es;
    vector<T> b;
    MoTree_vertex (int _n, vector<T> _b) : n(_n), b(_b) {
        es.resize(n);
    }
    void add_edge(int u, int v){
        es[u].emplace_back(v);
        es[v].emplace_back(u);
    }
    vector<int> in;
    vector<pair<int,T>> vals;
    vector<int> lcas;
    Mo mo;
    void build(int q){
        vals.reserve(2*n-2);
        lcas.reserve(q);
        int tnow = 0;
        auto dfs = [&](auto dfs, int v, int f) -> void {
            in[v] = tnow++;
            for (auto u : es[v]){
                if (u == f) continue;
                vals.emplace_back(u,b[u]);
                dfs(dfs,u,v);
                vals.emplace_back(u,b[u]);
                tnow++;
            }
        };
        in.resize(n);
        dfs(dfs,0,-1);
        mo = Mo(2*n-2,q);
    }
    
    void insert(int u, int v, int lca){
        u = in[u], v = in[v];
        if (u > v) swap(u,v);
        mo.insert(u,v);
        lcas.push_back(lca);
    }
    template<typename ADD, typename DEL, typename REM>
    void run(const ADD &add, const DEL &del, const REM &rem){
        vector<bool> contain(n,false);
        auto change = [&](int i){
            int id = vals[i].first;
            if (contain[id]){
                del(vals[i].second);
                contain[id] = false;
            }
            else {
                add(vals[i].second);
                contain[id] = true;
            }
        };
        auto rem_add_lca = [&](int i){
            add(b[lcas[i]]);
            rem(i);
            del(b[lcas[i]]);
        };
        mo.run(change,change,change,change,rem_add_lca);
    }
};

} // 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 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 6 "test/tree/aoj_0489.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;
}

using ar = array<int,3>;

int main(){
    int n, m; cin >> n >> m;
    vector<int> a(n);
    rep(i,0,n) cin >> a[i];
    vector<ar> 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--; k--;
                querys.push_back({u,v,k});
            }
        }
        n = es.size()+1;
        m = querys.size();
    }
    MoTree_vertex<int> mo(n,a);
    for (auto &[u, v] : es){
        u--, v--;
        mo.add_edge(u,v);
    }
    LowestCommonAncestor g(mo.es);
    mo.build(querys.size());
    for (auto [u, v, k] : querys){
        mo.insert(u,v,g.lca(u,v));
    }
    segtree<int,op,e> seg(mx);
    vector<int> ans(querys.size());
    auto get = [&](int k){
        auto f = [&](int cnt){
            return cnt <= k;
        };
        return seg.max_right(0,f) - geta;
    };
    auto add = [&](int v){
        v += geta;
        seg.set(v,seg.get(v)+1);
    };
    auto del = [&](int v){
        v += geta;
        seg.set(v,seg.get(v)-1);
    };
    auto ask = [&](int i){
        ans[i] = get(querys[i][2]);
    };
    mo.run(add,del,ask);
    for (auto z : ans) cout << z << '\n';
}

Back to top page