Build Cartesian Tree (verify/data_structures/treap/cartesian_tree.test.cpp)

View this file on GitHub
Last update: 2024-06-11 01:57:14+02:00
Problem: https://judge.yosupo.jp/problem/cartesian_tree

Depends on

Code

// @brief Build Cartesian Tree
#define PROBLEM "https://judge.yosupo.jp/problem/cartesian_tree"
#include "cp-algo/data_structures/treap/metas/base.hpp"
#include "cp-algo/data_structures/treap.hpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::data_structures::treap;

struct val_meta: metas::base_meta {
    int val;
    val_meta(int val): val(val){}
};

using node_t = node<val_meta>;
using treap = node_t::treap;

void solve() {
    istream_iterator<int> input(cin);
    int n = *input++;
    vector<treap> nodes(n);
    for(int i = 0; i < n; i++) {
        nodes[i] = node_t::make_treap(val_meta(i), *input++);
    }
    auto me = node_t::build(nodes);
    vector<int> p(n, -1);
    node_t::exec_on_each(me, [&](auto t) {
        for(auto child: t->children) {
            if(child) {
                p[_safe_meta(child, val)] = _safe_meta(t, val);
            }
        }
    });
    for(int i = 0; i < n; i++) {
        cout << (p[i] == -1 ? i : p[i]) << ' ';
    }
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    while(t--) {
        solve();
    }
}

#line 1 "verify/data_structures/treap/cartesian_tree.test.cpp"
// @brief Build Cartesian Tree
#define PROBLEM "https://judge.yosupo.jp/problem/cartesian_tree"
#line 1 "cp-algo/data_structures/treap/metas/base.hpp"


#line 1 "cp-algo/data_structures/treap/common.hpp"


#define _safe(t, op) (t ? t->op : typename std::remove_reference_t<decltype(t->op)>())

#line 4 "cp-algo/data_structures/treap/metas/base.hpp"
#include <functional>
#include <algorithm>
#include <cstdint>
#define _safe_meta(i, op) _safe(i, _meta.op)
namespace cp_algo::data_structures::treap::metas {
    struct base_meta {
        void pull(auto const, auto const){}
        void push(auto&, auto&){}
    };
}

#line 1 "cp-algo/data_structures/treap.hpp"


#line 1 "cp-algo/random/rng.hpp"


#include <chrono>
#include <random>
namespace cp_algo::random {
    uint64_t rng() {
        static std::mt19937_64 rng(
            std::chrono::steady_clock::now().time_since_epoch().count()
        );
        return rng();
    }
}

#line 5 "cp-algo/data_structures/treap.hpp"
#include <array>
namespace cp_algo::data_structures::treap {
    template<typename meta>
    struct node {
        using treap = node*;
        meta _meta;
        int prior = random::rng();
        size_t size = 1;
        treap children[2] = {nullptr, nullptr};
        enum subtree {L, R};

        node() {}
        node(meta _meta): _meta(_meta) {}
        node(meta _meta, int prior): _meta(_meta), prior(prior) {}

        static treap make_treap(auto...args) {
            return new node(args...);
        }

        treap pull() {
            _meta.pull(children[L], children[R]);
            size = 1 + _safe(children[L], size) + _safe(children[R], size);
            return this;
        }

        treap push() {
            _meta.push(children[L], children[R]);
            return this;
        }

        // set i-th child and pull metadata
        treap set(subtree i, treap t) {
            children[i] = t;
            return pull();
        }

        // push changes and detach the i-th child
        treap cut(subtree i) {
            return children[i];
        }

        static treap merge(treap A, treap B) {
            if(!_safe(A, push()) || !_safe(B, push())) {
                return A ? A : B;
            } else if(A->prior < B->prior) {
                return A->set(R, merge(A->cut(R), B));
            } else {
                return B->set(L, merge(A, B->cut(L)));
            }
        }

        // return {L, R}, where |L|=k or L=A when |A| < k
        static std::array<treap, 2> split(treap A, size_t k) {
            if(!_safe(A, push())) {
                return {nullptr, nullptr};
            } else if(_safe(A->children[L], size) >= k) {
                auto [split_L, split_R] = split(A->cut(L), k);
                return {split_L, A->set(L, split_R)};
            } else {
                k -= _safe(A->children[L], size) + 1;
                auto [split_L, split_R] = split(A->cut(R), k);
                return {A->set(R, split_L), split_R};
            }
        }

        static void exec_on_segment(treap &A, size_t l, size_t r, auto func) {
            auto [LM, R] = split(A, r);
            auto [L, M] = split(LM, l);
            func(M);
            A = merge(L, merge(M, R));
        }

        static void insert(treap &A, size_t pos, treap t) {
            auto [L, R] = split(A, pos);
            A = merge(L, merge(t, R));
        }

        static void erase(treap &A, size_t pos) {
            auto [L, MR] = split(A, pos);
            auto [M, R] = split(MR, 1);
            delete M;
            A = merge(L, R);
        }

        static void exec_on_each(treap &A, auto func) {
            if(A) {
                exec_on_each(A->children[L], func);
                func(A);
                exec_on_each(A->children[R], func);
            }
        }

        treap pull_all() {
            _safe(children[L], pull_all());
            _safe(children[R], pull_all());
            return pull();
        }

        treap push_all() {
            push();
            _safe(children[L], push_all());
            _safe(children[R], push_all());
            return this;
        }

        static treap build(auto const& nodes) {
            std::vector<treap> st;
            for(auto cur: nodes) {
                while(st.size() >= 2 && st[st.size() - 2]->prior > cur->prior) {
                    st.pop_back();
                }
                if(!st.empty() && st.back()->prior > cur->prior) {
                    cur->set(L, st.back());
                    st.pop_back();
                }
                if(!st.empty() && st.back()->prior < cur->prior) {
                    st.back()->set(R, cur);
                }
                st.push_back(cur);
            }
            return st.empty() ? nullptr : st[0]->pull_all();
        }
    };

    struct null_meta {
        void pull(auto const, auto const) {}
        void push(auto&, auto&) {}
    };
}

#line 5 "verify/data_structures/treap/cartesian_tree.test.cpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::data_structures::treap;

struct val_meta: metas::base_meta {
    int val;
    val_meta(int val): val(val){}
};

using node_t = node<val_meta>;
using treap = node_t::treap;

void solve() {
    istream_iterator<int> input(cin);
    int n = *input++;
    vector<treap> nodes(n);
    for(int i = 0; i < n; i++) {
        nodes[i] = node_t::make_treap(val_meta(i), *input++);
    }
    auto me = node_t::build(nodes);
    vector<int> p(n, -1);
    node_t::exec_on_each(me, [&](auto t) {
        for(auto child: t->children) {
            if(child) {
                p[_safe_meta(child, val)] = _safe_meta(t, val);
            }
        }
    });
    for(int i = 0; i < n; i++) {
        cout << (p[i] == -1 ? i : p[i]) << ' ';
    }
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    while(t--) {
        solve();
    }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	almost-decreasing_00	AC	191 ms	85 MB
g++	almost-decreasing_01	AC	88 ms	41 MB
g++	almost-increasing_00	AC	195 ms	89 MB
g++	almost-increasing_01	AC	93 ms	43 MB
g++	decreasing_00	AC	192 ms	85 MB
g++	decreasing_01	AC	88 ms	41 MB
g++	example_00	AC	6 ms	3 MB
g++	example_01	AC	6 ms	3 MB
g++	increasing_00	AC	185 ms	89 MB
g++	increasing_01	AC	99 ms	43 MB
g++	random_00	AC	193 ms	62 MB
g++	random_01	AC	87 ms	30 MB
g++	random_02	AC	109 ms	37 MB
g++	random_03	AC	86 ms	28 MB
g++	random_04	AC	157 ms	50 MB
g++	small_00	AC	6 ms	3 MB
g++	small_01	AC	5 ms	3 MB
g++	small_02	AC	5 ms	3 MB
g++	small_03	AC	6 ms	3 MB
g++	small_04	AC	5 ms	3 MB
g++	small_05	AC	5 ms	3 MB
g++	small_06	AC	6 ms	3 MB
g++	small_07	AC	5 ms	3 MB
g++	small_08	AC	5 ms	3 MB
g++	small_09	AC	5 ms	3 MB