DataStructure/test/persistent_fenwick_tree_rmq.test.cpp

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Last update: 2023-01-07 01:54:04+08:00
Problem: https://judge.yosupo.jp/problem/staticrmq

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#include "../../template.h"
#include "../Fenwick/PartiallyPersistentFenwick.h"

struct Data {
    int x;
    Data() : x(INT_MAX) {}
    Data(int _x) : x(_x) {}
};
Data operator + (const Data& a, const Data& b) {
    return Data{min(a.x, b.x)};
}
bool operator < (const Data&, const Data&) {
    return false;
}

void solve() {
    int n, q; cin >> n >> q;
    vector<int> a(n);
    REP(i,n) cin >> a[i];

    PartiallyPersistentFenwick<Data> fen(n);
    FORD(i,n-1,0) fen.update(n-i, i, Data{a[i]});

    while (q--) {
        int l, r; cin >> l >> r;
        auto res = fen.get(n-l, r);
        cout << res.x << '\n';
    }
}

#line 1 "DataStructure/test/persistent_fenwick_tree_rmq.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#line 1 "template.h"
#include <bits/stdc++.h>
using namespace std;

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)
#define EACH(it,a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); ++it)

#define DEBUG(x) { cout << #x << " = "; cout << (x) << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }

#define sqr(x) ((x) * (x))

// For printing pair, container, etc.
// Copied from https://quangloc99.github.io/2021/07/30/my-CP-debugging-template.html
template<class U, class V> ostream& operator << (ostream& out, const pair<U, V>& p) {
    return out << '(' << p.first << ", " << p.second << ')';
}

template<class Con, class = decltype(begin(declval<Con>()))>
typename enable_if<!is_same<Con, string>::value, ostream&>::type
operator << (ostream& out, const Con& con) {
    out << '{';
    for (auto beg = con.begin(), it = beg; it != con.end(); it++) {
        out << (it == beg ? "" : ", ") << *it;
    }
    return out << '}';
}
template<size_t i, class T> ostream& print_tuple_utils(ostream& out, const T& tup) {
    if constexpr(i == tuple_size<T>::value) return out << ")"; 
    else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); 
}
template<class ...U> ostream& operator << (ostream& out, const tuple<U...>& t) {
    return print_tuple_utils<0, tuple<U...>>(out, t);
}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
long long get_rand(long long r) {
    return uniform_int_distribution<long long> (0, r-1)(rng);
}

template<typename T>
vector<T> read_vector(int n) {
    vector<T> res(n);
    for (int& x : res) cin >> x;
    return res;
}

void solve();

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    solve();
    return 0;
}
#line 1 "DataStructure/Fenwick/PartiallyPersistentFenwick.h"
// NOTE:
// - 0-based index
// - for updates: time must be in increasing order
// - Update: O(log), Get: O(log^2)
//
// Partially Persistent FenwickTree {{{
template<
    typename T  // need to support operators + - <
> struct PartiallyPersistentFenwick {
    PartiallyPersistentFenwick(int _n) : n(_n), f(_n + 1) {
        for (int i = 0; i <= n; ++i) {
            f[i].emplace_back(INT_MIN, T{});
        }
    }

    // a[u] += val
    void update(int time, int u, T val) {
        assert(0 <= u && u < n);
        assert(last_updated_time <= time);
        last_updated_time = time;
        ++u;
        for (; u <= n; u += u & -u) {
            f[u].emplace_back(time, f[u].back().second + val);
        }
    }

    // return a[0] + .. + a[u-1]
    T get(int time, int u) const {
        assert(0 <= u && u <= n);
        T res{};
        for (; u > 0; u -= u & -u) {
            auto it = lower_bound(f[u].begin(), f[u].end(), make_pair(time+1, T{}));
            res = res + prev(it)->second;
        }
        return res;
    }

    // return a[l] + .. + a[r-1]
    T get(int time, int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        if (l == r) return T{};  // empty
        return get(time, r) - get(time, l);
    }

    int n;
    int last_updated_time = INT_MIN;
    vector<vector<pair<int, T>>> f;  // (time, data)
};
// }}}
#line 4 "DataStructure/test/persistent_fenwick_tree_rmq.test.cpp"

struct Data {
    int x;
    Data() : x(INT_MAX) {}
    Data(int _x) : x(_x) {}
};
Data operator + (const Data& a, const Data& b) {
    return Data{min(a.x, b.x)};
}
bool operator < (const Data&, const Data&) {
    return false;
}

void solve() {
    int n, q; cin >> n >> q;
    vector<int> a(n);
    REP(i,n) cin >> a[i];

    PartiallyPersistentFenwick<Data> fen(n);
    FORD(i,n-1,0) fen.update(n-i, i, Data{a[i]});

    while (q--) {
        int l, r; cin >> l >> r;
        auto res = fen.get(n-l, r);
        cout << res.x << '\n';
    }
}