test/math/Inversion_Number.test.cpp

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Last update: 2024-02-25 23:03:04+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_5_D

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_5_D"

#include "../../math/inversion_number.hpp"

#include <iostream>
#include <vector>

int main() {
    int n;
    std::cin >> n;
    std::vector<int> a(n);
    for (int i = 0; i < n; i++) std::cin >> a[i];
    std::cout << ebi::inversion_number(a) << '\n';
}

#line 1 "test/math/Inversion_Number.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/ALDS1_5_D"

#line 2 "math/inversion_number.hpp"

#include <cassert>
#include <limits>
#include <vector>

#line 2 "data_structure/compress.hpp"

#include <algorithm>
#line 6 "data_structure/compress.hpp"

namespace ebi {

template <class T> struct compress {
  private:
    std::vector<T> cp;

  public:
    compress() = default;

    compress(std::vector<T> cp_) : cp(cp_) {
        build();
    }

    void build() {
        std::sort(cp.begin(), cp.end());
        cp.erase(std::unique(cp.begin(), cp.end()), cp.end());
    }

    void add(const T &val) {
        cp.emplace_back(val);
    }

    int get(const T &val) const {
        return std::lower_bound(cp.begin(), cp.end(), val) - cp.begin();
    }

    int size() const {
        return cp.size();
    }

    bool find(const T &val) const {
        auto itr = std::lower_bound(cp.begin(), cp.end(), val);
        if (itr == cp.end())
            return false;
        else
            return *itr == val;
    }

    T val(int idx) const {
        assert(0 <= idx && idx < (int)cp.size());
        return cp[idx];
    }
};

}  // namespace ebi
#line 2 "data_structure/fenwick_tree.hpp"

#line 5 "data_structure/fenwick_tree.hpp"

namespace ebi {

template <class T> struct fenwick_tree {
  private:
    int n;
    std::vector<T> data;

  public:
    fenwick_tree(int _n) : n(_n), data(std::vector<T>(_n + 1, T(0))) {}

    void add(int i, T val) {
        i++;
        for (int x = i; x <= n; x += x & -x) {
            data[x] += val;
        }
    }

    T prefix_sum(int i) const {
        assert(0 <= i && i <= n);
        T ret = 0;
        for (int x = i; x > 0; x -= x & -x) {
            ret += data[x];
        }
        return ret;
    }

    T sum(int l, int r) const {
        return prefix_sum(r) - prefix_sum(l);
    }

    T all_sum() const {
        return prefix_sum(n);
    }

    // prefix_sum(x) >= key となる最小のxを返す関数 O(log N)

    int lower_bound(T key) {
        if (key <= 0) return 0;
        int x = 0;
        int max = 1;
        while ((max << 1) <= n) max <<= 1;
        for (int k = max; k > 0; k >>= 1) {
            if (x + k <= n && data[x + k] < key) {
                x += k;
                key -= data[x];
            }
        }
        return x + 1;
    }
};

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#include <cstdint>

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 10 "math/inversion_number.hpp"

namespace ebi {

i64 inversion_number_max_n(const std::vector<int> &a, int n = 200000) {
    fenwick_tree<i64> fw(n);
    i64 res = 0;
    for (auto x : a) {
        assert(0 <= x && x < n);
        res += fw.sum(x + 1, n);
        fw.add(x, 1);
    }
    return res;
}

template <class T> i64 inversion_number(const std::vector<T> &a) {
    compress<T> cp;
    for (const auto &x : a) {
        cp.add(x);
    }
    cp.build();
    std::vector<int> ca;
    ca.reserve(a.size());
    for (const auto &x : a) {
        ca.emplace_back(cp.get(x));
    }
    return inversion_number_max_n(ca, cp.size());
}

}  // namespace ebi
#line 4 "test/math/Inversion_Number.test.cpp"

#include <iostream>
#line 7 "test/math/Inversion_Number.test.cpp"

int main() {
    int n;
    std::cin >> n;
    std::vector<int> a(n);
    for (int i = 0; i < n; i++) std::cin >> a[i];
    std::cout << ebi::inversion_number(a) << '\n';
}