DP/count_inversions.h

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• Last update: 2023-01-07 01:54:04+08:00

Depends on

• DataStructure/Fenwick/Fenwick.h
• Misc/compress.h

Verified with

• DP/tests/aizu_alds1_5_d_count_inversions.test.cpp

Code

#include "../Misc/compress.h"
#include "../DataStructure/Fenwick/Fenwick.h"

// Given vector vs, return number of inversions
template<typename T>
long long count_inversions(vector<T> vs) {
    int n = vs.size();
    auto compressor = CompressorBuilder<T>{vs}.build();
    compressor.compress_inplace(vs);
    Fenwick<int> bit(n);

    long long res = 0;
    for (auto v : vs) {
        res += bit.get(v+1, n);
        bit.update(v, +1);
    }
    return res;
}

#line 1 "Misc/compress.h"
// Compressor {{{
/* Example usage:
    auto compressor = CompressorBuilder<T>{vs}.build();
    int x = compessor.must_eq(vs[0]);
    compressor.compress_inplace(vs);
*/
// Based on https://suisen-cp.github.io/cp-library-cpp/library/util/coordinate_compressor.hpp
template<typename T>
struct CompressorBuilder {
    // Do not use directly. Use builder.build()
    struct Compressor {
        // Number of unique keys
        int size() const { return xs.size(); }

        void compress_inplace(std::vector<T>& vals) {
            for (int& val : vals) {
                val = must_eq(val);
            }
        }

        [[nodiscard]] std::vector<T> compress(const std::vector<T>& vals) {
            std::vector<T> res(vals.size());
            for (int i = 0; i < static_cast<int> (res.size()); ++i) {
                res[i] = must_eq(vals[i]);
            }
            return res;
        }

        bool has_key(const T& key) const {
            return std::binary_search(xs.begin(), xs.end(), key);
        }

#define LB(key) std::lower_bound(xs.begin(), xs.end(), key)
#define UB(key) std::upper_bound(xs.begin(), xs.end(), key)
        std::optional<int> eq(const T& key) {
            auto it = LB(key);
            return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
        }
        std::optional<int> geq(const T& key) {
            auto it = LB(key);
            return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
        }
        std::optional<int> gt(const T& key) {
            auto it = UB(key);
            return it == xs.end() ? std::nullopt : std::optional<int>{it - xs.begin()};
        }
        std::optional<int> leq(const T& key) {
            auto it = UB(key);
            return it == xs.begin() ? std::nullopt : std::optional<int>{it - xs.begin() - 1};
        }
        std::optional<int> lt(const T& key) {
            auto it = LB(key);
            return it == xs.begin() ? std::nullopt : std::optional<int>{it - xs.begin() - 1};
        }

        // throw exception if no such key is found
        int must_eq(const T& key) {
            auto it = LB(key);
            assert(it != xs.end());
            return it - xs.begin();
        }
        // throw exception if no such key is found
        int must_geq(const T& key) {
            auto it = LB(key);
            assert(it != xs.end());
            return it - xs.begin();
        }
        // throw exception if no such key is found
        int must_gt(const T& key) {
            auto it = UB(key);
            assert(it != xs.end());
            return it - xs.begin();
        }
        // throw exception if no such key is found
        int must_leq(const T& key) {
            auto it = UB(key);
            assert(it != xs.begin());
            return it - xs.begin() - 1;
        }
        // throw exception if no such key is found
        int must_lt(const T& key) {
            auto it = LB(key);
            assert(it != xs.begin());
            return it - xs.begin() - 1;
        }
#undef LB
#undef UB

        std::vector<T> xs;
    };

    auto build() {
        std::sort(xs.begin(), xs.end());
        xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
        return Compressor{xs};
    }

    void add(const T& key) { xs.push_back(key); }
    void add(T&& key) { xs.push_back(std::move(key)); }

    std::vector<T> xs;
};
// }}}
#line 1 "DataStructure/Fenwick/Fenwick.h"
// 1D Fenwick {{{
// 0 based index
//
// Tested:
// - https://judge.yosupo.jp/problem/static_range_sum
// - https://judge.yosupo.jp/problem/point_add_range_sum
template<
    typename T  // need to support operators + -
> struct Fenwick {
    Fenwick(int _n) : n(_n), f(_n + 1) {}

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

    // return a[0] + .. + a[u-1]
    T get(int u) const {
        assert(0 <= u && u <= n);
        T res = 0;
        for (; u > 0; u -= u & -u) {
            res += f[u];
        }
        return res;
    }

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

    void reset() {
        std::fill(f.begin(), f.end(), T(0));
    }

    int n;
    vector<T> f;
};
// }}}
#line 3 "DP/count_inversions.h"

// Given vector vs, return number of inversions
template<typename T>
long long count_inversions(vector<T> vs) {
    int n = vs.size();
    auto compressor = CompressorBuilder<T>{vs}.build();
    compressor.compress_inplace(vs);
    Fenwick<int> bit(n);

    long long res = 0;
    for (auto v : vs) {
        res += bit.get(v+1, n);
        bit.update(v, +1);
    }
    return res;
}

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