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:heavy_check_mark: test/convolution/Min_Plus_Convolution_Convex_and_Arbitary.test.cpp

Depends on

Code

#define PROBLEM \
    "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#include "../../convolution/min_plus_convolution.hpp"
#include "../../template/template.hpp"

namespace ebi {

void main_() {
    int n, m;
    std::cin >> n >> m;
    std::vector<int> a(n), b(m);
    std::cin >> a >> b;
    auto c = min_plus_convolution_convex_and_arbitary(a, b);
    std::cout << c << '\n';
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
#line 1 "test/convolution/Min_Plus_Convolution_Convex_and_Arbitary.test.cpp"
#define PROBLEM \
    "https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary"

#line 2 "convolution/min_plus_convolution.hpp"

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

#line 2 "algorithm/monotone_minima.hpp"

#include <functional>
#include <utility>
#line 6 "algorithm/monotone_minima.hpp"

namespace ebi {

template <class F,
          class T = decltype(std::declval<F>()(std::declval<int>(),
                                               std::declval<int>())),
          class Compare = std::less<T>>
std::pair<std::vector<int>, std::vector<T>> monotone_minima(
    int n, int m, F f, const Compare &compare = Compare()) {
    std::vector<int> argmin(n);
    std::vector<T> min_val(n);
    auto dfs = [&](auto &&self, int top, int bottom, int left,
                   int right) -> void {
        if (top > bottom) return;
        int mid = (top + bottom) >> 1;
        argmin[mid] = left;
        min_val[mid] = f(mid, left);
        for (int i = left + 1; i <= right; i++) {
            T val = f(mid, i);
            if (min_val[mid] == val || compare(val, min_val[mid])) {
                argmin[mid] = i;
                min_val[mid] = val;
            }
        }
        self(self, top, mid - 1, left, argmin[mid]);
        self(self, mid + 1, bottom, argmin[mid], right);
    };
    dfs(dfs, 0, n - 1, 0, m - 1);
    return {argmin, min_val};
}

template <class T, class F, class Compare = std::less<T>>
std::pair<std::vector<int>, std::vector<T>> slide_monotone_minima(
    int n, int m, F f, const Compare &compare = Compare()) {
    std::vector<int> argmin(n);
    std::vector<T> min_val(n);
    auto dfs = [&](auto &&self, int top, int bottom, int left, int right,
                   int depth) -> void {
        if (top > bottom) return;
        int mid = (top + bottom) >> 1;
        argmin[mid] = left;
        min_val[mid] = f(mid, left, depth);
        for (int i = left + 1; i <= right; i++) {
            T val = f(mid, i, depth);
            if (min_val[mid] == val || compare(val, min_val[mid])) {
                argmin[mid] = i;
                min_val[mid] = val;
            }
        }
        self(self, top, mid - 1, left, argmin[mid], depth + 1);
        self(self, mid + 1, bottom, argmin[mid], right, depth + 1);
    };
    dfs(dfs, 0, n - 1, 0, m - 1, 0);
    return {argmin, min_val};
}

}  // namespace ebi
#line 8 "convolution/min_plus_convolution.hpp"

namespace ebi {

template <class T>
std::vector<T> min_plus_convolution_convex_and_arbitary(
    const std::vector<T> &a, const std::vector<T> &b) {
    int n = (int)a.size();
    int m = (int)b.size();
    for (int i = 0; i < n - 2; i++) {
        assert(a[i + 1] - a[i] <= a[i + 2] - a[i + 1]);
    }
    auto f = [&](int i, int j) -> T {
        if (i - j < 0 || i - j >= n) return std::numeric_limits<T>::max();
        return a[i - j] + b[j];
    };
    auto [argmin, min_val] = monotone_minima(n + m - 1, m, f);
    return min_val;
}

}  // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

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

#line 4 "template/int_alias.hpp"

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 2 "template/io.hpp"

#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

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

#line 5 "template/utility.hpp"

#line 2 "graph/base.hpp"

#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        return edges;
    }

    const auto operator[](int i) const {
        return csr[i];
    }
    auto operator[](int i) {
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int,edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 8 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 6 "test/convolution/Min_Plus_Convolution_Convex_and_Arbitary.test.cpp"

namespace ebi {

void main_() {
    int n, m;
    std::cin >> n >> m;
    std::vector<int> a(n), b(m);
    std::cin >> a >> b;
    auto c = min_plus_convolution_convex_and_arbitary(a, b);
    std::cout << c << '\n';
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
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