#1000155 (C++23) No.913 木の燃やし方

提出ソース

結果

問題	No.913 木の燃やし方
ユーザー	AC2K
提出日時	2024-08-07 15:14:45
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	10,262 bytes
コンパイル時間	3,250 ms
コンパイル使用メモリ	257,756 KB
実行使用メモリ	14,108 KB
最終ジャッジ日時	2024-08-07 15:14:56
合計ジャッジ時間	10,657 ms
ジャッジサーバーID （参考情報）	judge5 / judge3

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 13,756 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	21 ms 6,940 KB
testcase_04	AC	23 ms 6,940 KB
testcase_05	AC	26 ms 6,940 KB
testcase_06	AC	13 ms 6,940 KB
testcase_07	AC	5 ms 6,940 KB
testcase_08	TLE	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
testcase_33	--	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-

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ソースコード

raw source code

#line 1 "Library/src/debug.hpp"
#ifdef ONLINE_JUDGE
#define debug(x) void(0)
#else
#define _GLIBCXX_DEBUG
#define debug(x) std::cerr << __LINE__ << " : " << #x << " = " << (x) << std::endl
#endif

/**
 * @brief Debugger
*/
#line 2 "Library/src/data-structure/CHT.hpp"
#include <set>
namespace kyopro {

/**
 * @tparam query_type trueにすると, クエリで最大値を求めるように変更する
 */
template <class T = long long, bool query_type = false> class CHT {
    class line {
    public:
        T a, b;
        bool is_query;
        mutable T nxt_a, nxt_b;
        mutable bool has_nxt;
        T get(T x) const { return a * x + b; }
        T get_nxt(T x) const { return nxt_a * x + nxt_b; }
        line(T a, T b, bool q = false)
            : a(a), b(b), is_query(q), has_nxt(false) {}
        friend bool operator<(const line& l, const line& r) {
            if (l.is_query) {
                if (!r.has_nxt) return true;
                return r.get(l.a) < r.get_nxt(l.a);
            }
            if (r.is_query) {
                if (!l.has_nxt) return false;
                return l.get(r.a) > l.get_nxt(r.a);
            }
            return l.a == r.a ? l.b < r.b : l.a < r.a;
        }
    };

    std::set<line> ls;
    bool is_needed(const typename std::set<line>::iterator& it) {
        if (it != ls.begin() && it->a == prev(it)->a) {
            return it->b < prev(it)->b;
        }
        if (next(it) != ls.end() && it->a == next(it)->a) {
            return it->b < next(it)->b;
        }
        if (it == ls.begin() || next(it) == ls.end()) {
            return true;
        }
        return 1. * (it->b - prev(it)->b) * (next(it)->a - it->a) <
               1. * (it->b - next(it)->b) * (prev(it)->a - it->a);
    }

public:
    void insert(T a, T b) {
        if (query_type) {
            ls.emplace(-a, -b);
        } else {
            ls.emplace(a, b);
        }

        const line& ln = (query_type ? line{-a, -b} : line{a, b});
        auto it = ls.find(ln);
        if (!is_needed(it)) {
            ls.erase(it);
            return;
        }
        while (it != ls.begin() && !is_needed(prev(it))) {
            ls.erase(prev(it));
        }
        while (next(it) != ls.end() && !is_needed(next(it))) {
            ls.erase(next(it));
        }
        if (it != ls.begin()) {
            prev(it)->has_nxt = true;
            prev(it)->nxt_a = it->a;
            prev(it)->nxt_b = it->b;
        }
        if (next(it) != ls.end()) {
            it->has_nxt = true;
            it->nxt_a = next(it)->a;
            it->nxt_b = next(it)->b;
        }
    }
    T operator()(T x) const {
        const auto& it = ls.lower_bound(line(x, 0, true));

        if (query_type) {
            return -it->a * x - it->b;
        } else {
            return it->a * x + it->b;
        }
    }
};

};  // namespace kyopro

/**
 * @brief Convex Hull Trick
*/
#line 2 "Library/src/stream.hpp"
#include <ctype.h>
#include <stdio.h>
#include <string>
#line 2 "Library/src/internal/type_traits.hpp"
#include <iostream>
#include <limits>
#include <numeric>
#include <typeinfo>
#include <cstdint>

namespace kyopro {
namespace internal {
template <typename... Args> struct first_enabled {};

template <typename T, typename... Args>
struct first_enabled<std::enable_if<true, T>, Args...> {
    using type = T;
};
template <typename T, typename... Args>
struct first_enabled<std::enable_if<false, T>, Args...>
    : first_enabled<Args...> {};
template <typename T, typename... Args> struct first_enabled<T, Args...> {
    using type = T;
};

template <typename... Args>
using first_enabled_t = typename first_enabled<Args...>::type;

template <int dgt, std::enable_if_t<dgt <= 128>* = nullptr> struct int_least {
    using type = first_enabled_t<std::enable_if<dgt <= 8, std::int8_t>,
                                 std::enable_if<dgt <= 16, std::int16_t>,
                                 std::enable_if<dgt <= 32, std::int32_t>,
                                 std::enable_if<dgt <= 64, std::int64_t>,
                                 std::enable_if<dgt <= 128, __int128_t>>;
};

template <int dgt, std::enable_if_t<dgt <= 128>* = nullptr> struct uint_least {
    using type = first_enabled_t<std::enable_if<dgt <= 8, std::uint8_t>,
                                 std::enable_if<dgt <= 16, std::uint16_t>,
                                 std::enable_if<dgt <= 32, std::uint32_t>,
                                 std::enable_if<dgt <= 64, std::uint64_t>,
                                 std::enable_if<dgt <= 128, __uint128_t>>;
};

template <int dgt> using int_least_t = typename int_least<dgt>::type;
template <int dgt> using uint_least_t = typename uint_least<dgt>::type;

template <typename T>
using double_size_uint_t = uint_least_t<2 * std::numeric_limits<T>::digits>;

template <typename T>
using double_size_int_t = int_least_t<2 * std::numeric_limits<T>::digits>;

struct modint_base {};
template <typename T> using is_modint = std::is_base_of<modint_base, T>;
template <typename T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;


// is_integral
template <typename T>
using is_integral_t =
    std::enable_if_t<std::is_integral_v<T> || std::is_same_v<T, __int128_t> ||
                   std::is_same_v<T, __uint128_t>>;
};  // namespace internal
};  // namespace kyopro

/**
 * @brief Type Traits
 * @see https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8
 */
#line 6 "Library/src/stream.hpp"

namespace kyopro {

inline void single_read(char& c) {
    c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
}
template <typename T, internal::is_integral_t<T>* = nullptr>
inline void single_read(T& a) {
    a = 0;
    bool is_negative = false;
    char c = getchar_unlocked();
    while (isspace(c)) {
        c = getchar_unlocked();
    }
    if (c == '-') is_negative = true, c = getchar_unlocked();
    while (isdigit(c)) {
        a = 10 * a + (c - '0');
        c = getchar_unlocked();
    }
    if (is_negative) a *= -1;
}
template <typename T, internal::is_modint_t<T>* = nullptr>
inline void single_read(T& a) {
    long long x;
    single_read(x);
    a = T(x);
}
inline void single_read(std::string& str) noexcept {
    char c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
    while (!isspace(c)) {
        str += c;
        c = getchar_unlocked();
    }
}
template<typename T>
inline void read(T& x) noexcept {single_read(x);}
template <typename Head, typename... Tail>
inline void read(Head& head, Tail&... tail) noexcept {
    single_read(head), read(tail...);
}

inline void single_write(char c) noexcept { putchar_unlocked(c); }
template <typename T, internal::is_integral_t<T>* = nullptr>
inline void single_write(T a) noexcept {
    if (!a) {
        putchar_unlocked('0');
        return;
    }
    if constexpr (std::is_signed_v<T>) {
        if (a < 0) putchar_unlocked('-'), a *= -1;
    }
    constexpr int d = std::numeric_limits<T>::digits10;
    char s[d + 1];
    int now = d + 1;
    while (a) {
        s[--now] = (char)'0' + a % 10;
        a /= 10;
    }
    while (now <= d) putchar_unlocked(s[now++]);
}
template <typename T, internal::is_modint_t<T>* = nullptr>
inline void single_write(T a) noexcept {
    single_write(a.val());
}
inline void single_write(const std::string& str) noexcept {
    for (auto c : str) {
        putchar_unlocked(c);
    }
}
template <typename T> inline void write(T x) noexcept { single_write(x); }
template <typename Head, typename... Tail>
inline void write(Head head, Tail... tail) noexcept {
    single_write(head);
    putchar_unlocked(' ');
    write(tail...);
}
template <typename... Args> inline void put(Args... x) noexcept {
    write(x...);
    putchar_unlocked('\n');
}
};  // namespace kyopro

/**
 * @brief Fast IO(高速入出力)
 */
#line 2 "Library/src/template.hpp"
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) std::begin(x), std::end(x)
#define popcount(x) __builtin_popcountll(x)
using i128 = __int128_t;
using ll = long long;
using ld = long double;
using graph = std::vector<std::vector<int>>;
using P = std::pair<int, int>;
constexpr int inf = std::numeric_limits<int>::max() / 2;
constexpr ll infl = std::numeric_limits<ll>::max() / 2;
const long double pi = acosl(-1);
constexpr int dx[] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
template <typename T1, typename T2> constexpr inline bool chmax(T1& a, T2 b) {
    return a < b && (a = b, true);
}
template <typename T1, typename T2> constexpr inline bool chmin(T1& a, T2 b) {
    return a > b && (a = b, true);
}

/**
 * @brief Template
*/
#line 5 "a.cpp"

using namespace std;
using namespace kyopro;

int main() {
    int n;
    read(n);

    vector a(n, 0);
    rep(i, n) read(a[i]);

    vector sa(n + 1, 0LL);
    rep(i, n) sa[i + 1] = sa[i] + a[i];

    vector answer(n, infl);

    // calc for all i \in [l,r)
    auto f = [&](const auto& f, int l, int r) -> void {
        if (l == r) return;
        if (r - l == 1) {
            chmin(answer[l], 1 + a[l]);
            return;
        }

        int m = (l + r) / 2;
        // mを燃やす?

        // mを燃やさない(mをまたがない)なら下に潜る
        f(f, l, m);
        f(f, m, r);

        // 燃やすなら...
        {
            CHT<ll> cht;
            for (int i = m + 1; i <= r; ++i) {
                cht.insert(-2 * i, ll(i) * i + sa[i]);
            }

            ll pref_min = infl;
            for (int i = 0; i <= m; ++i) {
                chmin(pref_min, ll(i) * i - sa[i] + cht(i));
                chmin(answer[i], pref_min);
            }
        }

        {
            CHT<ll> cht;
            for (int i = l; i <= m; ++i) {
                // debug(i);
                // debug(2 * i);
                // debug(i * i - sa[i]);

                cht.insert(-2 * i, (ll)i * i - sa[i]);
            }

            ll suff_min = infl;

            for (int i = r - 1; i > m; --i) {
                // debug(suff_min);
                
                chmin(answer[i], suff_min);
                chmin(suff_min, ll(i) * i + sa[i] + cht(i));
            }
        }
    };

    f(f, 0, n);

    rep(i, n) put(answer[i]);
}

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結果

テストケース

ソースコード