結果

問題 No.952 危険な火薬庫
コンテスト
ユーザー ebi_fly
提出日時 2023-11-08 15:35:04
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 7,597 bytes
コンパイル時間 2,316 ms
コンパイル使用メモリ 190,232 KB
実行使用メモリ 195,608 KB
最終ジャッジ日時 2024-09-25 23:41:15
合計ジャッジ時間 5,649 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other TLE * 1 -- * 22
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "template/template.hpp"
#include <algorithm>
#include <bit>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <memory>
#include <numbers>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#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 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 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 7 "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 2 "algorithm/monge_d_edge_shortest_path.hpp"

#line 4 "algorithm/monge_d_edge_shortest_path.hpp"

#line 2 "algorithm/golden_section_search.hpp"

#line 4 "algorithm/golden_section_search.hpp"
#include <concepts>
#line 7 "algorithm/golden_section_search.hpp"

#line 9 "algorithm/golden_section_search.hpp"

namespace ebi {

// ref: https://x.com/noshi91/status/1399003086362865673
template <class S, class F,
          class T = decltype(std::declval<F>()(std::declval<S>())),
          class Compare = std::less<T>>
std::pair<S, T> golden_section_search(F f, S min, S max,
                                      const Compare &compare = Compare()) {
    assert(min <= max);
    S a = min - 1, x, b;
    {
        S s = 1, t = 2;
        while (t < max - min + 2) {
            std::swap(s += t, t);
        }
        x = a + t - s;
        b = a + t;
    }
    T fx = f(x), fy;
    while (a + b != 2 * x) {
        S y = a + b - x;
        if (max < y || compare(fx, (fy = f(y)))) {
            b = a;
            a = y;
        } else {
            a = x;
            x = y;
            fx = fy;
        }
    }
    return {x, fx};
}

}  // namespace ebi
#line 2 "algorithm/monge_shortest_path.hpp"

#line 5 "algorithm/monge_shortest_path.hpp"

namespace ebi {

template <class F, class T = decltype(std::declval<F>()(std::declval<int>(),
                                                        std::declval<int>()))>
std::vector<T> monge_shortest_path(int n, F f) {
    const T max = std::numeric_limits<T>::max();
    std::vector<int> argmin(n, 0);
    std::vector<T> dp(n, max);
    dp[0] = 0;
    auto get = [&](int i, int j) -> T {
        T val = f(j, i);
        if (val == max || dp[j] == max) return max;
        return dp[j] + val;
    };
    auto check = [&](int i, int j) -> void {
        T val = get(i, j);
        if (val < dp[i]) {
            dp[i] = val;
            argmin[i] = j;
        }
    };
    dp[n - 1] = get(n - 1, 0);
    auto dfs = [&](auto &&self, int l, int r) -> void {
        if (r - l == 1) return;
        int m = (l + r) >> 1;
        for (int i = argmin[l]; i <= argmin[r]; i++) {
            check(m, i);
        }
        self(self, l, m);
        for (int i = l + 1; i <= m; i++) {
            check(r, i);
        }
        self(self, m, r);
    };
    dfs(dfs, 0, n - 1);
    return dp;
}

}  // namespace ebi
#line 7 "algorithm/monge_d_edge_shortest_path.hpp"

namespace ebi {

template <class F, class T = decltype(std::declval<F>()(std::declval<int>(),
                                                        std::declval<int>()))>
T monge_d_edge_shortest_path(int n, int d, T upper, F f) {
    auto dp = [&](T x) -> T {
        auto g = [&](int i, int j) -> T { return f(i, j) + x; };
        T c = monge_shortest_path(n, g)[n - 1];
        return c - x * d;
    };
    return golden_section_search(dp, -upper, upper, std::greater<T>()).second;
}

}  // namespace ebi
#line 3 "a.cpp"

namespace ebi {

void main_() {
    int n;
    std::cin >> n;
    std::vector<i64> a(n);
    std::cin >> a;
    a.insert(a.begin(), 0);
    n++;
    std::vector<i64> sum(n+1, 0);
    rep(i,0,n) sum[i+1] = sum[i] + a[i];
    auto f = [&](int i, int j) -> i128 {
        return (sum[j] - sum[i+1]) * (sum[j] - sum[i+1]);
    };
    rrep(i,1,n) {
        i64 ans = monge_d_edge_shortest_path(n+1, i, i128(1'000'000'000'000'000'000), f);
        std::cout << ans << '\n';
    }
}

}  // namespace ebi

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