結果

問題 No.952 危険な火薬庫
ユーザー PachicobuePachicobue
提出日時 2019-12-15 00:46:34
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 712 ms / 2,000 ms
コード長 7,655 bytes
コンパイル時間 2,422 ms
コンパイル使用メモリ 213,920 KB
実行使用メモリ 246,656 KB
最終ジャッジ日時 2024-06-28 09:22:09
合計ジャッジ時間 8,913 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 452 ms
159,488 KB
testcase_04 AC 439 ms
156,160 KB
testcase_05 AC 343 ms
125,568 KB
testcase_06 AC 550 ms
186,752 KB
testcase_07 AC 157 ms
63,360 KB
testcase_08 AC 633 ms
208,768 KB
testcase_09 AC 659 ms
211,968 KB
testcase_10 AC 220 ms
80,128 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 232 ms
84,224 KB
testcase_13 AC 249 ms
87,040 KB
testcase_14 AC 45 ms
22,528 KB
testcase_15 AC 404 ms
141,184 KB
testcase_16 AC 59 ms
27,136 KB
testcase_17 AC 46 ms
22,784 KB
testcase_18 AC 88 ms
41,728 KB
testcase_19 AC 3 ms
5,376 KB
testcase_20 AC 3 ms
5,376 KB
testcase_21 AC 217 ms
77,952 KB
testcase_22 AC 37 ms
19,328 KB
testcase_23 AC 4 ms
5,376 KB
testcase_24 AC 16 ms
9,088 KB
testcase_25 AC 712 ms
246,656 KB
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 # 

#include <bits/stdc++.h>
// created [2019/12/15] 00:08:40

constexpr unsigned int mod                  = 1000000007;
template<typename T> constexpr T inf_v      = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
using i32   = int32_t;
using i64   = int64_t;
using u32   = uint32_t;
using u64   = uint64_t;
using uint  = unsigned int;
using usize = std::size_t;
using ll    = long long;
using ull   = unsigned long long;
using ld    = long double;
template<typename T, usize n>
using arr = T (&)[n];
template<typename T, usize n>
using c_arr = const T (&)[n];
template<typename Elem, typename Val = Elem>
struct simple_cht
{
private:
    using line = std::pair<Elem, Elem>;
    static bool check(line l1, line l2, line l3)
    {
        const element_type a1 = l1.first, b1 = l1.second, a2 = l2.first, b2 = l2.second, a3 = l3.first, b3 = l3.second;
        const value_type da1 = a1 - a2, da2 = a2 - a3, db1 = b1 - b2, db2 = b2 - b3;
        return (da1 + da2) * db1 > da1 * (db1 + db2) and da2 * (db1 + db2) > (da1 + da2) * db2;
    }
    static Val eval(const line& l, const Elem x) { return static_cast<Val>(l.first) * static_cast<Val>(x) + static_cast<Val>(l.second); }
    usize query_head = 0;
    Elem px          = -inf_v<Elem>;
    std::vector<line> lines;

public:
    using element_type = Elem;
    using value_type   = Val;
    void add(const element_type a, const element_type b)
    {
        if (lines.empty()) { return lines.push_back(line{a, b}); }
        const element_type pa = lines.back().first, pb = lines.back().second;
        assert(pa >= a);
        if (pa == a and pb <= b) { return; }
        if (lines.size() == 1) { return lines.push_back(line{a, b}); }
        const line l{a, b};
        while (lines.size() >= 2 and not check(lines[lines.size() - 2], lines[lines.size() - 1], l)) { lines.pop_back(); }
        lines.push_back(l), query_head = std::min(query_head, lines.size() - 1);
    }
    value_type query(const element_type x)
    {
        assert(px <= x), px = x;
        if (lines.empty()) { return inf_v<element_type>; }
        for (; query_head + 1 < lines.size() and eval(lines[query_head], x) > eval(lines[query_head + 1], x); query_head++) {}
        return eval(lines[query_head], x);
    }
    bool empty() const { return lines.empty(); }
    friend std::ostream& operator<<(std::ostream& os, const simple_cht& cht)
    {
        os << "[";
        for (usize i = 0; i < cht.lines.size(); i++) { os << cht.lines[i].first << "x+" << cht.lines[i].second << (i + 1 == cht.lines.size() ? "" : ","); }
        return (os << "]\n");
    }
};
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
auto fix_point = [](auto f) { return [=](auto&&... args) { return f(f, std::forward<decltype(args)>(args)...); }; };

template<typename T>
T in()
{
    T v;
    return std::cin >> v, v;
}
template<typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) { return in<T>(); }
template<typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type& szs)
{
    const usize s = (usize)szs[i];
    std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
    for (usize j = 0; j < s; j++) { ans[j] = in_v<T, Uint, n, i + 1>(szs); }
    return ans;
}
template<typename T, typename Uint, usize n>
auto in_v(c_arr<Uint, n> szs) { return in_v<T, Uint, n, 0>(szs); }
template<typename... Types>
auto in_t() { return std::tuple<std::decay_t<Types>...>{in<Types>()...}; }
struct io_init
{
    io_init()
    {
        std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
        std::cout << std::fixed << std::setprecision(20);
    }
} hogechan;
template<typename T>
void out(const T& v) { std::cout << v; }
template<typename T, typename... Args>
void out(const T& v, const Args... args) { std::cout << v << ' ', out(args...); }
template<typename T, typename... Args>
void outln(const T& v, const Args... args) { std::cout << v << ' ', out(args...), std::cout << '\n'; }
template<typename T, typename... Args>
void outel(const T& v, const Args... args) { std::cout << v << ' ', out(args...), std::cout << std::endl; }
#    define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }

template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type, const T& v = T{}) { return v; }
template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type szs, const T& v = T{})
{
    const usize s = (usize)szs[i];
    return std::vector<decltype(make_v<T, Uint, n, i + 1>(szs, v))>(s, make_v<T, Uint, n, i + 1>(szs, v));
}
template<typename T, typename Uint, usize n>
auto make_v(c_arr<Uint, n> szs, const T& t = T{}) { return make_v<T, Uint, n, 0>(szs, t); }
int main()
{
    const auto N = in<int>();
    std::vector<ll> S(N + 2, 0);
    for (int i = 1; i <= N; i++) { S[i] = in<ll>(); }
    for (int i = 1; i <= N + 1; i++) { S[i] += S[i - 1]; }
    std::vector<simple_cht<ll, __int128_t>> chts(N + 2);  // i個閉めるときのCHT
    auto dp  = make_v({N + 2, N + 2}, inf_v<ll>);         // ドアiを閉めて/合計j個のドアを閉める
    dp[0][0] = 0;
    chts[0].add(-2LL * S[0], S[0] * S[0] + dp[0][0]);
    for (int i = 1; i <= N + 1; i++) {
        for (int j = 1; j <= N + 1; j++) {
            if (chts[j - 1].empty()) { continue; }
            chmin(dp[i][j], S[i - 1] * S[i - 1] + (ll)chts[j - 1].query(S[i - 1]));
            chts[j].add(-2LL * S[i], dp[i][j] + S[i] * S[i]);
        }
    }
    for (int j = N; j >= 1; j--) { std::cout << dp[N + 1][j] << std::endl; }
    return 0;
}
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