結果

問題 No.1117 数列分割
ユーザー iiljjiiljj
提出日時 2020-07-19 23:36:49
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 534 ms / 3,000 ms
コード長 10,830 bytes
コンパイル時間 2,646 ms
コンパイル使用メモリ 216,532 KB
実行使用メモリ 74,112 KB
最終ジャッジ日時 2024-12-17 18:30:12
合計ジャッジ時間 8,183 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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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
6,820 KB
testcase_01 AC 1 ms
6,820 KB
testcase_02 AC 1 ms
6,816 KB
testcase_03 AC 27 ms
8,704 KB
testcase_04 AC 21 ms
8,192 KB
testcase_05 AC 2 ms
6,816 KB
testcase_06 AC 2 ms
6,820 KB
testcase_07 AC 2 ms
6,820 KB
testcase_08 AC 27 ms
7,552 KB
testcase_09 AC 8 ms
6,816 KB
testcase_10 AC 30 ms
7,808 KB
testcase_11 AC 141 ms
21,632 KB
testcase_12 AC 140 ms
23,040 KB
testcase_13 AC 199 ms
30,848 KB
testcase_14 AC 217 ms
32,256 KB
testcase_15 AC 244 ms
39,040 KB
testcase_16 AC 290 ms
43,776 KB
testcase_17 AC 29 ms
7,808 KB
testcase_18 AC 331 ms
74,112 KB
testcase_19 AC 473 ms
74,112 KB
testcase_20 AC 254 ms
37,376 KB
testcase_21 AC 527 ms
73,984 KB
testcase_22 AC 507 ms
72,704 KB
testcase_23 AC 524 ms
72,832 KB
testcase_24 AC 506 ms
71,936 KB
testcase_25 AC 534 ms
71,552 KB
testcase_26 AC 2 ms
6,820 KB
testcase_27 AC 11 ms
6,816 KB
testcase_28 AC 11 ms
6,816 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 # 

/* #region Head */

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region Num */

// テスト用
template <class T> struct Num {
    T x;
    Num(T x) : x(x) {}
    // member function
    Num &operator+=(const Num &another) { return *this = *this + another; }
    Num &operator-=(const Num &another) { return *this = *this - another; }
    Num &operator*=(const Num &another) { return *this = *this * another; }
    Num &operator/=(const Num &another) { return *this = *this / another; }
    Num &operator++() { return *this = *this + 1; }
    Num operator++(int) {
        Num before = *this;
        *this = *this + 1;
        return before;
    }
    Num &operator--() { return *this = *this - 1; }
    Num operator--(int) {
        Num before = *this;
        *this = *this - 1;
        return before;
    }
    Num operator+() const { return *this; }
    Num operator-() const { return Num{-x}; }

    // friend functions
    friend Num operator+(const Num &left, const Num &right) {
        if (abs(left.x) == INF) return Num{left.x};
        if (abs(right.x) == INF) return Num{right.x};
        return Num{left.x + right.x};
    }
    friend Num operator-(const Num &left, const Num &right) { return left + (-right); }
    friend Num operator*(const Num &left, const Num &right) {
        if (abs(left.x) == INF || abs(right.x) == INF) return (left.x == INF ^ right.x == INF) ? Num{-INF} : Num{INF};
        return Num{left.x * right.x};
    }
    friend Num operator/(const Num &left, const Num &right) {
        if (abs(left.x) == INF) return (right.x > 0) ? Num{left.x} : Num{-left.x};
        if (abs(right.x) == INF) return Num{0};
        return Num{left.x / right.x};
    }
    friend bool operator==(const Num &left, const Num &right) { return left.x == right.x; }
    friend bool operator!=(const Num &left, const Num &right) { return left.x != right.x; }
    friend bool operator<(const Num &left, const Num &right) { return left.x < right.x; }
    friend bool operator>(const Num &left, const Num &right) { return left.x > right.x; }
    friend bool operator<=(const Num &left, const Num &right) { return left.x <= right.x; }
    friend bool operator>=(const Num &left, const Num &right) { return left.x >= right.x; }
    friend ostream &operator<<(ostream &os, const Num &obj) {
        if (obj.x == INF)
            os << "INF";
        else if (obj.x == -INF)
            os << "-INF";
        else
            os << obj.x;
        return os;
    }
    friend istream &operator>>(istream &is, Num &obj) {
        is >> obj.x;
        return is;
    }
};

/* #endregion */

/* #region SlideMinMax */

// seq: シーケンス
// w: ウィンドウ幅
// f: 要素同士の比較（キュー末尾，追加要素）-> 末尾を捨てるかどうか
template <typename T> vc<int> slideMinMax(vc<T> &seq, int w, function<bool(T, T)> f) {
    ll n = SIZE(seq);
    // ret[i]: 区間 [i-w+1,i] (閉区間) における seq の最大値・最小値を与えるインデックス．
    //         末尾が i 番目になる長さ w の部分列の最大値・最小値を与えるインデックス．
    //         （長さ w 未満の左側領域・右側領域もついでに計算）
    vc<int> ret(n + w - 1);
    deque<int> q;

    REP(i, 0, n) {
        if (!q.empty() && q.front() == i - w) q.pop_front(); // 期限切れ
        while (!q.empty() && f(seq[q.back()], seq[i])) q.pop_back();
        q.push_back(i);
        ret[i] = q.front();
    }
    REP(i, n, n + w - 1) {
        if (!q.empty() && q.front() == i - w) q.pop_front(); // 期限切れ
        ret[i] = q.front();
    }
    return ret;
}

/* #endregion */

// Problem
void solve() {
    ll n, k, m;
    cin >> n >> k >> m;
    vll a(n);
    cin >> a;

    vll acc(n + 1);
    REP(i, 0, n) acc[i + 1] += acc[i] + a[i];

    using N = Num<ll>;
    // dp[i+1][j] := i 番目の要素まで見て j 個グループを作ったときの最大スコア
    vc<vc<N>> dp(n + 1, vc<N>(k + 1, -INF));
    dp[0][0] = 0;

    // REP(i, 0, n) REPM(j, 1, k) REPM(l, 0, i) {
    //     // dump(i, j, l, dp[i + 1][j], dp[l][j - 1] + abs(acc[i + 1] - acc[l]));

    //     // 愚直
    //     // chmax(dp[i + 1][j], dp[l][j - 1] + abs(acc[i + 1] - acc[l]));

    //     // abs を分けて整理
    //     // chmax(dp[i + 1][j], dp[l][j - 1] - acc[l] + acc[i + 1]);
    //     // chmax(dp[i + 1][j], dp[l][j - 1] + acc[l] - acc[i + 1]);
    // }

    auto f = [](N a, N latest) -> bool { return a < latest; };

    REPM(j, 1, k) {
        // dp[l][j-1]-acc[l], および dp[l][j-1]+acc[l] の幅 m のスライド最大値
        vc<N> data1(n, 0), data2(n, 0);
        REP(l, 0, n) {
            data1[l] = dp[l][j - 1] - acc[l];
            data2[l] = dp[l][j - 1] + acc[l];
        }
        vc<int> indices1 = slideMinMax<N>(data1, m, f);
        vc<int> indices2 = slideMinMax<N>(data2, m, f);

        REP(i, 0, n) {
            chmax(dp[i + 1][j], data1[indices1[i]] + acc[i + 1]);
            chmax(dp[i + 1][j], data2[indices2[i]] - acc[i + 1]);
        }
    }
    // dump(dp);
    cout << dp[n][k] << endl;
}

// entry point
int main() {
    solve();
    return 0;
}
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