#874583 (C++23) No.2332 Make a Sequence

提出ソース

結果

問題	No.2332 Make a Sequence
ユーザー	👑 hitonanode
提出日時	2023-05-28 14:53:52
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	224 ms / 2,000 ms
コード長	12,433 bytes
コンパイル時間	2,307 ms
コンパイル使用メモリ	193,880 KB
実行使用メモリ	35,736 KB
最終ジャッジ日時	2023-08-27 10:49:59
合計ジャッジ時間	14,991 ms
ジャッジサーバーID （参考情報）	judge11 / judge13

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	1 ms 4,376 KB
testcase_01	AC	2 ms 4,376 KB
testcase_02	AC	2 ms 4,376 KB
testcase_03	AC	2 ms 4,380 KB
testcase_04	AC	2 ms 4,376 KB
testcase_05	AC	1 ms 4,380 KB
testcase_06	AC	1 ms 4,376 KB
testcase_07	AC	113 ms 34,028 KB
testcase_08	AC	24 ms 5,224 KB
testcase_09	AC	86 ms 20,392 KB
testcase_10	AC	101 ms 33,488 KB
testcase_11	AC	68 ms 19,156 KB
testcase_12	AC	134 ms 35,472 KB
testcase_13	AC	133 ms 35,640 KB
testcase_14	AC	134 ms 35,456 KB
testcase_15	AC	134 ms 35,576 KB
testcase_16	AC	133 ms 35,380 KB
testcase_17	AC	134 ms 35,732 KB
testcase_18	AC	133 ms 35,472 KB
testcase_19	AC	133 ms 35,580 KB
testcase_20	AC	132 ms 35,392 KB
testcase_21	AC	133 ms 35,456 KB
testcase_22	AC	136 ms 35,392 KB
testcase_23	AC	136 ms 35,540 KB
testcase_24	AC	137 ms 35,456 KB
testcase_25	AC	137 ms 35,524 KB
testcase_26	AC	136 ms 35,584 KB
testcase_27	AC	136 ms 35,404 KB
testcase_28	AC	138 ms 35,544 KB
testcase_29	AC	138 ms 35,380 KB
testcase_30	AC	137 ms 35,460 KB
testcase_31	AC	136 ms 35,412 KB
testcase_32	AC	142 ms 35,456 KB
testcase_33	AC	142 ms 35,524 KB
testcase_34	AC	141 ms 35,548 KB
testcase_35	AC	142 ms 35,588 KB
testcase_36	AC	145 ms 35,400 KB
testcase_37	AC	142 ms 35,412 KB
testcase_38	AC	142 ms 35,452 KB
testcase_39	AC	144 ms 35,672 KB
testcase_40	AC	141 ms 35,540 KB
testcase_41	AC	141 ms 35,408 KB
testcase_42	AC	161 ms 35,380 KB
testcase_43	AC	159 ms 35,396 KB
testcase_44	AC	158 ms 35,736 KB
testcase_45	AC	160 ms 35,472 KB
testcase_46	AC	160 ms 35,392 KB
testcase_47	AC	224 ms 35,540 KB
testcase_48	AC	222 ms 35,480 KB
testcase_49	AC	223 ms 35,472 KB
testcase_50	AC	223 ms 35,384 KB
testcase_51	AC	222 ms 35,452 KB
testcase_52	AC	139 ms 35,380 KB
testcase_53	AC	137 ms 35,544 KB
testcase_54	AC	136 ms 35,528 KB
testcase_55	AC	137 ms 35,476 KB
testcase_56	AC	138 ms 35,512 KB
testcase_57	AC	108 ms 35,532 KB
testcase_58	AC	108 ms 35,396 KB
testcase_59	AC	109 ms 35,488 KB
testcase_60	AC	109 ms 35,544 KB
testcase_61	AC	108 ms 35,576 KB
testcase_62	AC	186 ms 35,476 KB

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ソースコード

raw source code

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>

// Li-Chao tree
// init() : set x's where we will execute get(x) queries
// add_segment(l, r, a, b): update by ax + b in [l, r)
// get(x): get min
template <class T, class T_MP> struct li_chao_tree {
    int _n, _head;
    std::vector<T> xs;
    li_chao_tree() : _n(0), _head(0) {}

    struct _Line {
        T a, b;
        int line_idx;
        bool is_valid;
        T_MP eval(T x) const noexcept { return T_MP(a) * x + b; }
    };

    std::vector<_Line> lines;
    struct LCR {
        T l, c, r;
    };
    std::vector<LCR> lcr;

    void init(const std::vector<T> &xs_) {
        xs = xs_;
        std::sort(xs.begin(), xs.end());
        xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
        _n = xs.size();
        _head = 1;
        while (_head < _n) _head <<= 1;
        lines.assign(_head * 2, {0, 0, -1, false});
        lcr.resize(_head * 2);
        for (int i = 0; i < _n; ++i) lcr[_head + i] = {xs[i], xs[i], xs[i]};
        for (int i = _head - 1; i; --i) {
            int l = i * 2, r = i * 2 + 1;
            lcr[i] = {lcr[l].l, lcr[r].l, lcr[r].r};
        }
    }

    int il, ir;
    void _rec(int now, int nowl, int nowr, _Line line_add) {
        const int nowc = (nowl + nowr) / 2;

        if (nowl >= ir or nowr <= il) {
            return;
        } else if (il <= nowl and nowr <= ir) {
            if (!lines[now].is_valid) {
                lines[now] = line_add;
                return;
            }
            bool upd_l = lines[now].eval(lcr[now].l) > line_add.eval(lcr[now].l);
            bool upd_c = lines[now].eval(lcr[now].c) > line_add.eval(lcr[now].c);
            bool upd_r = lines[now].eval(lcr[now].r) > line_add.eval(lcr[now].r);
            if (upd_l and upd_c and upd_r) {
                lines[now] = line_add;
                return;
            } else if (upd_c and upd_r) {
                std::swap(lines[now], line_add);
                _rec(now * 2, nowl, nowc, line_add);
            } else if (upd_l and upd_c) {
                std::swap(lines[now], line_add);
                _rec(now * 2 + 1, nowc, nowr, line_add);
            } else if (upd_l) {
                _rec(now * 2, nowl, nowc, line_add);
            } else if (upd_r) {
                _rec(now * 2 + 1, nowc, nowr, line_add);
            } else {
                return;
            }
        } else {
            if (il < nowc) _rec(now * 2, nowl, nowc, line_add);
            if (ir > nowc) _rec(now * 2 + 1, nowc, nowr, line_add);
        }
    }

    void add_line(T a, T b, int idx = -1) {
        il = 0, ir = _n;
        if (il >= ir) return;
        _rec(1, 0, _head, _Line{a, b, idx, true});
    }
    void add_segment(T xl, T xr, T a, T b, int idx = -1) {
        il = std::lower_bound(xs.begin(), xs.end(), xl) - xs.begin();
        ir = std::lower_bound(xs.begin(), xs.end(), xr) - xs.begin();
        if (il >= ir) return;
        _rec(1, 0, _head, _Line{a, b, idx, true});
    }
    struct Ret {
        T line_a, line_b;
        int line_idx;
        bool is_valid;
        T_MP minval;
    };
    Ret _get_i(int i, T x) {
        i += _head;
        _Line ret = lines[i];
        T_MP val = ret.is_valid ? ret.eval(x) : 0;
        for (i /= 2; i; i /= 2) {
            if (!lines[i].is_valid) continue;
            T_MP tmp = lines[i].eval(x);
            if (!ret.is_valid or tmp < val) ret = lines[i], val = tmp;
        }
        return {ret.a, ret.b, ret.line_idx, ret.is_valid, val};
    }

    Ret get(T x) {
        int i = std::lower_bound(xs.begin(), xs.end(), x) - xs.begin();
        assert(i < _n and xs[i] == x);
        return _get_i(i, x);
    }
};



// Z algorithm (length of longest common prefix for s[0:N] & s[i:N] for each i)
// Input: std::vector<T> / std::string of length N
// Output: std::vector<int> of size N
// Complexity: O(N)
// Sample:
// - `teletelepathy` -> [13, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0]
// Reference: <http://snuke.hatenablog.com/entry/2014/12/03/214243>
template <typename T> std::vector<int> z_algorithm(const std::vector<T> &s) {
    const int N = s.size();
    if (N == 0) return {};
    std::vector<int> ans(N);
    ans[0] = N;
    int i = 1, j = 0;
    while (i < N) {
        while (i + j < N and s[j] == s[i + j]) ++j;
        ans[i] = j;
        if (!j) {
            ++i;
            continue;
        }
        int k = 1;
        while (i + k < N and k + ans[k] < j) ans[i + k] = ans[k], ++k;
        i += k;
        j -= k;
    }
    return ans;
}

std::vector<int> z_algorithm(const std::string &s) {
    const int N = int(s.size());
    std::vector<int> v(N);
    for (int i = 0; i < N; i++) v[i] = s[i];
    return z_algorithm(v);
}

int main() {
    int N, M;
    cin >> N >> M;
    vector<int> A(N), B(M);
    cin >> A >> B;
    vector<int> z = A;
    z.insert(z.end(), B.begin(), B.end());
    z = z_algorithm(z);
    z.erase(z.begin(), z.begin() + A.size());
    for (auto &x : z) chmin(x, N);
    dbg(z);

    vector<lint> C(M);
    cin >> C;

    vector<lint> xs(M + 1);
    std::iota(xs.begin(), xs.end(), 0);
    dbg(xs);
    li_chao_tree<lint, lint> lct;
    lct.init(xs);
    REP(i, M) {
        lint yi = 0;
        if (i) {
            auto p = lct.get(i);
            if (!p.is_valid) continue;
            yi = p.minval;
        }
        lct.add_segment(i + 1, i + 1 + z.at(i), C.at(i), -C.at(i) * i + yi, i);
    }
    auto p = lct.get(M);
    if (!p.is_valid) {
        puts("-1");
        return 0;
    }
    cout << p.minval << endl;
}

yukicoder

結果

テストケース

ソースコード