Submission #1156819

#	Time	Username	Problem	Language	Result	Execution time	Memory
1156819		agrim_09	Split the sequence (APIO14_sequence)	C++20	71 / 100	2099 ms	173640 KiB

sequence

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define endl '\n';
#define fastio ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define py cout << "YES" << endl;
#define pn cout << "NO" << endl;
#define pb push_back
#define int long long
typedef long double lld;
#define double lld
typedef long long ll;
typedef unsigned long long ull;
const ll inf = 1e18;
const ll mod = 1e9+7;
const int N = 2e5;
vector<int>primes = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97};

void judge(){
    srand(time(NULL));
    #ifndef ONLINE_JUDGE
    freopen("1.txt","r",stdin);
    freopen("2.txt","w",stdout);
    freopen("Error.txt", "w", stderr);
    #define debug(x...) cerr << #x <<" = "; _print(x); cerr << endl;
    #else
    #define debug(x...)
    #endif
}

void usaco(string s) {
    freopen((s + ".in").c_str(),"r",stdin);
    freopen((s + ".out").c_str(),"w",stdout);
}
struct IOPre
{
    static constexpr int TEN = 10, SZ = TEN * TEN * TEN * TEN;
    std::array<char, 4 * SZ> num;
    constexpr IOPre() : num{}
    {
        for (int i = 0; i < SZ; i++)
        {
            int n = i;
            for (int j = 3; j >= 0; j--)
            {
                num[i * 4 + j] = static_cast<char>(n % TEN + '0');
                n /= TEN;
            }
        }
    }
};
struct IO
{
#if !HAVE_DECL_FREAD_UNLOCKED
#define fread_unlocked fread
#endif
#if !HAVE_DECL_FWRITE_UNLOCKED
#define fwrite_unlocked fwrite
#endif
    static constexpr int SZ = 1 << 17, LEN = 32, TEN = 10, HUNDRED = TEN * TEN,
                         THOUSAND = HUNDRED * TEN, TENTHOUSAND = THOUSAND * TEN,
                         MAGIC_MULTIPLY = 205, MAGIC_SHIFT = 11, MASK = 15,
                         TWELVE = 12, SIXTEEN = 16;
    static constexpr IOPre io_pre = {};
    std::array<char, SZ> input_buffer, output_buffer;
    int input_ptr_left, input_ptr_right, output_ptr_right;

    IO()
        : input_buffer{},
          output_buffer{},
          input_ptr_left{},
          input_ptr_right{},
          output_ptr_right{} {}
    IO(const IO &) = delete;
    IO(IO &&) = delete;
    IO &operator=(const IO &) = delete;
    IO &operator=(IO &&) = delete;

    ~IO() { flush(); }

    template <class T>
    struct is_char
    {
        static constexpr bool value = std::is_same_v<T, char>;
    };

    template <class T>
    struct is_bool
    {
        static constexpr bool value = std::is_same_v<T, bool>;
    };

    template <class T>
    struct is_string
    {
        static constexpr bool value =
            std::is_same_v<T, std::string> || std::is_same_v<T, const char *> ||
            std::is_same_v<T, char *> || std::is_same_v<std::decay_t<T>, char *>;
    };

    template <class T, class D = void>
    struct is_custom
    {
        static constexpr bool value = false;
    };

    template <class T>
    struct is_custom<T, std::void_t<typename T::internal_value_type>>
    {
        static constexpr bool value = true;
    };

    template <class T>
    struct is_default
    {
        static constexpr bool value = is_char<T>::value || is_bool<T>::value ||
                                      is_string<T>::value ||
                                      std::is_integral_v<T>;
    };

    template <class T, class D = void>
    struct is_iterable
    {
        static constexpr bool value = false;
    };

    template <class T>
    struct is_iterable<
        T, typename std::void_t<decltype(std::begin(std::declval<T>()))>>
    {
        static constexpr bool value = true;
    };

    template <class T, class D = void, class E = void>
    struct is_applyable
    {
        static constexpr bool value = false;
    };

    template <class T>
    struct is_applyable<T, std::void_t<typename std::tuple_size<T>::type>,
                        std::void_t<decltype(std::get<0>(std::declval<T>()))>>
    {
        static constexpr bool value = true;
    };

    template <class T>
    static constexpr bool needs_newline = (is_iterable<T>::value ||
                                           is_applyable<T>::value) &&
                                          (!is_default<T>::value);

    template <typename T, typename U>
    struct any_needs_newline
    {
        static constexpr bool value = false;
    };
    template <typename T>
    struct any_needs_newline<T, std::index_sequence<>>
    {
        static constexpr bool value = false;
    };
    template <typename T, std::size_t I, std::size_t... Is>
    struct any_needs_newline<T, std::index_sequence<I, Is...>>
    {
        static constexpr bool value =
            needs_newline<decltype(std::get<I>(std::declval<T>()))> ||
            any_needs_newline<T, std::index_sequence<Is...>>::value;
    };

    inline void load()
    {
        memmove(std::begin(input_buffer),
                std::begin(input_buffer) + input_ptr_left,
                input_ptr_right - input_ptr_left);
        input_ptr_right =
            input_ptr_right - input_ptr_left +
            static_cast<int>(fread_unlocked(
                std::begin(input_buffer) + input_ptr_right - input_ptr_left, 1,
                SZ - input_ptr_right + input_ptr_left, stdin));
        input_ptr_left = 0;
    }

    inline void read_char(char &c)
    {
        if (input_ptr_left + LEN > input_ptr_right)
            load();
        c = input_buffer[input_ptr_left++];
    }
    inline void read_string(std::string &x)
    {
        char c;
        while (read_char(c), c < '!')
            continue;
        x = c;
        while (read_char(c), c >= '!')
            x += c;
    }
    inline void read_string(char *a)
    {
        char c;
        while (read_char(c), c < '!')
            continue;
        *(a++) = c;
        while (read_char(c), c >= '!')
            *(a++) = c;
    }
    template <class T>
    inline std::enable_if_t<std::is_integral_v<T>, void> read_int(T &x)
    {
        if (input_ptr_left + LEN > input_ptr_right)
            load();
        char c = 0;
        do
            c = input_buffer[input_ptr_left++];
        while (c < '-');
        [[maybe_unused]] bool minus = false;
        if constexpr (std::is_signed<T>::value == true)
            if (c == '-')
                minus = true, c = input_buffer[input_ptr_left++];
        x = 0;
        while (c >= '0')
            x = x * TEN + (c & MASK), c = input_buffer[input_ptr_left++];
        if constexpr (std::is_signed<T>::value == true)
            if (minus)
                x = -x;
    }

    inline void skip_space()
    {
        if (input_ptr_left + LEN > input_ptr_right)
            load();
        while (input_buffer[input_ptr_left] <= ' ')
            input_ptr_left++;
    }

    inline void flush()
    {
        fwrite_unlocked(std::begin(output_buffer), 1, output_ptr_right, stdout);
        output_ptr_right = 0;
    }

    inline void write_char(char c)
    {
        if (output_ptr_right > SZ - LEN)
            flush();
        output_buffer[output_ptr_right++] = c;
    }

    inline void write_bool(bool b)
    {
        if (output_ptr_right > SZ - LEN)
            flush();
        output_buffer[output_ptr_right++] = b ? '1' : '0';
    }

    inline void write_string(const std::string &s)
    {
        for (auto x : s)
            write_char(x);
    }

    inline void write_string(const char *s)
    {
        while (*s)
            write_char(*s++);
    }

    inline void write_string(char *s)
    {
        while (*s)
            write_char(*s++);
    }

    template <typename T>
    inline std::enable_if_t<std::is_integral_v<T>, void> write_int(T x)
    {
        if (output_ptr_right > SZ - LEN)
            flush();
        if (!x)
        {
            output_buffer[output_ptr_right++] = '0';
            return;
        }
        if constexpr (std::is_signed<T>::value == true)
            if (x < 0)
                output_buffer[output_ptr_right++] = '-', x = -x;
        int i = TWELVE;
        std::array<char, SIXTEEN> buf{};
        while (x >= TENTHOUSAND)
        {
            memcpy(std::begin(buf) + i,
                   std::begin(io_pre.num) + (x % TENTHOUSAND) * 4, 4);
            x /= TENTHOUSAND;
            i -= 4;
        }
        if (x < HUNDRED)
        {
            if (x < TEN)
            {
                output_buffer[output_ptr_right++] = static_cast<char>('0' + x);
            }
            else
            {
                std::uint32_t q =
                    (static_cast<std::uint32_t>(x) * MAGIC_MULTIPLY) >>
                    MAGIC_SHIFT;
                std::uint32_t r = static_cast<std::uint32_t>(x) - q * TEN;
                output_buffer[output_ptr_right] = static_cast<char>('0' + q);
                output_buffer[output_ptr_right + 1] =
                    static_cast<char>('0' + r);
                output_ptr_right += 2;
            }
        }
        else
        {
            if (x < THOUSAND)
            {
                memcpy(std::begin(output_buffer) + output_ptr_right,
                       std::begin(io_pre.num) + (x << 2) + 1, 3),
                    output_ptr_right += 3;
            }
            else
            {
                memcpy(std::begin(output_buffer) + output_ptr_right,
                       std::begin(io_pre.num) + (x << 2), 4),
                    output_ptr_right += 4;
            }
        }
        memcpy(std::begin(output_buffer) + output_ptr_right,
               std::begin(buf) + i + 4, TWELVE - i);
        output_ptr_right += TWELVE - i;
    }
    template <typename T_>
    IO &operator<<(T_ &&x)
    {
        using T = typename std::remove_cv<
            typename std::remove_reference<T_>::type>::type;
        static_assert(is_custom<T>::value or is_default<T>::value or
                      is_iterable<T>::value or is_applyable<T>::value);
        if constexpr (is_custom<T>::value)
        {
            write_int(x.get());
        }
        else if constexpr (is_default<T>::value)
        {
            if constexpr (is_bool<T>::value)
            {
                write_bool(x);
            }
            else if constexpr (is_string<T>::value)
            {
                write_string(x);
            }
            else if constexpr (is_char<T>::value)
            {
                write_char(x);
            }
            else if constexpr (std::is_integral_v<T>)
            {
                write_int(x);
            }
        }
        else if constexpr (is_iterable<T>::value)
        {
            // strings are immune
            using E = decltype(*std::begin(x));
            constexpr char sep = needs_newline<E> ? '\n' : ' ';
            int i = 0;
            for (const auto &y : x)
            {
                if (i++)
                    write_char(sep);
                operator<<(y);
            }
        }
        else if constexpr (is_applyable<T>::value)
        {
            // strings are immune
            constexpr char sep =
                (any_needs_newline<
                    T, std::make_index_sequence<std::tuple_size_v<T>>>::value)
                    ? '\n'
                    : ' ';
            int i = 0;
            std::apply(
                [this, &sep, &i](auto const &...y)
                {
                    (((i++ ? write_char(sep) : void()), this->operator<<(y)),
                     ...);
                },
                x);
        }
        return *this;
    }
    template <typename T>
    IO &operator>>(T &x)
    {
        static_assert(is_custom<T>::value or is_default<T>::value or
                      is_iterable<T>::value or is_applyable<T>::value);
        static_assert(!is_bool<T>::value);
        if constexpr (is_custom<T>::value)
        {
            typename T::internal_value_type y;
            read_int(y);
            x = y;
        }
        else if constexpr (is_default<T>::value)
        {
            if constexpr (is_string<T>::value)
            {
                read_string(x);
            }
            else if constexpr (is_char<T>::value)
            {
                read_char(x);
            }
            else if constexpr (std::is_integral_v<T>)
            {
                read_int(x);
            }
        }
        else if constexpr (is_iterable<T>::value)
        {
            for (auto &y : x)
                operator>>(y);
        }
        else if constexpr (is_applyable<T>::value)
        {
            std::apply([this](auto &...y)
                       { ((this->operator>>(y)), ...); }, x);
        }
        return *this;
    }

    IO *tie(std::nullptr_t) { return this; }
    void sync_with_stdio(bool) {}
};
IO io;
#define cin io
#define cout io


struct line {
	mutable int m, c, p;
    int pos;
	bool operator<(const line& l) const { return m < l.m; }
	bool operator<(int x) const { return p < x; }
};
// Returns max for a convex hull
struct LineContainer : multiset<line, less<>> {
	// (for doubles, use inf = 1/.0, ceil(a,b) = a/b)
	int div(int a, int b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b);
	}

    bool isect(iterator x, iterator y) {
		if (y == end()){
            x -> p = inf;
            return false;
        }
		if (x->m==y->m){
			x->p = -1*inf;
            if (x->c > y->c) {
                x->p = inf;
            }
        }
		else{
            x->p = div(y->c - x->c, x->m - y->m);
        }
		return x->p >= y->p;
	}
	void add(int m, int c, int idx) {
		auto it = insert({m, c, 0, idx}) , next = it++, prev = next;
		while (isect(next, it)){
            it = erase(it);
        }
		if (prev != begin() && isect(--prev, next)){
            isect(prev, next = erase(next));
        }
		while ((next = prev) != begin() && (--prev)->p >= next->p){
            isect(prev, erase(next));
        }
	}
	pair<int,int> query(int x) {
		auto l = *lower_bound(x);
		return {l.m * x + l.c,l.pos};
	}
};



signed main(){
    fastio; //judge();
    int n,k; cin >> n >> k;
    k++;
    vector<int>a(n);
    for(auto &x : a) cin >> x;
    int sum = accumulate(a.begin(),a.end(),0);

    vector<int>dp1(n);
    vector<vector<int>>pos(n,vector<int>(k+1,-1));
    vector<int>pref(n);
    int curr = 0;
    for(int i = 0;i<n;i++){
        curr += a[i];
        dp1[i] = curr*curr;
        pos[i][1] = 0;
        pref[i] = curr;
    }
    vector<int>dp2(n);

    for(int kx = 2;kx<=k;kx++){
        LineContainer cht;
        for(int i = kx-2;i<=kx-2;i++){
            cht.add(2*pref[i],-1*(pref[i]*pref[i] + dp1[i]),i);
        }
        for(int i = kx-1;i<n;i++){
            curr = a[i];
            pair<int,int>tmp = cht.query(pref[i]);
            dp2[i] = pref[i]*pref[i] - 1*tmp.first;
            pos[i][kx] = tmp.second;
            cht.add(2 * pref[i], -1 * (pref[i] * pref[i] + dp1[i]), i);
        }
        dp1 = dp2;
    }
    cout << (sum*sum - dp1[n-1])/2 << endl;
    int num = n-1;
    vector<int>ordering;
    for(int i = k;i>=2;i--){
        ordering.pb(pos[num][i]+1);
        num = pos[num][i];
    }
    reverse(ordering.begin(),ordering.end());
    for(auto x : ordering)
        cout << x << ' ';
}

Compilation message (stderr)

sequence.cpp: In function 'void judge()':
sequence.cpp:27:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   27 |     freopen("1.txt","r",stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~
sequence.cpp:28:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   28 |     freopen("2.txt","w",stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~
sequence.cpp:29:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   29 |     freopen("Error.txt", "w", stderr);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void usaco(std::string)':
sequence.cpp:37:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   37 |     freopen((s + ".in").c_str(),"r",stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:38:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   38 |     freopen((s + ".out").c_str(),"w",stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 0 / 29