Submission #565539

#	Time	Username	Problem	Language	Result	Execution time	Memory
565539		Forested	Split the sequence (APIO14_sequence)	C++17	100 / 100	1862 ms	31792 KiB

sequence

// ===== template.hpp =====
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

template <typename F, typename Comp = less<>>
Vec<i32> sort_index(i32 n, F f, Comp comp = Comp()) {
    Vec<i32> idx(n);
    iota(ALL(idx), 0);
    sort(ALL(idx), [&](i32 i, i32 j) -> bool {
        return comp(f(i), f(j));
    });
    return idx;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;

struct FastIO {
    FastIO() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(10);
    }
} fast_io;
// ===== template.hpp =====

#ifdef DEBUGF
#include "cpl/template/debug.hpp"
#else
#define DBG(x) (void) 0
#endif

// ===== utils.hpp =====

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = static_cast<unsigned>(static_cast<unsigned long long>(ret) * self % mod);
        }
        self = static_cast<unsigned>(static_cast<unsigned long long>(self) * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ===== utils.hpp =====

// monotone
class CHT {
    deque<tuple<i64, i64, i32>> que;
    
    bool need(const tuple<i64, i64, i32> &a, const tuple<i64, i64, i32> &b, const tuple<i64, i64, i32> &c) const {
        i64 ab = floor_div(get<1>(b) - get<1>(a), get<0>(a) - get<0>(b));
        i64 bc = floor_div(get<1>(c) - get<1>(b), get<0>(b) - get<0>(c));
        return ab < bc;
    }
    
public:
    CHT() : que() {}
    
    void add(i64 a, i64 b, i32 idx) {
        if (!que.empty() && get<0>(que.back()) == a) {
            if (get<1>(que.back()) > b) {
                que.pop_back();
            } else {
                return;
            }
        }
        que.emplace_back(a, b, idx);
        while (que.size() >= 3) {
            if (!need(que[que.size() - 3], que[que.size() - 2], que[que.size() - 1])) {
                swap(que[que.size() - 2], que[que.size() - 1]);
                que.pop_back();
            } else {
                break;
            }
        }
    }
    
    i32 argmin(i64 x) {
        assert(!que.empty());
        while (que.size() >= 2) {
            i64 fi = get<0>(que[0]) * x + get<1>(que[0]);
            i64 se = get<0>(que[1]) * x + get<1>(que[1]);
            if (fi >= se) {
                que.pop_front();
            } else {
                break;
            }
        }
        return get<2>(que[0]);
    }
};

int main() {
    i32 n, k;
    cin >> n >> k;
    ++k;
    Vec<i64> a(n);
    REP(i, n) {
        cin >> a[i];
    }
    
    Vec<i64> sum(n + 1, 0), sqsum(n + 1, 0);
    REP(i, n) {
        sum[i + 1] = sum[i] + a[i];
        sqsum[i + 1] = sqsum[i] + a[i] * a[i];
    }
    const auto product_sum = [&](i32 l, i32 r) -> i64 {
        i64 s = sum[r] - sum[l], sq = sqsum[r] - sqsum[l];
        return (s * s - sq) / 2;
    };
    
    Vec<i64> dp(n + 1, INF64);
    dp[0] = 0;
    Vec<Vec<i64>> hist;
    const i32 interval = 10;
    REP(i, k) {
        if (i % interval == 0) {
            hist.push_back(dp);
        }
        Vec<i64> ndp(n + 1, INF64);
        CHT cht;
        REP(j, i + 1, n + 1) {
            cht.add(-sum[j - 1], dp[j - 1] + (sum[j - 1] * sum[j - 1] + sqsum[j - 1]) / 2, j - 1);
            i32 arg = cht.argmin(sum[j]);
            ndp[j] = dp[arg] + product_sum(arg, j);
        }
        dp = move(ndp);
    }
    hist.push_back(dp);
    
    i64 ans = product_sum(0, n) - dp[n];
    
    Vec<i64> prevs;
    prevs.reserve(k);
    i32 now = n;
    PER(i, hist.size() - 1) {
        i32 l = interval * i;
        i32 r = min(k, interval * (i + 1));
        Vec<i64> dp_ = hist[i];
        Vec<Vec<i64>> args(r - l, Vec<i64>(n + 1, -1));
        REP(j, r - l) {
            Vec<i64> ndp(n + 1, INF64);
            CHT cht;
            REP(m, l + j + 1, n + 1) {
                cht.add(-sum[m - 1], dp_[m - 1] + (sum[m - 1] * sum[m - 1] + sqsum[m - 1]) / 2, m - 1);
                i32 arg = cht.argmin(sum[m]);
                ndp[m] = dp_[arg] + product_sum(arg, m);
                args[j][m] = arg;
            }
            DBG(ndp);
            dp_ = move(ndp);
        }
        DBG(dp_);
        DBG(hist[i + 1]);
        PER(j, r - l) {
            now = args[j][now];
            prevs.push_back(now);
        }
    }
    reverse(ALL(prevs));
    
    cout << ans << '\n';
    REP(i, 1, k) {
        cout << prevs[i] << " \n"[i + 1 == k];
    }
}

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