Submission #891939

#	Time	Username	Problem	Language	Result	Execution time	Memory
891939		abysmal	Split the sequence (APIO14_sequence)	C++14	0 / 100	2066 ms	90688 KiB

sequence

#include<iostream>
#include<stdio.h>
#include<stdint.h>
#include<vector>
#include<algorithm>
#include<utility>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<iomanip>
#include<string>
#include<math.h>
#include<assert.h>

using namespace std;

const double PI = (double) atan(1.0) * 4;
const int64_t INF = (int64_t) 1e18 + 777;
const int64_t mINF = (int64_t) 2e9 + 777;
const int64_t offset = (int64_t) 1e6 + 777;
const int64_t MOD = 1e9 + 7;
const int nbit = 11;
const int ndig = 10;
const int nchar = 26;
const int p1 = 31;
const int p2 = 53;
const int D = 4;
int dr[D] = {0, 1, 0, -1};
int dc[D] = {1, 0, -1, 0};
// 0 right // 1 down // 2 left // 3 up
bool Q = false;

int modadd(int t1, int t2)
{
    int res = t1 + t2;
    if(res >= MOD) res -= MOD;

    return res;
}

int modmul(int t1, int t2)
{
    int64_t res = 1LL * t1 * t2;
    return (res % MOD);
}

struct Line
{
    int64_t k; int64_t m;
    int id;
    mutable int64_t p;

    bool operator < (const Line& o) const
    {
        if(Q) return p < o.p;
        return k < o.k;
    }
};

struct LineContainer : multiset<Line, less<> >
{
    int64_t div(int64_t a, int64_t b)
    {
        return a / b - ((a ^ b) < 0 && (a % b));
    }

    bool isect(iterator x, iterator y)
    {
        if(y == end())
        {
            x->p = INF;
            return false;
        }

        if(x->k == y->k)
        {
            if(x->m > y->m) x->p = INF;
            else x->p = -INF;
        }
        else x->p = div(y->m - x->m, x->k - y->k);

        return x->p >= y->p;
    }

    void add(int64_t k, int64_t m, int i)
    {
        auto z = insert({k, m, i, 0});
        auto y = z++;
        auto x = y;

        while(isect(y, z)) z = erase(z);
        if(x != begin() && isect(--x, y)) erase(x, y = erase(y));

        while((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y));
    }

    pair<int64_t, int> query(int64_t x)
    {
        assert(!empty());

        Q = true;
        auto l = *lower_bound({0, 0, 0, x});
        Q = false;

        return {l.k * x + l.m, l.id};
    }
};

struct Solution
{
    int n; int k;
    vector<int> a;
    Solution() {}

    void solve()
    {
        cin >> n >> k;
        a.resize(n);
        for(int i = 0; i < n; i++)
        {
            cin >> a[i];
        }

        vector<int64_t> prefix(n + 1, 0);
        vector<int64_t> suffix(n + 2, 0);
        for(int i = 1; i <= n; i++)
        {
            prefix[i] = prefix[i - 1] + a[i - 1];
        }
        for(int i = n; i >= 1; i--)
        {
            suffix[i] = suffix[i + 1] + a[i - 1];
        }

        vector<int64_t> dp(n + 1, -INF);
        vector<int64_t> f(n + 1, -INF);
        vector<vector<int> > trace(k, vector<int>(n + 1, -1));
        dp[0] = 0;
        int e = -1;
        int64_t ans = -INF;
        for(int t = 0; t < k; t++)
        {
            LineContainer lc;
            for(int i = 0; i <= n; i++)
            {
                f[i] = dp[i];
                int64_t p = prefix[i];
                int64_t suf = suffix[i + 1];
                if(!lc.empty())
                {
                    pair<int64_t, int> pr = lc.query(suf);
                    int64_t val = pr.first;
                    int id = pr.second;

                    f[i] = max(f[i], val + p * suf);
                    trace[t][i] = id;
                }

                if(ans < f[i])
                {
                    ans = f[i];
                    e = i;
                }
                lc.add(-p, dp[i], i);
            }

            swap(f, dp);
        }

        cout << ans << "\n";
        vector<int> path;
        for(int i = k - 1; i >= 0; i--)
        {
            path.push_back(e);
            e = trace[i][e];
        }

        reverse(path.begin(), path.end());
        for(int i = 0; i < k; i++)
        {
            cout << path[i] << " ";
        }
    }

    int modsub(int t1, int t2)
    {
        int res = t1 - t2;
        if(res < 0) res += MOD;

        return res;
    }

    bool BIT(int& mask, int& j)
    {
        return (mask & MASK(j));
    }

    int64_t Abs(int64_t t1)
    {
        if(t1 < 0) return -t1;
        return t1;
    }

    int MASK(int j)
    {
        return (1 << j);
    }
};

void __startup()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);

//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
}

int main()
{
    __startup();
    int t = 1;
//    cin >> t;

    for(int i = 1; i <= t; i++)
    {
        Solution().solve();
    }

    return 0;
}

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