Submission #729499

#	Time	Username	Problem	Language	Result	Execution time	Memory
729499		danikoynov	Split the sequence (APIO14_sequence)	C++14	0 / 100	33 ms	8524 KiB

sequence

#include<bits/stdc++.h>
#define endl '\n'

using namespace std;
typedef long long ll;

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

const int maxn = 1e5 + 10, maxk = 210;
const ll inf = 1e18;

int n, k;
ll a[maxn], pref[maxn], dp[maxk][maxn];
int  bef[maxk][maxn];
void input()
{
    cin >> n >> k;
    k ++;
    for (int i = 1; i <= n; i ++)
        cin >> a[i];
}

void calculate_prefix()
{
    for (int i = 1; i <= n; i ++)
        pref[i] = pref[i - 1] + a[i];
}

ll get_range(int l, int r)
{
    return pref[r] - pref[l - 1];
}

struct line
{
    ll k, m, idx;

    line(ll _k, ll _m, ll _idx)
    {
        k = _k;
        m = _m;
        idx = _idx;
    }

    ll value(ll x)
    {
        return k * x + m;
    }
};

ll cost(int l, int r)
{
    return pref[r] * pref[n] - pref[r] * pref[r] - pref[l - 1] * pref[n] + pref[l - 1] * pref[r];
    /**
        (pref[r]) * pref[l - 1] + pref[r] * pref[n] - pref[r] * pref[r];
    */
}

void solve_layer(int layer, int left, int right, int optl, int optr)
{
    ///cout << layer << " " << left << " " << right << endl;
    if (left > right)
        return;

    int opt = -1, mid = (left + right) / 2;
    ll best = -inf;
    for (int i = optl; i <= min(mid, optr); i ++)
    {
        ll sum = cost(i, mid) + dp[layer - 1][i - 1];
        if (sum > best)
        {
            best = sum;
            opt = i;
        }
    }
    if (opt == -1)
    {
        opt = 1;
    }
    bef[layer][mid] = opt - 1;
    dp[layer][mid] = best;
    solve_layer(layer, left, mid - 1, optl, opt);
    solve_layer(layer, mid + 1, right, opt, optr);
}


double intersection(line l1, line l2)
{
    return (double)(l2.m - l1.m) / (double)(l1.k - l2.k);
}

bool order(line l1, line l2, line l3)
{
    if (intersection(l1, l3) < intersection(l1, l2))
        return true;
    return false;
}

void calculate_states()
{
    for (int j = 0; j <= k; j ++)
        for (int i = 0; i <= n; i ++)
        dp[j][i] = -inf;

        dp[0][0] = 0;


        ///cout << cost(1, 1) << endl;
    for (int j = 1; j <= k; j ++)
    {
        deque < line > d;
        for (int i = 1; i <= n; i ++)
        {
            line cur(pref[i - 1], - pref[n] * pref[i - 1] + dp[j - 1][i - 1], i - 1);
            int sz = d.size();
            while(d.size() > 1)
            {
                line bk2 = d[sz - 1], bk1 = d[sz - 2];
                if (order(bk1, bk2, cur))
                    d.pop_back();
                else
                    break;
            }
            d.push_back(cur);
            while(d.size() > 1 && d[0].value(pref[i]) <= d[1].value(pref[i]))
                    d.pop_front();

            bef[j][i] = d.front().idx;
            ///cout << dp[j - 1][i - 1] << endl;
            ///cout << d.front().k << " " << d.front().m << endl;
            ///dp[j][i] = cost(bef[j][i] + 1, i) + dp[j - 1][bef[j][i]];
            if (dp[j - 1][bef[j][i]] == -inf)
                continue;
            dp[j][i] = d.front().value(pref[i]) + pref[i] * (pref[n] - pref[i]);

        }

        /**for (int i = 1; i <= n; i ++)
            cout << dp[j][i] << " ";
        cout << endl;*/
    }

    /**for (int j = 1; j <= k; j ++, cout << endl)
        for (int i = 1; i <= n; i ++)
        cout << dp[j][i] << " ";*/
}

void print_answer()
{
    cout << dp[k][n] << endl;
    int pos = n, part = k;
    vector < int > path;
    while(bef[part][pos] != 0)
    {
        pos = bef[part][pos];
        part --;
        path.push_back(pos);
    }

    reverse(path.begin(), path.end());
    for (int v : path)
        cout << v << " ";
    cout << endl;
}
void solve()
{
    input();
    calculate_prefix();
    calculate_states();
    print_answer();

}

int main()
{
    solve();
    return 0;
}
/**
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In function 'void calculate_states()':
sequence.cpp:106:5: warning: this 'for' clause does not guard... [-Wmisleading-indentation]
  106 |     for (int j = 0; j <= k; j ++)
      |     ^~~
sequence.cpp:110:9: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'for'
  110 |         dp[0][0] = 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