Submission #729456

#	Time	Username	Problem	Language	Result	Execution time	Memory
729456		danikoynov	Split the sequence (APIO14_sequence)	C++14	71 / 100	79 ms	131072 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];
}

ll cost(int l, int r)
{
    return get_range(l, r) * get_range(r + 1, n);
}

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);
}

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

    for (int i = 0; i <= n; i ++)
        dp[0][i] = 0;
    if (n > 1e4 && k > 150)
        return;
        for (int j = 1; j <= k; j ++)
        solve_layer(j, 1, n, 1, n); /// for (int i = 1; i <= n; i ++)
         ///   cout << bef[2][i] << " ";
        ///cout << endl;
    /**for (int j = 1; j <= k; j ++)
        for (int i = 1; i <= n; i ++)
    {
        for (int d = 1; d <= i; d ++)
        {
            ll sum = dp[j - 1][d - 1] + get_range(d, i) * get_range(i + 1, n);
            if (sum > dp[j][i])
            {
                dp[j][i] = sum;
                bef[j][i] = d - 1;
            }
        }
    }*/


    /**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:79:5: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
   79 |     if (n > 1e4 && k > 150)
      |     ^~
sequence.cpp:81:9: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
   81 |         for (int j = 1; j <= k; j ++)
      |         ^~~

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