Submission #498469

#	Time	Username	Problem	Language	Result	Execution time	Memory
498469		Stickfish	Split the sequence (APIO14_sequence)	C++17	71 / 100	421 ms	131076 KiB

sequence

#include <iostream>
using namespace std;
using ll = long long;

const ll INF = 1.77013e18;
const int MAXN = 100004;
const int MAXK = 202;
ll a[MAXN];
ll psm_[MAXN];
ll psqsm_[MAXN];
ll* psm = psm_ + 1;
ll* psqsm = psqsm_ + 1;
ll dp_[MAXK][MAXN];
ll* dp[MAXN];
ll opt[MAXK][MAXN];

void get_layer(int t, int l, int r, int pl, int pr) {
    if (r - l <= 0)
        return;
    int m = (l + r) / 2;
    opt[t][m] = pl;
    for (int i = pl; i <= pr && i < m; ++i) {
        ll sqsm = psqsm[m] - psqsm[i];
        ll sm = psm[m] - psm[i];
        if (dp[t][m] > dp[t - 1][i] + (sm * sm - sqsm) / 2) {
            dp[t][m] = dp[t - 1][i] + (sm * sm - sqsm) / 2;
            opt[t][m] = i;
        }
    }
    get_layer(t, l, m, pl, opt[t][m]);
    get_layer(t, m + 1, r, opt[t][m], pr);
}

signed main() {
    int n, k;
    cin >> n >> k;
    ++k;
    for (int i = 0; i < n; ++i)
        cin >> a[i];
    for (int i = 0; i < k; ++i) {
        dp[i] = dp_[i] + 1;
    }
    for (int i = 0; i < n; ++i) {
        psm[i] = psm[i - 1] + a[i];
        psqsm[i] = psqsm[i - 1] + a[i] * a[i];
        dp[0][i] = (psm[i] * psm[i] - psqsm[i]) / 2;
        opt[0][i] = -1;
    }
    for (int t = 1; t < k; ++t) {
        for (int i = 0; i < n; ++i) {
            dp[t][i] = INF;
        }
        get_layer(t, t, n, t - 1, n - 1);
    }
    ll ans = 0;
    for (int i = 0; i < n; ++i)
        ans += a[i];
    ans *= ans;
    for (int i = 0; i < n; ++i)
        ans -= a[i] * a[i];
    ans /= 2;
    ans -= dp[k - 1][n - 1];
    cout << ans << endl;
    int i = n - 1;
    int t = k;
    while (--t) {
        i = opt[t][i];
        if (i != -1) {
            cout << i + 1 << ' ';
        }
    }
    cout << endl;
}

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