Submission #238054

#	Time	Username	Problem	Language	Result	Execution time	Memory
238054		DS007	Split the sequence (APIO14_sequence)	C++14	100 / 100	797 ms	84712 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define evaluate(pt, x) (pt.first.first * x + pt.first.second)

const int N = 1e5, K = 201;
int a[N], p[K], n, k, last[N][K];
ll s[N], dp[N], dp_prev[N];
vector<pair<pair<ll, ll>, int>> hull;

ll find(int i, int j, ll x) {
    for (; p[j] < (int)hull.size() - 1; p[j]++) {
        if (evaluate(hull[p[j]], x) > evaluate(hull[p[j] + 1], x))
            break;
    }
    last[i][j + 1] = hull[p[j]].second;
    return evaluate(hull[p[j]], x);
}

bool inter(pair<ll, ll> a, pair<ll, ll> b, pair<ll, ll> c) {
    return (a.second - b.second) * (c.first - a.first) > (a.second - c.second) * (b.first - a.first);
}

void insert(int j, pair<pair<ll, ll>, int> nl) {
    while (hull.size() > 1) {
        auto temp = hull.back();
        hull.pop_back();

        if (inter(nl.first, temp.first, hull.back().first)) {
            hull.push_back(temp);
            break;
        }

        p[j] = min(p[j], (int)hull.size() - 1);
    }
    hull.push_back(nl);
}

int solveTestCase() {
    cin >> n >> k;
    for (int i = 0; i < n; i++) cin >> a[i];

    s[0] = a[0];
    for (int i = 1; i < n; i++) s[i] = s[i - 1] + a[i];

    /*for (int i = 1; i < n; i++) {
        for (int j = 1; j <= k && j <= i; j++) {
            dp[i][j] = find(i, j - 1, s[i]);
            insert(j - 1, {{s[i], dp[i][j - 1] - s[i] * s[i]}, i});
        }
        insert(min(i, k), {{s[i], dp[i][min(i, k)] - s[i] * s[i]}, i});
    }*/

    for (int j = 1; j <= k; j++) {
        insert(j - 1, {{s[j - 1], dp_prev[j - 1] - s[j - 1] * s[j - 1]}, j - 1});
        for (int i = j; i < n; i++) {
            dp[i] = find(i, j - 1, s[i]);
            insert(j - 1, {{s[i], dp_prev[i] - s[i] * s[i]}, i});
            dp_prev[i] = dp[i];
        }
        hull.clear();
    }

    cout << dp[n - 1] << "\n";
    for (int i = last[n - 1][k], j = k; j > 0; --j, i = last[i][j]) cout << i + 1 << " ";
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    int test = 1;
    // cin >> test;
    while (test--)
        solveTestCase();
}

Compilation message (stderr)

sequence.cpp: In function 'int solveTestCase()':
sequence.cpp:66:1: warning: no return statement in function returning non-void [-Wreturn-type]
 }
 ^

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