Submission #113087

#	Time	Username	Problem	Language	Result	Execution time	Memory
113087		dolphingarlic	Split the sequence (APIO14_sequence)	C++14	60 / 100	418 ms	131072 KiB

sequence

#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
 
int n, k;
ll dp[201][100001];
ll pref[100001]{0};
 
bool case1(int x, int y, int i, int indx) {
    return (dp[indx][y] - dp[indx][x] >=
            (pref[y] - pref[x]) * (pref[n] - pref[i]));
}
 
bool case2(int x, int y, int i, int indx) {
    return ((dp[indx][y] - dp[indx][x]) * (pref[i] - pref[y]) <=
            (dp[indx][i] - dp[indx][y]) * (pref[y] - pref[x]));
}
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin >> n >> k;
    FOR(i, 1, n + 1) {
        int x;
        cin >> x;
        pref[i] = pref[i - 1] + x;
    }
 
    fill(dp[0], dp[0] + n + 1, 0);
    FOR(i, 1, k + 1) {
        deque<int> q;
        q.push_back(0);
        dp[i][0] = 0;
        FOR(j, 1, n + 1) {
            while (q.size() > 1 && case1(q[0], q[1], j, i - 1)) q.pop_front();
 
            ll x = q[0];
            dp[i][j] = dp[i - 1][x] + (pref[j] - pref[x]) * (pref[n] - pref[j]);
 
            while (q.size() > 1 && case2(q[q.size() - 2], q[q.size() - 1], j, i - 1)) q.pop_back();
            q.push_back(j);
        }
    }
 
    ll mx = -1;
    int indx = -1;
    FOR(i, 1, n + 1) {
        if (dp[k][i] > mx) mx = dp[k][i], indx = i;
    }
    cout << mx << '\n';
    FOR(i, 1, k + 1) {
        cout << indx << ' ';
        FOR(j, 0, indx) {
            if (dp[k - i][j] + (pref[indx] - pref[j]) * (pref[n] - pref[indx]) == mx) {
                mx = dp[k - i][j];
                indx = j;
                break;
            }
        }
    }
    cout << '\n';
    return 0;
}

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