Submission #670207

#	Time	Username	Problem	Language	Result	Execution time	Memory
670207		JooDdae	Split the sequence (APIO14_sequence)	C++17	100 / 100	391 ms	84320 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
using ll = long long;


int n, k, a[100100], bt[202][100100];
ll s[100100], dp[100100], pdp[100100];

array<ll, 3> t[100100];
int front, back;

bool check(int a, int b, int c) {
    return (t[b][0]-t[a][0]) * (t[c][1]-t[a][1]) >= (t[c][0]-t[a][0]) * (t[b][1]-t[a][1]);
}


void f(int k, int u) {
    if(k == 0) return;
    f(k-1, bt[k][u]);
    cout << u << " ";
}

int main(){
    cin.tie(0)->sync_with_stdio(0);
    cin >> n >> k;
    for(int i=1;i<=n;i++) cin >> a[i];

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

    for(int j=1;j<=k;j++) {
        front = back = 0;
        t[0] = {s[n]+s[j-1], dp[j-1] - s[n]*s[j-1], j-1};

        for(int i=j;i<n;i++) {
            auto &f = front, &b = back;
            while(f < b && t[f][0]*s[i]+t[f][1] <= t[f+1][0]*s[i]+t[f+1][1]) f++;

            auto [X, Y, id] = t[f];
            dp[i] = X*s[i]+Y - s[i]*s[i], bt[j][i] = id;

            t[++b] = {s[n]+s[i], pdp[i] - s[n]*s[i], i};
            while(f+1 < b && check(b-2, b-1, b)) b--, t[b] = t[b+1];

            if(j == k && dp[i] >= dp[mx]) mx = i;
        }

        for(int i=1;i<=n;i++) pdp[i] = dp[i];
    }

    cout << dp[mx] << "\n";
    f(k, mx);
}

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