Submission #660394

#	Time	Username	Problem	Language	Result	Execution time	Memory
660394		leroycut	Split the sequence (APIO14_sequence)	C++17	71 / 100	81 ms	131072 KiB

sequence

#include <bits/stdc++.h>
 
using namespace std;
using ll = long long;
using ld = long double;
 
const int N = 1e5 + 3;
const ll INF = 2e12 + 3;
 
int n, k;
ll dp[N][203], p[N], ppm[N];
 
ld cross(int i, int j, int c){
    ld rb = (dp[j][c - 1] - p[j] * p[j]) - (dp[i][c - 1] - p[i] * p[i]);
    ld rk = p[i] - p[j];
    return rb / rk;
}
 
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
 
    cin >> n >> k;
    for(int i = 1; i <= n; ++i){
        ll a;
        cin >> a;
        p[i] = p[i - 1] + a;
        ppm[i] = ppm[i - 1] + a * p[i - 1];
    }
 
 
    for(int j = 1; j <= k; ++j){
        deque<int> q;
        for(int i = 1; i < j + 1; ++i){
            while(q.size() > 1 && cross(q[0], q[1], j) <= p[i]) q.pop_front();
            dp[i][j] = ppm[i];
            while(q.size() > 1){
                if(p[q.back()] == p[i] && dp[i][j - 1] - p[i] * p[i] > dp[q.back()][j - 1] - p[q.back()] * p[q.back()]){
                    q.pop_back();
                    continue;
                }
                if(cross(q.back(), i, j) <= cross(q[q.size() - 2], q.back(), j)){
                    q.pop_back();
                    continue;
                }
                break;
            }
            if(q.size() > 0 && p[q.back()] == p[i]){
                if(dp[i][j - 1] - p[i] * p[i] > dp[q.back()][j - 1] - p[q.back()] * p[q.back()]){
                    q.pop_back();
                    q.push_back(i);
                }
                continue;
            }
            q.push_back(i);
        }
        for(int i = j + 1; i <= n; ++i){
            while(q.size() > 1 && cross(q[0], q[1], j) <= p[i]) q.pop_front();
            int t = q.front();
            dp[i][j] = dp[t][j - 1] + p[t] * (p[i] - p[t]);
            while(q.size() > 1){
                if(p[q.back()] == p[i] && dp[i][j - 1] - p[i] * p[i] > dp[q.back()][j - 1] - p[q.back()] * p[q.back()]){
                    q.pop_back();
                    continue;
                }
                if(cross(q.back(), i, j) <= cross(q[q.size() - 2], q.back(), j)){
                    q.pop_back();
                    continue;
                }
                break;
            }
            if(p[q.back()] == p[i]){
                if(dp[i][j - 1] - p[i] * p[i] > dp[q.back()][j - 1] - p[q.back()] * p[q.back()]){
                    q.pop_back();
                    q.push_back(i);
                }
                continue;
            }
            q.push_back(i);
        }
    }
 
    cout << dp[n][k] << "\n";
    int poi = n - 1, end = n, cnt = k - 1;
    for(; poi >= 1 && cnt >= 0; --poi){
        if(dp[poi][cnt] + p[poi] * (p[end] - p[poi]) == dp[end][cnt + 1]){
            cout << poi << " ";
            end = poi;
            cnt--;
        }
    }
}

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