Submission #390043

#	Time	Username	Problem	Language	Result	Execution time	Memory
390043		vonatlus	Split the sequence (APIO14_sequence)	C++17	50 / 100	214 ms	131072 KiB

sequence

/// adil sultanov | vonat1us 

#pragma GCC optimize("O3")
//#pragma comment(linker, "/STACK:36777216")

#include<bits/stdc++.h>

#define x first
#define y second
#define pb push_back
#define sz(x) (int) x.size()
#define all(z) (z).begin(), (z).end()
 
using namespace std;

using ll = long long;
using pii = pair<int, int>;                                   

const int MOD = 1e9 + 7; 
const int INF = 1e9 + 1e2;
  
void fin() {
#ifdef AM
    freopen(".in", "r", stdin);
#endif        
}                   

const bool flag = 0;

const int N = 1e5+10;
const int K = 210;

int p[N];

ll dp[N][2];

int pr[N][K];

void f(int r, int k) {
    if (k == 1) return;
    int cut = pr[r][k];
    cout << cut+1 << " ";
    f(cut, k-1);                 
}

struct Line {
    ll k, b, id;
    Line() {}
    
    Line(int k, ll b, int id): k(k), b(b), id(id) {}
    
    ll get(int x) {
        return x*1ll*k + b;
    }

    ll cross(Line l) {
        if (k == l.k) return -INF;
        return (b-l.b)/(l.k-k);
    }
} v[N*2];

int l, r;

void add(Line L) {
    while (r > 1 && v[r-1].cross(L) <= v[r-2].cross(v[r-1])) {
        r--;
    }
    v[r++] = L;
}

int get(int x) {
    while (l+1 < r && v[l].get(x) > v[l+1].get(x)) ++l;
    return v[l].get(x);
}

int n;

void solve(int k) {
    l = 0, r = 0;
    int h = (k&1);      
    for (int i = 0; i < n; ++i) {
        if (i >= k-1) {
            int pos = get(p[i]);
            dp[i][h] = v[pos].get(p[i]);
            pr[i][k] = v[pos].id;
        }
        add(Line(p[i], dp[i][1-h]-p[i]*1ll*p[i], i));
    }
}

void ma1n() {
    int k;
    cin >> n >> k;
    k++;
    for (int i = 0, x; i < n; ++i) {
        cin >> x;
        p[i] = (i ? p[i-1] : 0)+x;
    }
    memset(pr, -1, sizeof(pr));
    if (n <= 1000) {
        for (int l = 2; l <= k; ++l) {
            int h = (l&1);
            for (int i = 0; i < n; ++i) {   
                dp[i][h] = -INF;
                for (int j = 0; j < i; ++j) {
                    ll res = dp[j][1-h] + (p[i]-p[j])*1ll*p[j];
                    if (res >= dp[i][h]) {
                        dp[i][h] = res, pr[i][l] = j;
                    }
                }
            }       
        } 
    } else {
        for (int l = 2; l <= k; ++l) {
            solve(l);
        }
    }
    cout << dp[n-1][k&1] << "\n";
    f(n-1, k);
} 

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(nullptr), fin();
    int ts = 1;
    if (flag) {
        cin >> ts;
    }
    while (ts--) {
        ma1n(); 
    }
    return 0;
}

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