Submission #768160

#	Time	Username	Problem	Language	Result	Execution time	Memory
768160		hafo	Split the sequence (APIO14_sequence)	C++14	0 / 100	15 ms	7680 KiB

sequence

#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define pb push_back
#define pa pair<int, int>
#define pall pair<ll, int>
#define fi first
#define se second
#define TASK "test"
#define Size(x) (int) x.size()
#define all(x) x.begin(), x.end()
using namespace std;

template<typename T1, typename T2> bool mini (T1 &a, T2 b) {if(a > b) a = b; else return 0; return 1;}
template<typename T1, typename T2> bool maxi (T1 &a, T2 b) {if(a < b) a = b; else return 0; return 1;}

const int MOD = 1e9 + 7;
const int LOG = 20;
const int maxn = 1e5 + 7;
const ll oo = 1e18 + 69;

int n, k, a[maxn], trace[207][maxn];
ll f[maxn], dp[207][maxn];

struct cht{
    struct line {
        ll m, b;
        int id;
    };
    vector<line> lines;
    int pointer;
 
    void init() {
        lines.clear();
        pointer = 0;
    }
 
    double inter(line &x, line &y) {
        return (double) (y.b - x.b) / (double) (x.m - y.m);
    }
 
    bool bad(int i, int j, int k) {
        return inter(lines[i], lines[k]) < inter(lines[i], lines[j]);
    }
    
    ll calc(line &a, ll &x) {
        return a.m * x + a.b;
    }

    void add(ll m, ll b, int id) {
        lines.pb({m, b, id}); 
        while(Size(lines) >= 3 && bad(Size(lines) - 3, Size(lines) - 2, Size(lines) - 1)) lines.erase(lines.end() - 2);
    }
 
    pair<ll, int> query(ll x) {
        if(pointer >= Size(lines)) pointer = Size(lines) - 1;
        while(pointer < Size(lines) - 1 && calc(lines[pointer], x) < calc(lines[pointer + 1], x)) pointer++;
        return {calc(lines[pointer], x), lines[pointer].id};
    }
} cht;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    //freopen(TASK".inp", "r", stdin);
    //freopen(TASK".out", "w", stdout);

    cin>>n>>k;
    for(int i = 1; i <= n; i++) {
        cin>>a[i];
        f[i] = f[i - 1] + a[i];
    }

    for(int c = 1; c <= k; c++) {
        cht.init();
        cht.add(0, 0, 0);
        for(int i = 1; i <= n; i++) {
            // for(int j = 1; j <= i; j++) {
            //     if(maxi(dp[c][i], f[i] * f[n] - f[i] * f[i] + f[j - 1] * f[i] - f[j - 1] * f[n] + dp[c - 1][j - 1])) trace[c][i] = j;
            // }
            auto tmp = cht.query(f[i]);
            dp[c][i] = f[i] * f[n] - f[i] * f[i] + tmp.fi;
            trace[c][i] = tmp.se + 1;
            cht.add(f[i], -f[i] * f[n] + dp[c - 1][i], i);
        }
    }  

    ll ans = 0;
    int pos;
    vector<int> res;
    for(int i = 1; i <= n; i++) {
        if(maxi(ans, dp[k][i])) pos = i;
    }  
    for(int i = k; i >= 1; i--) {
        res.pb(pos);
        pos = trace[i][pos - 1];
    }
    reverse(all(res));
    cout<<ans<<"\n";
    for(auto i:res) cout<<i<<" ";
    return 0;
}

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