Submission #752534

#	Time	Username	Problem	Language	Result	Execution time	Memory
752534		inventiontime	Split the sequence (APIO14_sequence)	C++17	71 / 100	115 ms	131072 KiB

sequence

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

#define int ll
#define endl '\n' //comment for interactive
#define fast_io ios::sync_with_stdio(0); cin.tie(0); cout.tie(0)

#define pb push_back
#define re resize
#define ff first
#define ss second

#define all(x) (x).begin(), (x).end()
#define all1(x) (x).begin()+1, (x).end()
#define loop(i, n) for(int i = 0; i < n; i++)
#define loop1(i, n) for(int i = 1; i <= n; i++)

#define print(x) cout << #x << ": " << x << endl << flush

typedef long long ll;
typedef vector<int> vi;
typedef array<int, 2> ii;
typedef array<int, 3> ti;
typedef vector<ii> vii;
typedef vector<ti> vti;
typedef vector<vi> vvi;
typedef priority_queue<int> pq;

template<class T> bool ckmin(T&a, T b) { bool B = a > b; a = min(a, b); return B; }
template<class T> bool ckmax(T&a, T b) { bool B = a < b; a = max(a, b); return B; }

const int inf = 1e17;

ii dp[100'005][205];

struct line {
    int m, c, id;
    int eval(int x) { return m*x + c; }
};

double isect(line a, line b) {
    assert(b.m != a.m);
    return (double) (a.c - b.c) / (b.m - a.m);
}

void solve() {
    
    int n, k; cin >> n >> k;
    k++;
    vi a(n+1);
    loop1(i, n) cin >> a[i];
    vi pref(n+1);
    loop1(i, n)
        pref[i] = pref[i-1] + a[i];
    
    deque<line> dq[k+1];
    dq[0].pb({0, 0, 0});
    loop(i, k+1) dp[0][i] = {0, 0};
    loop1(i, n) for(int j = k; j >= 1; j--) if(!dq[j-1].empty()) {
        // query
        while(dq[j-1].size() >= 2) {
            line a = dq[j-1][0];
            line b = dq[j-1][1];
            if(a.eval(pref[i]) < b.eval(pref[i]))
                dq[j-1].pop_front();
            else break;
        }
        dp[i][j] = {dq[j-1].front().eval(pref[i]), dq[j-1].front().id};
        // update
        line nl = {pref[i], dp[i][j][0] - pref[i] * pref[i], i};
        while(!dq[j].empty()) {
            if(dq[j].back().m == nl.m)
                dq[j].pop_back();
            else break;
        }
        while(dq[j].size() >= 2) {
            line a = dq[j][dq[j].size()-1];
            line b = dq[j][dq[j].size()-2];
            if(isect(nl, a) <= isect(nl, b))
                dq[j].pop_back();
            else break;
        }
        dq[j].pb(nl);
    }

    cout << dp[n][k][0] << endl;
    int x = n;
    int l = k;
    while(l > 1) {
        x = dp[x][l][1];
        l--;
        cout << x << " ";
    }
    cout << endl;

}

signed main() {

    fast_io;

    int t = 1; //cin >> t;
    while(t--)
        solve();

    return 0;

}

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