Submission #795617

#	Time	Username	Problem	Language	Result	Execution time	Memory
795617		winthemcut3	Split the sequence (APIO14_sequence)	C++14	100 / 100	612 ms	81620 KiB

sequence

#include <bits/stdc++.h>
#define FastIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define ll long long
#define PB push_back
#define ALL(v) (v).begin(), (v).end()
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define FORD(i, b, a) for (int i = (b), _a = (a); i >= _a; i--)
#define fi   first
#define se   second
#define BIT(x, i) (((x) >> (i)) & 1)
using namespace std;

/** END OF TEMPLATE **/

const int mxN = 1e5 + 5;
int n, k;
ll a[mxN];
struct line {
    ll a, b; int id;
    line() = default;
    line(ll a_, ll b_, int id_) : a(a_), b(b_), id(id_) {}
    ll f(ll x) {
        return a*x + b;
    }
};
struct CHTrick {
    deque<line> Y;
    int iter;
    CHTrick() = default;
    bool invalid(const line &l1, const line &l2, const line &l3) {
        return (l3.b - l1.b)*(l1.a - l2.a) <= (l2.b - l1.b)*(l1.a - l3.a);
    }
    void add(line L) {
        while(Y.size() >= 2 && invalid(Y[Y.size()-2], Y.back(), L))
            Y.pop_back();
        Y.push_back(L);
    }
    line getMax(ll x) {
        while(Y.size() >= 2 && Y[0].f(x) <= Y[1].f(x)) {
            Y.pop_front();
        }
        return Y.front();
    }
    void Clear() {
        while(Y.size()) Y.pop_back();
    }
};
ll dp[mxN];
int trace[205][mxN];
int main()
{
    FastIO;
    //freopen(".inp", "r", stdin);
    //freopen(".out", "w", stdout);
    cin >> n >> k;
    FOR(i, 1, n) cin >> a[i], a[i] += a[i-1];
    CHTrick CH;

    CH.iter = 0;
    FOR(i, 1, k) {
        CH.Clear();
        CH.add(line(0, 0, 0));
        FOR(j, 1, n) {
            ll tmp = dp[j];
            line L = CH.getMax(a[j]);
            dp[j] = L.f(a[j]);
            trace[i][j] = L.id;
            CH.add(line(a[j], -a[j]*a[j] + tmp, j));
        }
    }
    cout << dp[n] << '\n';
    int id = trace[k][n];
    while(k--) {
        cout << id << ' ';
        id = trace[k][id];
    }
    return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

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