Submission #222170

#	Time	Username	Problem	Language	Result	Execution time	Memory
222170		VEGAnn	새로운 문제 (COCI19_akvizna)	C++14	20 / 130	1600 ms	23764 KiB

Main

#include <bits/stdc++.h>
#define sz(x) ((int)x.size())
#define pii pair<int,int>
#define ft first
#define sd second
#define MP make_pair
#define all(x) x.begin(),x.end()
#define PB push_back
using namespace std;
typedef long long ll;
typedef long double ld;
const int N = 100100;
const ll OO = 1e18;
const ld E = 1e-9;
vector<int> vc;
pair<ld, int> f[N];
int n, k;

struct line{
    ld k, b;
    int bl;

    line(): k(0.0), b(0.0), bl(0) {}
    line(ld _k, ld _b, int i): k(_k), b(_b), bl(i) {}
};

deque<line> hull;

ld get_cross_point(line fi, line se){
    return (fi.b - se.b) / (se.k - fi.k);
}

void insert(line nw){
    if (sz(hull) == 0){
        hull.PB(nw);
        return;
    }

    while (sz(hull) > 1){
        ld pt1 = get_cross_point(nw, hull[1]);
        ld pt2 = get_cross_point(hull.back(), hull[0]);

        if (pt2 > pt1) break;

        hull.pop_front();
    }

    hull.push_front(nw);
}

bool check(ld extra){
    fill(f, f + n + 1, MP(-1.0, 0));

    f[n] = MP(0.0, 0);

    insert({-1.0 / ld(n), f[n].ft + 1.0, 0});

    for (int j = n - 1; j >= 0; j--){

        if (sz(hull)) {

            int l = 0, r = sz(hull) - 1;

            while (l < r) {
                int md = (l + r + 1) >> 1;

                assert(md > 0);

                if (get_cross_point(hull[md], hull[md - 1]) + E <= j)
                    l = md;
                else r = md - 1;
            }

            f[j] = MP(hull[l].b + hull[l].k * ld(j) + extra, hull[l].bl + 1);
        }

        // may be this should be after update f[i][j]
        if (f[j].ft >= -E)
            insert({-1.0 / ld(j), f[j].ft + 1.0, f[j].sd});
    }

    return (f[0].sd <= k);
}

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);

//    freopen("in.txt","r",stdin);

    cin >> n >> k;

    ld l = 0, r = ld(1e12);

    for (int it = 0; it < 100; it++){
        ld md = (l + r) / 2.0;

        if (check(-md))
            r = md;
        else l = md;

        if (f[0].sd == k){
            l = md;
            break;
        }
    }

    check(-l);

    assert(f[0].sd == k);

    cout << fixed << setprecision(10) << f[0].ft + l * ld(k);

    return 0;
}

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