Submission #225885

#	Time	Username	Problem	Language	Result	Execution time	Memory
225885		VEGAnn	Aliens (IOI16_aliens)	C++14	100 / 100	437 ms	14048 KiB

aliens

#include <bits/stdc++.h>
#include "aliens.h"
#define sz(x) ((int)x.size())
#define pii pair<int, int>
#define MP make_pair
#define PB push_back
#define ft first
#define sd second
#define all(x) x.begin(),x.end()
using namespace std;
typedef long long ll;
typedef long double ld;
const int N = 1000100;
const int K = 110;
const ll OO = 1e18;
const ld E = 1e-9;
vector<pii> vc, seg;
int n, m, k, kl[N];
ld f[N], val[N];

ll sqr(ll x) { return x * x; }

struct line{
    ld k, b;
    int kol;

    line(): k(0), b(0), kol(0) {}

    line(ld _b, ld _k, int kl): k(_k), b(_b), kol(kl) {}
};

vector<line> cht;

ld get_cross_point(line a, line b){
    ld K = a.k - b.k;
    ld B = b.b - a.b;

    return B / K;
}

void insert_to_cht(line nw){
    while (sz(cht) > 1){
        ld fi = get_cross_point(nw, cht.back());
        ld se = get_cross_point(cht.back(), cht[sz(cht) - 2]);

        if (se + E < fi) break;

        cht.pop_back();
    }

    cht.PB(nw);
}

int calc(ld extra){
    f[0] = 0;

    cht.clear();

    cht.PB({f[0] + (ld)sqr(seg[0].ft), -2 * ld(seg[0].ft), 0});

    int ptr = 0;

    for (int i = 1; i <= n; i++){
        ptr = min(ptr, sz(cht) - 1);

        while (ptr + 1 < sz(cht) && get_cross_point(cht[ptr], cht[ptr + 1]) + E < ld(seg[i - 1].sd))
            ptr++;

        ld nw = cht[ptr].b + cht[ptr].k * ld(seg[i - 1].sd) + (ld)sqr(seg[i - 1].sd);

        f[i] = nw + extra;
        kl[i] = cht[ptr].kol + 1;

        if (i < n)
            insert_to_cht({f[i] + val[i] + (ld)sqr(seg[i].ft), -2 * ld(seg[i].ft), kl[i]});
    }

    return kl[n];
}

long long take_photos(int N, int M, int K, std::vector<int> r, std::vector<int> c) {
    n = N; m = M; k = K;

    for (int i = 0; i < n; i++)
        vc.PB(MP(min(r[i], c[i]), -max(r[i], c[i])));

    sort(all(vc));

    int lst = -vc[0].sd;

    seg.PB(vc[0]);
    seg.back().sd *= -1;
    seg.back().ft--;

    for (int i = 1; i < sz(vc); i++){
        pii cr = vc[i];

        if (-cr.sd <= lst) continue;

        lst = -cr.sd;

        seg.PB(cr);
        seg.back().sd *= -1;
        seg.back().ft--;
    }

    n = sz(seg);
    k = min(n, k);

    for (int j = 1; j <= n; j++)
        if (seg[j - 1].sd > seg[j].ft)
            val[j] = -sqr(seg[j - 1].sd - seg[j].ft);

    ld l1 = 0, r1 = ll(1e12);

    for (int it = 0; it < 60; it++){
        ld md = (l1 + r1) / 2.0;

        if (calc(md) <= k)
            r1 = md;
        else l1 = md;
    }

    calc(l1);

    return ll(round(f[n] - l1 * ld(k)));
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40