Submission #165363

#	Time	Username	Problem	Language	Result	Execution time	Memory
165363		johutha	Aliens (IOI16_aliens)	C++14	100 / 100	296 ms	10740 KiB

aliens

#include "aliens.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>

#define int long long

using namespace std;

struct line
{
	int a, b, num;

	int getval(int x)
	{
		return a*x + b;
	}
};

struct convhull
{
	deque<line> hull;
	vector<line> all;

	bool bad(line newl)
	{
		if (hull.size() < 2) return false;
		line snlt = hull[hull.size() - 2];
		line last = hull.back();
		long double int1 = ((long double) (last.b - newl.b)) / ((long double)(newl.a - last.a));
		long double int2 = ((long double) (snlt.b - last.b)) / ((long double)(last.a - snlt.a));
		return  int1 <= int2;
	}

	void insert(int a, int b, int num)
	{
		line newl;
		newl.a = a;
		newl.b = b;
		newl.num = num;
		while (bad(newl)) hull.pop_back();
		hull.push_back(newl);
	}

	pair<int,int> query(int x)
	{
		if (hull.empty()) return {0, -1};
		while (hull.size() > 1 && hull[0].getval(x) >= hull[1].getval(x)) hull.pop_front();
		return {hull[0].getval(x), hull[0].num};
	}
};

struct dpstruct
{
	int n;
	int k;
	int m;
	vector<int> l;
	vector<int> r;

	pair<int,int> run(int c)
	{
		vector<int> dp(n + 1, 1e17);
		dp[0] = 0;

		vector<int> nr(n + 1, -1);
		nr[0] = 0;

		convhull hull;

		for (int i = 0; i < n; i++)
		{
			int ovlp = 0;
			if (i > 0) ovlp = max(0ll, r[i - 1] - l[i]);
			hull.insert(-2*l[i], dp[i] + l[i]*l[i] - ovlp*ovlp + c, i);
			auto q = hull.query(r[i]);
			dp[i + 1] = q.first + (r[i]*r[i]);
			nr[i + 1] = nr[q.second] + 1;
		}

		/*
		for (int i : dp) cerr << i << " ";
		cerr << "\n";
		for (int i : nr) cerr << i << " ";
		cerr << "\n";
		*/

		return {dp[n], nr[n]};
	}

	int calc()
	{
		k = min(k, n);
		int minb = -1;
		int maxb = m*m + 1;

		while (maxb - minb > 1)
		{
			int mid = (minb + maxb)/2;

			if (run(mid).second < k)
			{
				maxb = mid;
			}
			else
			{
				minb = mid;
			}
		}
		if (run(minb).second == k)
		{
			return run(minb).first - k*minb;
		}

		auto rmin = run(minb);
		auto rmax = run(maxb);

		int minres = rmin.first - rmin.second*minb;
		int maxres = rmax.first - rmax.second*maxb;

		int resdiff = (maxres - minres) / (rmin.second - rmax.second);

		/*
		cerr << minb << " " << rmin.first << " " << rmin.second << " " << minres << "\n";
		cerr << maxb << " " << rmax.first << " " << rmax.second << " " << maxres << "\n";

		cerr << resdiff << "\n";*/
		return minres + resdiff*(rmin.second - k);
	}
};


int take_photos(signed n, signed m, signed k, vector<signed> r, vector<signed> c)
{
    vector<pair<int,int>> prs;

	for (int i = 0; i < n; i++)
	{
		prs.emplace_back(min(r[i], c[i]), -max(r[i], c[i]));
	}

	sort(prs.begin(), prs.end());

	vector<int> nl;
	vector<int> nr;

	nl.push_back(prs[0].first);
	nr.push_back(-prs[0].second + 1);

	int last = -prs[0].second;

	for (int i = 1; i < n; i++)
	{
		prs[i].second = -prs[i].second;
		if (last < prs[i].second)
		{
			nl.push_back(prs[i].first);
			nr.push_back(prs[i].second + 1);
		}
		last = max(prs[i].second, last);
	}

	dpstruct dps;
	dps.n = nl.size();
	dps.k = k;
	dps.m = m;
	dps.l = nl;
	dps.r = nr;

	return dps.calc();
}


int take_photos_slow(signed n, signed m, signed k, vector<signed> r, vector<signed> c)
{
    vector<pair<int,int>> intervals;
    for (int i = 0; i < n; i++)
    {
        intervals.push_back({min(r[i], c[i]), -max(r[i], c[i])});
    }
    sort(intervals.begin(), intervals.end());
    vector<int> nl;
    vector<int> nr;
    int mmx = -1;
    for (int i = 0; i < n; i++)
    {
        if (-intervals[i].second > mmx)
        {
            nl.push_back(intervals[i].first);
            nr.push_back(-intervals[i].second);
            mmx = -intervals[i].second;
        }
    }
    int nn = nl.size();
    vector<vector<int>> dp(nn + 1, vector<int>(k + 1, 1e12));
    dp[0][0] = 0;
    for (int i = 1; i <= nn; i++)
    {
        for (int j = 1; j <= k; j++)
        {
            dp[i][j] = min(dp[i][j], dp[i][j - 1]);
            for (int q = 0; q < i; q++)
            {
                int ol = 0;
                if (q > 0 && nl[q] <= nr[q - 1])
                {
                    ol = nr[q - 1] - nl[q] + 1;
                    ol *= ol;
                }
                dp[i][j] = min(dp[i][j], dp[q][j - 1] + (nr[i - 1] - nl[q] + 1)*(nr[i - 1] - nl[q] + 1) - ol);
            }
        }
    }
    return dp[nn][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