This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include "aliens.h"
using namespace std;
// <|°_°|>
const long long INFINI = (1LL << 60);
const int MAX_POINTS = (4001);
const int LOG = (40);
struct droite {
long long pente, cst;
int prix;
};
long long DP[MAX_POINTS][MAX_POINTS];
pair <long long, long long> Points[MAX_POINTS];
pair <int, int> Aliens[MAX_POINTS];
droite Deque[MAX_POINTS][MAX_POINTS];
int deb[MAX_POINTS];
int fin[MAX_POINTS];
int nbPoints = 0;
bool Compare(pair <int, int> a, pair <int, int> b) {
if (a.first != b.first)
return a.first < b.first;
return a.second > b.second;
}
long double Inter(droite a, droite b) {
if (a.pente == b.pente)
return INFINI;
if (a.pente < b.pente)
swap(a, b);
return (long double)(b.cst - a.cst) / (long double)(a.pente - b.pente);
}
void Insert(droite a, int id) {
while (fin[id] > deb[id] + 1 && Inter(Deque[fin[id] - 2][id], a) <= Inter(Deque[fin[id] - 2][id], Deque[fin[id] - 1][id]))
fin[id] --;
Deque[fin[id] ++][id] = a;
return;
}
pair <long long, int> GetMin(long long absc, int id) {
while (fin[id] > deb[id] + 1 && (long double)absc >= Inter(Deque[deb[id]][id], Deque[deb[id] + 1][id]))
deb[id] ++;
return {Deque[deb[id]][id].pente * absc + Deque[deb[id]][id].cst, Deque[deb[id]][id].prix};
}
// pair <long long, int> FindDP(long long lambda) {
// deb = 0, fin = 0;
// pair <long long, int> DP = {0LL, 0};
// Insert({- 2 * Points[0].first, Points[0].first * Points[0].first, 0});
// for (int i = 0; i < nbPoints; i ++)
// {
// DP = GetMin(Points[i].second);
// DP.first += Points[i].second * Points[i].second + lambda;
// DP.second ++;
// if (i + 1 < nbPoints)
// {
// long long d = max(0LL, Points[i].second - Points[i + 1].first);
// Insert({- 2 * Points[i + 1].first,
// Points[i + 1].first * Points[i + 1].first - d * d + DP.first, DP.second});
// }
// }
// return DP;
// }
void Treat(int noeud) {
for (int i = 1; i <= nbPoints; i ++)
{
DP[noeud][i] = GetMin(Points[noeud].second, i - 1).first + Points[noeud].second * Points[noeud].second;
}
if (noeud + 1 == nbPoints)
return;
for (int i = 1; i <= nbPoints; i ++)
{
long long d = max(0LL, Points[noeud].second - Points[noeud + 1].first);
Insert({- 2 * Points[noeud + 1].first, Points[noeud + 1].first * Points[noeud + 1].first - d * d + DP[noeud][i], 0}, i);
}
return;
}
void DPDebile() {
Insert({- 2 * Points[0].first, Points[0].first * Points[0].first, 0}, 0);
for (int i = 0; i < nbPoints; i ++)
{
Treat(i);
}
return;
}
long long take_photos(int nbAliens, int tailleMax, int nbPhotos, vector<int> Lignes, vector<int> Colonnes) {
tailleMax ++;
for (int i = 0; i < nbAliens; i ++)
{
if (Lignes[i] > Colonnes[i])
swap(Lignes[i], Colonnes[i]);
Aliens[i] = {Lignes[i], Colonnes[i] + 1};
}
sort(Aliens, Aliens + nbAliens, Compare);
for (int i = 0; i < nbAliens; i ++)
{
if (nbPoints == 0 || Aliens[i].second > (int)Points[nbPoints - 1].second)
Points[nbPoints ++] = Aliens[i];
}
DPDebile();
return DP[nbPoints - 1][min(nbPhotos, nbPoints)];
/*
long long lambda = -1;
long long ans = 0;
for (long long i = (1LL << LOG); i > 0; i /= 2)
{
pair <long long, int> DP = FindDP(lambda + i);
if (DP.second <= nbPhotos)
ans = DP.first - (lambda + i) * DP.second;
else
lambda += i;
}
return ans;*/
}
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