#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include "aliens.h"
using namespace std;
// <|°_°|>
const long long INFINI = (1LL << 60);
const int MAX_POINTS = (100 * 1000);
const int LOG = (40);
struct droite {
long long pente, cst;
int prix;
};
pair <long long, long long> Points[MAX_POINTS];
pair <int, int> Aliens[MAX_POINTS];
droite Deque[MAX_POINTS];
int deb = 0, fin = 0;
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 long Inter(droite a, droite b) {
if (a.pente == b.pente)
return INFINI;
return (b.cst - a.cst + a.pente - b.pente - 1) / (a.pente - b.pente);
}
long long Eval(droite a, long long absc) {
return a.pente * absc + a.cst;
}
void Insert(droite a) {
while (fin > deb + 1 && Eval(a, Inter(Deque[fin - 2], Deque[fin - 1])) <= Eval(Deque[fin - 1], Inter(Deque[fin - 2], Deque[fin - 1])))
fin --;
Deque[fin ++] = a;
return;
}
pair <long long, int> GetMin(int absc) {
while (fin > deb + 1 && absc >= Inter(Deque[deb], Deque[deb + 1]))
deb ++;
return {Eval(Deque[deb], absc), Deque[deb].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;
}
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];
}
long long lambda = -1;
long long ans = INFINI;
for (long long i = (1LL << LOG); i > 0; i /= 2)
{
pair <long long, int> DP = FindDP(lambda + i);
if (DP.second <= nbPhotos)
ans = min(ans, DP.first - (lambda + i) * DP.second);
else
lambda += i;
}
return ans;
}
