// moreflags=grader.cpp
// {}
#include "aliens.h"
// 15
#include<algorithm>
#include<cmath>
#include<cstdint>
#include<climits>
#include<cfloat>
#if not LOCAL
#define NDEBUG
#endif
#include<cassert>
long long take_photos(int n, int m, int numPhoto, std::vector<int> r, std::vector<int> c) {
std::vector<std::pair<int, int>> points(r.size());
for(int index=0; index<(int)r.size(); ++index)
points[index]=std::minmax({r[index], c[index]});
std::sort(begin(points), end(points),
[&](auto first, auto sec){return first.first!=sec.first ? first.first<sec.first: first.second>sec.second;
});
{ // keep only extreme points
auto out=points.begin()+1;
std::for_each(out, points.end(),[&](auto it){
assert(it.first>=out[-1].first);
if(it.second>out[-1].second){
assert(it.first>out[-1].first);
*out++=it;
}
});
points.erase(out, points.end());
}
r.clear(); c.clear(); n=-1;
auto const square=[&](int it)->int64_t{return (int64_t)it*it;};
auto const check=[&](double slope)->std::pair<int64_t, int>{
std::vector<std::pair<double, int>> value(points.size()+1);
value[0]={0, 0};
for(int pos=1; pos<=(int)points.size(); ++pos){
auto& cur=value[pos];
cur={DBL_MAX, 0};
for(int last=0; last<pos; ++last){
cur=std::min(cur, std::make_pair(
value[last].first
+(double)square(points[pos-1].second-points[last].first+1)
-(double)square(last==0 ? 0: std::max(0, points[last-1].second-points[last].first+1))
+slope
, value[last].second+1));
}
}
auto const [result, resultf]=value[points.size()];
return {(int64_t)std::round(result-resultf*slope), resultf};
};
// the numPhoto>=(int)points.size() case can be special-handled
double slope1=0;
auto [v1, nf1]=check(slope1);
assert(nf1>=(int)points.size());
nf1=std::max(numPhoto, nf1);
double slope2; int64_t v2; int nf2;
for(slope2=1;; slope2*=2){
std::tie(v2, nf2)=check(slope2);
if(nf2<=numPhoto) break;
}
while(true){
assert(nf2<=numPhoto); assert(numPhoto<=nf1);
if(nf1==numPhoto and nf2==numPhoto){
assert(v1==v2);
return v1;
}
int64_t const lower=(int64_t)std::ceil(
std::max(
(double)v1+slope1*(nf1-numPhoto),
(double)v2+slope2*(nf2-numPhoto)
)-1e-12);
assert(nf1>nf2);
int64_t const upper=(v1*(numPhoto-nf2)+v2*(nf1-numPhoto))/(nf1-nf2);
assert(upper>=0);
assert(lower<=upper);
if(lower==upper) return lower;
assert(nf2<numPhoto); assert(numPhoto<nf1);
auto const [v3, nf3]=check(slope2);
(nf3<=numPhoto ? std::tie(v1, nf1): std::tie(v2, nf2))=std::pair(v3, nf3);
}
}
