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Submission #592555

# Submission time Handle Problem Language Result Execution time Memory
592555 2022-07-09T09:56:38 Z errorgorn Nicelines (RMI20_nicelines) C++17
97.1996 / 100
 27 ms 1352 KB 
#include "nice_lines.h"
 
#include <bits/stdc++.h>
using namespace std;
 
#define int long long
#define ii pair<int,int>
#define fi first
#define se second
#define endl '\n'
 
#define puf push_front
#define pof pop_front
#define pub push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
 
#define rep(x,s,e) for (int x=(s)-((s)>(e));x!=(e)-((s)>(e));((s)<(e))?x++:x--)
#define all(x) (x).begin(),(x).end()
#define sz(x) (int) (x).size()
 
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
 
#define double long double
 
struct line{
	double a,b; //ensure that a^2+b^2=1, i.e. norm vec
	double r;
	
	line(double A,double B){
		double g=sqrtl(A*A+1);
		a=-A/g,b=1.0/g;
		r=B/g;
	}
	
	double dist(double x,double y){
		return fabsl(a*x+b*y-r);
	}
};
vector<line> ans;
 
const double Y=0.420177013;
 
vector<pair<double,int>> v;
map<pair<double,double>,double> memo;

double Query(double X,double Y){
	if (!memo.count({X,Y})) memo[{X,Y}]=query(X,Y);
	return memo[{X,Y}];
}

double grad(double X){
	return (Query(X+1e-10,Y)-Query(X,Y))/1e-10;
}

double grad2(double X){
	return (Query(X,Y+1e-7)-Query(X,Y))/1e-7;
}

vector<signed> ansA,ansB;

void rec(double l,double r,double gl,double gr){
	if (gr-gl<2.1 && r-l<100){
		double g=grad2(r)-grad2(l);
		//cout<<l<<" "<<r<<" "<<g<<endl;
		
		double best=1e9;
		int idx=-1e9;
		for (auto [a,b]:v){
			if (fabsl(a-g)<best){
				best=fabsl(a-g);
				idx=b;
			}
		}
		
		ansA.pub(idx);
		
		double L=l,R=r;
		double ql=Query(L,Y);
		double qr=Query(R,Y);
		while (abs(idx)*(r-l)>0.4){
			double m=(r+l)/2,qm=query(m,Y);
			
			if (fabsl((qm-ql)/(m-L)-gl)<fabsl((qr-qm)/(R-m)-gr)) l=m;
			else r=m;
		}
		
		ansB.pub(roundl(Y-l*idx));
		ans.pub({ansA.back(),ansB.back()});
	}
	else{
		double m=(l+r)/2;
		double g=grad(m);
		if (fabsl(gl-g)>1e-2) rec(l,m,gl,g);
		if (fabsl(gr-g)>1e-2) rec(m,r,g,gr);
	}
}

void solve(signed subtask_id, signed N) {
	cout<<fixed<<setprecision(12);
	
	for (int x=1;x<=10000;x++){
		v.pub({-2.0/sqrtl(1+x*x),x});
		v.pub({2.0/sqrtl(1+x*x),-x});
	}
	
	rec(-10100,10100,grad(-10100),grad(10100));
	
	if (sz(ansA)!=N){
		double y=query(0,-10000);
		for (auto it:ans) y-=it.dist(0,-10000);
		ansA.pub(0);
		ansB.pub(roundl(y-10000));
	}
	
	the_lines_are(ansA,ansB);
}

Compilation message

nicelines.cpp: In function 'void rec(long double, long double, long double, long double)':
nicelines.cpp:90:21: warning: narrowing conversion of 'ansA.std::vector<int>::back()' from '__gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type' {aka 'int'} to 'long double' [-Wnarrowing]
   90 |   ans.pub({ansA.back(),ansB.back()});
      |            ~~~~~~~~~^~
nicelines.cpp:90:33: warning: narrowing conversion of 'ansB.std::vector<int>::back()' from '__gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type' {aka 'int'} to 'long double' [-Wnarrowing]
   90 |   ans.pub({ansA.back(),ansB.back()});
      |                        ~~~~~~~~~^~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1352 KB Output is correct
2 Correct 1 ms 1352 KB Output is correct
3 Correct 1 ms 1352 KB Output is correct
4 Correct 2 ms 1352 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1352 KB Output is correct
2 Correct 2 ms 1352 KB Output is correct
3 Correct 2 ms 1352 KB Output is correct
4 Correct 2 ms 1352 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 1352 KB Output is correct
2 Correct 2 ms 1352 KB Output is correct
3 Correct 2 ms 1352 KB Output is correct
4 Correct 2 ms 1352 KB Output is correct

Subtask #4
18.2628047519 / 19.0

# Verdict Execution time Memory Grader output
1 Partially correct 20 ms 1352 KB Output is partially correct
2 Partially correct 17 ms 1352 KB Output is partially correct
3 Partially correct 15 ms 1352 KB Output is partially correct
4 Partially correct 15 ms 1352 KB Output is partially correct

Subtask #5
22.8389664522 / 23.0

# Verdict Execution time Memory Grader output
1 Partially correct 7 ms 1352 KB Output is partially correct
2 Partially correct 9 ms 1352 KB Output is partially correct
3 Partially correct 10 ms 1352 KB Output is partially correct
4 Partially correct 7 ms 1352 KB Output is partially correct

Subtask #6
25.0977912075 / 27.0

# Verdict Execution time Memory Grader output
1 Partially correct 20 ms 1352 KB Output is partially correct
2 Partially correct 17 ms 1352 KB Output is partially correct
3 Partially correct 15 ms 1352 KB Output is partially correct
4 Partially correct 15 ms 1352 KB Output is partially correct
5 Partially correct 7 ms 1352 KB Output is partially correct
6 Partially correct 9 ms 1352 KB Output is partially correct
7 Partially correct 10 ms 1352 KB Output is partially correct
8 Partially correct 7 ms 1352 KB Output is partially correct
9 Partially correct 27 ms 1352 KB Output is partially correct
10 Partially correct 21 ms 1352 KB Output is partially correct
11 Partially correct 23 ms 1352 KB Output is partially correct
12 Partially correct 21 ms 1352 KB Output is partially correct