Problem: Example

Input

100 1 0
50 100


Output

14.57738

Solution (in CPP):

Solution:
// g++ -std=c++11 a.cpp
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<unordered_map>
#include<utility>
#include<cmath>
#include<random>
#include<cstring>
#include<queue>
#include<stack>
#include<bitset>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#include<typeinfo>
#define loop(i,a,b) for(int i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define FOR(i,a) for(auto i:a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define show1d(v) rep(_,v.size())cout<<" "<<v[_];cout<<endl;
#define show2d(v) rep(_,v.size()){rep(__,v[_].size())cout<<" "<<v[_][__];cout<<endl;}cout<<endl;
using namespace std;
//kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
#define mt make_tuple
typedef tuple<int,int,int,int> tp;
typedef vector<tp> vt;
template<typename A,typename B>bool cmin(A &a,const B &b){return a>b?(a=b,true):false;}
template<typename A,typename B>bool cmax(A &a,const B &b){return a<b?(a=b,true):false;}
//template<class C>constexpr int size(const C &c){return (int)c.size();}
//template<class T,size_t N> constexpr int size(const T (&xs)[N])noexcept{return (int)N;}
const double PI=acos(-1);
const double EPS=1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 1e18+10 : 1e9+10;
int dx[]={0,1,0,-1,1,1,-1,-1};
int dy[]={1,0,-1,0,1,-1,1,-1};//RDLU

signed main(){
	int d,n,b;
	cin>>d>>n>>b;
	vd p(n),h(n);
	rep(i,n)cin>>p[i]>>h[i];
	double out=inf;
	loop(i,1,b+2){		
		
		double l=sqrt((double)d/i/2),r=1000000;
		while(r-l>EPS){
			double vy=(l+r)/2;
			double vx=(double)d/i/2/vy;
			double x=0;
			bool ok=true;
			int t=0;
			rep(j,i){
				double nx=x+(double)d/i;
				while(t!=n&&p[t]<nx){
					// cout<<t<<" "<<p[t]-x<<" "<<-0.5*(p[t]-x)*(p[t]-x)/vx/vx<<" "<<vy*(p[t]-x)/vx<<endl;
					double y=-0.5*(p[t]-x)*(p[t]-x)/vx/vx+vy*(p[t]-x)/vx;
					// cout<<vx<<" "<<vy<<" "<<y<<endl;
					if(y<h[t])ok=false;
					t++;
				}
				x=nx;
			}
			if(ok)r=vy;
			else l=vy;
		}
		double vy=l,vx=(double)d/i/2/vy;
		cmin(out,hypot(vx,vy));
	}	
	cout<<shosu(9)<<out<<endl;
}