Problem: Example

Input

100 1 0
50 100


Output

14.57738

Solution (in CPP):

Solution:
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
using namespace std;
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 1000000007;
typedef long double ld;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ld, ld> LDP;
typedef pair<ll, ll> LP;
#define fr first
#define sc second

ld p[10], h[10];
ld d;
ld calc(ld vx,ld dd) {
	return sqrt(dd*dd / (4.0*vx*vx) + vx * vx);
}
void solve() {
	cout << fixed << setprecision(5);
	int n, b;
	cin >> d >> n >> b;
	rep(i, n) {
		cin >> p[i] >> h[i];
	}
	ld ans = INF;
	rep(i, b+ 1) {
		ld dd = d / (i + 1);
		vector<vector<int>> v(i + 1);
		rep(j, n) {
			int u = (int)(p[j] / dd+eps);
			v[u].push_back(j);
		}
		ld vx = sqrt(dd / 2.0);
		bool f = true;
		rep(j, i + 1) {
			ld le = j * dd;
			rep(k, v[j].size()) {
				int id = v[j][k];
				ld hei = (p[id]-le) * (dd - (p[id]-le)) / (2.0 * vx*vx);
				if (hei < h[id]) {
					f = false;
				}
			}
		}
		if (f) {
			ans = min(ans, calc(vx,dd));
			//cout << calc(vx, dd) << endl;
		}
		else {
			rep(j, i + 1) {
				ld le = j * dd;
				rep(k, v[j].size()) {
					int id = v[j][k];
					ld z = sqrt((p[id] - le)*(dd - p[id] + le) / (2.0*h[id]));
					vx = min(vx, z);
				}
			}
			//cout << vx << endl;
			ans = min(ans, calc(vx,dd));
			//cout << i << " " << calc(vx, dd) << endl;
		}
	}
	cout << ans << endl;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	solve();
	//stop
	return 0;
}