uva 1473 - Dome of Circus （几何 + 二分)

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;
const int maxn = 10005;
const double inf = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;

struct Point {
double x, y;
Point (double x = 0, double y = 0): x(x), y(y) {}
bool operator < (const Point& u) const {
if (fabs(x - u.x) > eps)
return x > u.x;
return y > u.y;
}
}p[maxn];

double slope(Point a, Point b) {
if (fabs(a.x - b.x) < eps)
return 0;
return (a.y - b.y) / (a.x - b.y);
}

int N, M;

void init () {
double x, y, z;
for (int i = 0; i < N; i++) {
scanf("%lf%lf%lf", &x, &y, &z);
p[i].x = sqrt(x * x + y * y);
p[i].y = z;
}
sort(p, p + N);

/*
M = 0;
for (int i = 1; i < N; i++) {
if (p[i].y - p[M].y < eps)
continue;
while (M && slope(p[i], p[M-1]) < slope(p[M], p[M-1]))
M--;
p[++M] = p[i];
}
*/

/*
for (int i = 0; i <= M; i++)
printf("%lf %lf\n", p[i].x, p[i].y);
*/
}

double find (double r) {
double ret = 0;
for (int i = 0; i < N; i++)
ret = max(ret, p[i].y * r / (r - p[i].x));
return ret;
}

void solve () {
double l = p[0].x, r = 1e10;
while (fabs(r - l) > eps) {
double rl = l + (r - l) / 3;
double rr = r - (r - l) / 3;

double hl = find(rl);
double hr = find(rr);

if (rl * rl * hl > rr * rr * hr)
l = rl;
else
r = rr;
}
printf("%lf %lf\n", find(l), l);
}

int main () {
while (scanf("%d", &N) == 1) {
init ();
solve ();
}
return 0;
}