#include <bits/stdc++.h>
using namespace std;
#define ld long double
const int mxN=5e4;
int n, x[mxN], y[mxN];
vector<array<ld, 2>> convexHull(vector<array<ld, 2>> l, ld xl, ld xr) {
sort(l.begin(), l.end(), greater<array<ld, 2>>());
vector<array<ld, 2>> v, p;
for(array<ld, 2> li : l) {
while(v.size()>1&&(v.back()[1]-v[v.size()-2][1])/(v[v.size()-2][0]-v.back()[0])>(li[1]-v.back()[1])/(v.back()[0]-li[0]))
v.pop_back();
v.push_back(li);
}
int jl=0;
while(jl+1<v.size()&&v[jl+1][0]*xl+v[jl+1][1]<v[jl][0]*xl+v[jl][1])
++jl;
p.push_back({xl, v[jl][0]*xl+v[jl][1]});
int jr=jl;
while(jr+1<v.size()&&v[jr+1][0]*xr+v[jr+1][1]<v[jr][0]*xr+v[jr][1])
++jr;
for(int i=jl; i+1<=jr; ++i) {
ld x=(v[i+1][1]-v[i][1])/(v[i][0]-v[i+1][0]), y=v[i][0]*x+v[i][1];
p.push_back({x, y});
}
p.push_back({xr, v[jr][0]*xr+v[jr][1]});
return p;
}
ld gy(array<ld, 2> p1, array<ld, 2> p2, ld x) {
return p1[1]+(p2[1]-p1[1])/(p2[0]-p1[0])*(x-p1[0]);
}
array<ld, 2> segmentIntersection(array<ld, 2> a, array<ld, 2> b, array<ld, 2> c, array<ld, 2> d) {
ld x=(gy(c, d, 0)-gy(a, b, 0))/((a[1]-b[1])/(a[0]-b[0])-(c[1]-d[1])/(c[0]-d[0]));
return {x, gy(a, b, x)};
}
vector<array<ld, 2>> halfplaneIntersection(vector<array<array<ld, 2>, 2>> a, ld xl, ld xr) {
if(xl>xr)
return vector<array<ld, 2>>();
vector<array<ld, 2>> tl, bl;
for(array<array<ld, 2>, 2> ai : a) {
if(ai[0][0]>ai[1][0]) {
tl.push_back({(ai[1][1]-ai[0][1])/(ai[1][0]-ai[0][0])});
tl.back()[1]=gy(ai[0], ai[1], 0);
} else {
ai[0][1]=-ai[0][1];
ai[1][1]=-ai[1][1];
bl.push_back({(ai[1][1]-ai[0][1])/(ai[1][0]-ai[0][0])});
bl.back()[1]=gy(ai[0], ai[1], 0);
}
}
/*
cout << "top lines" << endl;
for(array<ld, 2> ai : tl)
cout << ai[0] << " " << ai[1] << endl;
cout << "bottom lines" << endl;
for(array<ld, 2> ai : bl)
cout << ai[0] << " " << ai[1] << endl;
//*/
vector<array<ld, 2>> tp=convexHull(tl, xl, xr), bp=convexHull(bl, xl, xr);
for(array<ld, 2> &p : bp)
p[1]=-p[1];
/*
cout << "top points" << endl;
for(array<ld, 2> pi : tp)
cout << pi[0] << " " << pi[1] << endl;
cout << "bottom points" << endl;
for(array<ld, 2> pi : bp)
cout << pi[0] << " " << pi[1] << endl;
//*/
vector<array<ld, 2>> tp2, bp2;
int i1=0, i2=0;
if(tp[0][1]<bp[0][1]) {
i1=i2=1;
while(i1<tp.size()&&i2<bp.size()) {
if(tp[i1][0]<bp[i2][0]) {
if(tp[i1][1]>gy(bp[i2-1], bp[i2], tp[i1][0])) {
tp2.push_back(segmentIntersection(tp[i1-1], tp[i1], bp[i2-1], bp[i2]));
break;
}
++i1;
} else {
if(bp[i2][1]<gy(tp[i1-1], tp[i1], bp[i2][0])) {
tp2.push_back(segmentIntersection(tp[i1-1], tp[i1], bp[i2-1], bp[i2]));
//cout << "fi" << endl;
//cout << tp2.back()[0] << " " << tp2.back()[1] << endl;
break;
}
++i2;
}
}
}
if(i1>=tp.size()||i2>=bp.size())
return vector<array<ld, 2>>();
if(tp.back()[1]<bp.back()[1]) {
while(1) {
if(tp[i1][0]<bp[i2][0]) {
if(tp[i1][1]<gy(bp[i2-1], bp[i2], tp[i1][0])) {
tp2.push_back(segmentIntersection(tp[i1-1], tp[i1], bp[i2-1], bp[i2]));
break;
}
tp2.push_back(tp[i1++]);
} else {
if(bp[i2][1]>gy(tp[i1-1], tp[i1], bp[i2][0])) {
tp2.push_back(segmentIntersection(tp[i1-1], tp[i1], bp[i2-1], bp[i2]));
break;
}
bp2.push_back(bp[i2++]);
}
}
} else {
while(i1<tp.size())
tp2.push_back(tp[i1++]);
while(i2<bp.size())
bp2.push_back(bp[i2++]);
}
reverse(tp2.begin(), tp2.end());
tp2.insert(tp2.end(), bp2.begin(), bp2.end());
return tp2;
}
pair<ld, int> findOpt(vector<array<ld, 2>> &p, int m1, int l2, int r2) {
pair<ld, int> q{0, l2};
for(int i=l2; i<=r2; ++i)
q=max(make_pair(hypot(p[i][0]-p[m1][0], p[i][1]-p[m1][1]), i), q);
return q;
}
ld dc(vector<array<ld, 2>> &p, int l1, int r1, int l2, int r2) {
if(l1>r1)
return 0;
int m1=(l1+r1)/2;
pair<ld, int> q=findOpt(p, m1, l2, r2);
return max({q.first, dc(p, l1, m1-1, l2, q.second), dc(p, m1+1, r1, q.second, r2)});
}
bool chk(ld r) {
vector<array<array<ld, 2>, 2>> a;
ld xl=-1e8, xr=1e8;
for(int i=0; i<n; ++i) {
int j=(i+1)%n;
if(x[i]==x[j]) {
if(y[i]>y[j])
xl=max(x[i]+r, xl);
else
xr=min(x[i]-r, xr);
} else {
ld sm=hypot(x[j]-x[i], y[j]-y[i]), tx=-(y[j]-y[i])*r/sm, ty=(x[j]-x[i])*r/sm;
a.push_back({{{x[i]+tx, y[i]+ty}, {x[j]+tx, y[j]+ty}}});
}
}
vector<array<ld, 2>> p=halfplaneIntersection(a, xl, xr);
/*
cout << "new poly" << endl;
for(array<ld, 2> a : p)
cout << a[0] << " " << a[1] << endl;
//*/
if(!p.size())
return 0;
pair<ld, int> q=findOpt(p, 0, 0, p.size()-1);
return dc(p, 0, q.second, q.second, p.size()-1)>2*r;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n;
for(int i=0; i<n; ++i)
cin >> x[i] >> y[i];
//cout << chk(0.5);
//return 0;
ld lb=0, rb=1e7;
while(rb-lb>1e-4) {
ld mb=(lb+rb)/2;
//cout << "chk " << mb << endl;
if(chk(mb))
lb=mb;
else
rb=mb;
}
cout << fixed << setprecision(3) << lb;
}
Compilation message
twocircles.cpp: In function 'std::vector<std::array<long double, 2> > convexHull(std::vector<std::array<long double, 2> >, long double, long double)':
twocircles.cpp:18:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(jl+1<v.size()&&v[jl+1][0]*xl+v[jl+1][1]<v[jl][0]*xl+v[jl][1])
~~~~^~~~~~~~~
twocircles.cpp:22:12: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(jr+1<v.size()&&v[jr+1][0]*xr+v[jr+1][1]<v[jr][0]*xr+v[jr][1])
~~~~^~~~~~~~~
twocircles.cpp: In function 'std::vector<std::array<long double, 2> > halfplaneIntersection(std::vector<std::array<std::array<long double, 2>, 2> >, long double, long double)':
twocircles.cpp:79:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(i1<tp.size()&&i2<bp.size()) {
~~^~~~~~~~~~
twocircles.cpp:79:25: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(i1<tp.size()&&i2<bp.size()) {
~~^~~~~~~~~~
twocircles.cpp:97:7: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if(i1>=tp.size()||i2>=bp.size())
~~^~~~~~~~~~~
twocircles.cpp:97:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if(i1>=tp.size()||i2>=bp.size())
~~^~~~~~~~~~~
twocircles.cpp:116:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(i1<tp.size())
~~^~~~~~~~~~
twocircles.cpp:118:11: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while(i2<bp.size())
~~^~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
380 KB |
Output is correct |
| 3 |
Correct |
4 ms |
376 KB |
Output is correct |
| 4 |
Correct |
4 ms |
376 KB |
Output is correct |
| 5 |
Correct |
40 ms |
1240 KB |
Output is correct |
| 6 |
Correct |
254 ms |
3408 KB |
Output is correct |
| 7 |
Correct |
152 ms |
3652 KB |
Output is correct |
| 8 |
Correct |
202 ms |
5172 KB |
Output is correct |
| 9 |
Correct |
568 ms |
8156 KB |
Output is correct |
| 10 |
Correct |
976 ms |
12232 KB |
Output is correct |
