OJ-Problems-Source/HDOJ/5251_autoAC.cpp
2016-09-13 04:52:40 +08:00

174 lines
4.9 KiB
C++

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<math.h>
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
typedef double typev;
const double eps = 1e-8;
const int N = 50005;
int sign(double d){
return d < -eps ? -1 : (d > eps);
}
struct point{
typev x, y;
point operator-(point d){
point dd;
dd.x = this->x - d.x;
dd.y = this->y - d.y;
return dd;
}
point operator+(point d){
point dd;
dd.x = this->x + d.x;
dd.y = this->y + d.y;
return dd;
}
}ps[N];
//int n, cn;
double dist(point d1, point d2){
return sqrt(pow(d1.x - d2.x, 2.0) + pow(d1.y - d2.y, 2.0));
}
double dist2(point d1, point d2){
return pow(d1.x - d2.x, 2.0) + pow(d1.y - d2.y, 2.0);
}
bool cmp(point d1, point d2){
return d1.y < d2.y || (d1.y == d2.y && d1.x < d2.x);
}
typev xmul(point st1, point ed1, point st2, point ed2){
return (ed1.x - st1.x) * (ed2.y - st2.y) - (ed1.y - st1.y) * (ed2.x - st2.x);
}
typev dmul(point st1, point ed1, point st2, point ed2){
return (ed1.x - st1.x) * (ed2.x - st2.x) + (ed1.y - st1.y) * (ed2.y - st2.y);
}
struct poly{
static const int N = 50005;
point ps[N+5];
int pn;
poly() { pn = 0; }
void push(point tp){
ps[pn++] = tp;
}
int trim(int k){
return (k+pn)%pn;
}
void clear(){ pn = 0; }
};
poly graham(point* ps, int n){
sort(ps, ps + n, cmp);
poly ans;
if(n <= 2){
for(int i = 0; i < n; i++){
ans.push(ps[i]);
}
return ans;
}
ans.push(ps[0]);
ans.push(ps[1]);
point* tps = ans.ps;
int top = -1;
tps[++top] = ps[0];
tps[++top] = ps[1];
for(int i = 2; i < n; i++){
while(top > 0 && xmul(tps[top - 1], tps[top], tps[top - 1], ps[i]) <= 0) top--;
tps[++top] = ps[i];
}
int tmp = top;
for(int i = n - 2; i >= 0; i--){
while(top > tmp && xmul(tps[top - 1], tps[top], tps[top - 1], ps[i]) <= 0) top--;
tps[++top] = ps[i];
}
ans.pn = top;
return ans;
}
point getRoot(point p, point st, point ed){
point ans;
double u=((ed.x-st.x)*(ed.x-st.x)+(ed.y-st.y)*(ed.y-st.y));
u = ((ed.x-st.x)*(ed.x-p.x)+(ed.y-st.y)*(ed.y-p.y))/u;
ans.x = u*st.x+(1-u)*ed.x;
ans.y = u*st.y+(1-u)*ed.y;
return ans;
}
point change(point st, point ed, point next, double l){
point dd;
dd.x = -(ed - st).y;
dd.y = (ed - st).x;
double len = sqrt(dd.x * dd.x + dd.y * dd.y);
dd.x /= len, dd.y /= len;
dd.x *= l, dd.y *= l;
dd = dd + next;
return dd;
}
double getMinAreaRect(point* ps, int n, point* ds){
int cn, i;
double ans;
point* con;
poly tpoly = graham(ps, n);
con = tpoly.ps;
cn = tpoly.pn;
if(cn <= 2){
ds[0] = con[0]; ds[1] = con[1];
ds[2] = con[1]; ds[3] = con[0];
ans=0;
}else{
int l, r, u;
double tmp, len;
con[cn] = con[0];
ans = 1e40;
l = i = 0;
while(dmul(con[i], con[i+1], con[i], con[l])
>= dmul(con[i], con[i+1], con[i], con[(l-1+cn)%cn])){
l = (l-1+cn)%cn;
}
for(r=u=i = 0; i < cn; i++){
while(xmul(con[i], con[i+1], con[i], con[u])
<= xmul(con[i], con[i+1], con[i], con[(u+1)%cn])){
u = (u+1)%cn;
}
while(dmul(con[i], con[i+1], con[i], con[r])
<= dmul(con[i], con[i+1], con[i], con[(r+1)%cn])){
r = (r+1)%cn;
}
while(dmul(con[i], con[i+1], con[i], con[l])
>= dmul(con[i], con[i+1], con[i], con[(l+1)%cn])){
l = (l+1)%cn;
}
tmp = dmul(con[i], con[i+1], con[i], con[r]) - dmul(con[i], con[i+1], con[i], con[l]);
tmp *= xmul(con[i], con[i+1], con[i], con[u]);
tmp /= dist2(con[i], con[i+1]);
len = xmul(con[i], con[i+1], con[i], con[u])/dist(con[i], con[i+1]);
if(sign(tmp - ans) < 0){
ans = tmp;
ds[0] = getRoot(con[l], con[i], con[i+1]);
ds[1] = getRoot(con[r], con[i+1], con[i]);
ds[2] = change(con[i], con[i+1], ds[1], len);
ds[3] = change(con[i], con[i+1], ds[0], len);
}
}
}
return ans+eps;
}
int main ()
{
int t ,n ,i ,NN ,cas = 1;
point ds[10];
scanf("%d" ,&t);
while(t--)
{
scanf("%d" ,&NN);
int n = 0;
for(i = 1 ;i <= NN ;i ++)
{
for(int j = 1 ;j <= 4 ;j ++)
{
scanf("%lf %lf" ,&ps[n].x ,&ps[n].y);
n++;
}
}
double ans = getMinAreaRect(ps ,n ,ds);
printf("Case #%d:\n" ,cas ++);
printf("%.0lf\n" ,ans);
}
return 0;
}