POJ 2540 Hotter Colder(半平面交)
Description
Input
Output
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>
using namespace std; const int MAXN = ;
const double EPS = 1e-;
const double PI = acos(-1.0);//3.14159265358979323846 inline int sgn(double x) {
return (x > EPS) - (x < -EPS);
} struct Point {
double x, y, ag;
Point() {}
Point(double x, double y): x(x), y(y) {}
void read() {
scanf("%lf%lf", &x, &y);
}
bool operator == (const Point &rhs) const {
return sgn(x - rhs.x) == && sgn(y - rhs.y) == ;
}
bool operator < (const Point &rhs) const {
if(y != rhs.y) return y < rhs.y;
return x < rhs.x;
}
Point operator + (const Point &rhs) const {
return Point(x + rhs.x, y + rhs.y);
}
Point operator - (const Point &rhs) const {
return Point(x - rhs.x, y - rhs.y);
}
Point operator * (const int &b) const {
return Point(x * b, y * b);
}
Point operator / (const int &b) const {
return Point(x / b, y / b);
}
double length() const {
return sqrt(x * x + y * y);
}
Point unit() const {
return *this / length();
}
};
typedef Point Vector; double dist(const Point &a, const Point &b) {
return (a - b).length();
} double cross(const Point &a, const Point &b) {
return a.x * b.y - a.y * b.x;
}
//ret >= 0 means turn left
double cross(const Point &sp, const Point &ed, const Point &op) {
return sgn(cross(sp - op, ed - op));
} double area(const Point& a, const Point &b, const Point &c) {
return fabs(cross(a - c, b - c)) / ;
}
//counter-clockwise
Point rotate(const Point &p, double angle, const Point &o = Point(, )) {
Point t = p - o;
double x = t.x * cos(angle) - t.y * sin(angle);
double y = t.y * cos(angle) + t.x * sin(angle);
return Point(x, y) + o;
} struct Seg {
Point st, ed;
double ag;
Seg() {}
Seg(Point st, Point ed): st(st), ed(ed) {}
void read() {
st.read(); ed.read();
}
void makeAg() {
ag = atan2(ed.y - st.y, ed.x - st.x);
}
};
typedef Seg Line; void moveRight(Line &v, double r) {
double dx = v.ed.x - v.st.x, dy = v.ed.y - v.st.y;
dx = dx / dist(v.st, v.ed) * r;
dy = dy / dist(v.st, v.ed) * r;
v.st.x += dy; v.ed.x += dy;
v.st.y -= dx; v.ed.y -= dx;
} bool isOnSeg(const Seg &s, const Point &p) {
return (p == s.st || p == s.ed) ||
(((p.x - s.st.x) * (p.x - s.ed.x) < ||
(p.y - s.st.y) * (p.y - s.ed.y) < ) &&
sgn(cross(s.ed, p, s.st) == ));
} bool isIntersected(const Point &s1, const Point &e1, const Point &s2, const Point &e2) {
return (max(s1.x, e1.x) >= min(s2.x, e2.x)) &&
(max(s2.x, e2.x) >= min(s1.x, e1.x)) &&
(max(s1.y, e1.y) >= min(s2.y, e2.y)) &&
(max(s2.y, e2.y) >= min(s1.y, e1.y)) &&
(cross(s2, e1, s1) * cross(e1, e2, s1) >= ) &&
(cross(s1, e2, s2) * cross(e2, e1, s2) >= );
} bool isIntersected(const Seg &a, const Seg &b) {
return isIntersected(a.st, a.ed, b.st, b.ed);
} bool isParallel(const Seg &a, const Seg &b) {
return sgn(cross(a.ed - a.st, b.ed - b.st)) == ;
} //return Ax + By + C =0 's A, B, C
void Coefficient(const Line &L, double &A, double &B, double &C) {
A = L.ed.y - L.st.y;
B = L.st.x - L.ed.x;
C = L.ed.x * L.st.y - L.st.x * L.ed.y;
}
//point of intersection
Point operator * (const Line &a, const Line &b) {
double A1, B1, C1;
double A2, B2, C2;
Coefficient(a, A1, B1, C1);
Coefficient(b, A2, B2, C2);
Point I;
I.x = - (B2 * C1 - B1 * C2) / (A1 * B2 - A2 * B1);
I.y = (A2 * C1 - A1 * C2) / (A1 * B2 - A2 * B1);
return I;
} bool isEqual(const Line &a, const Line &b) {
double A1, B1, C1;
double A2, B2, C2;
Coefficient(a, A1, B1, C1);
Coefficient(b, A2, B2, C2);
return sgn(A1 * B2 - A2 * B1) == && sgn(A1 * C2 - A2 * C1) == && sgn(B1 * C2 - B2 * C1) == ;
} struct Poly {
int n;
Point p[MAXN];//p[n] = p[0]
void init(Point *pp, int nn) {
n = nn;
for(int i = ; i < n; ++i) p[i] = pp[i];
p[n] = p[];
}
double area() {
if(n < ) return ;
double s = p[].y * (p[n - ].x - p[].x);
for(int i = ; i < n; ++i)
s += p[i].y * (p[i - ].x - p[i + ].x);
return s / ;
}
}; void Graham_scan(Point *p, int n, int *stk, int &top) {//stk[0] = stk[top]
sort(p, p + n);
top = ;
stk[] = ; stk[] = ;
for(int i = ; i < n; ++i) {
while(top && cross(p[i], p[stk[top]], p[stk[top - ]]) >= ) --top;
stk[++top] = i;
}
int len = top;
stk[++top] = n - ;
for(int i = n - ; i >= ; --i) {
while(top != len && cross(p[i], p[stk[top]], p[stk[top - ]]) >= ) --top;
stk[++top] = i;
}
}
//use for half_planes_cross
bool cmpAg(const Line &a, const Line &b) {
if(sgn(a.ag - b.ag) == )
return sgn(cross(b.ed, a.st, b.st)) < ;
return a.ag < b.ag;
}
//clockwise, plane is on the right
bool half_planes_cross(Line *v, int vn, Poly &res, Line *deq) {
int i, n;
sort(v, v + vn, cmpAg);
for(i = n = ; i < vn; ++i) {
if(sgn(v[i].ag - v[i-].ag) == ) continue;
v[n++] = v[i];
}
int head = , tail = ;
deq[] = v[], deq[] = v[];
for(i = ; i < n; ++i) {
if(isParallel(deq[tail - ], deq[tail]) || isParallel(deq[head], deq[head + ]))
return false;
while(head < tail && sgn(cross(v[i].ed, deq[tail - ] * deq[tail], v[i].st)) > )
--tail;
while(head < tail && sgn(cross(v[i].ed, deq[head] * deq[head + ], v[i].st)) > )
++head;
deq[++tail] = v[i];
}
while(head < tail && sgn(cross(deq[head].ed, deq[tail - ] * deq[tail], deq[head].st)) > )
--tail;
while(head < tail && sgn(cross(deq[tail].ed, deq[head] * deq[head + ], deq[tail].st)) > )
++head;
if(tail <= head + ) return false;
res.n = ;
for(i = head; i < tail; ++i)
res.p[res.n++] = deq[i] * deq[i + ];
res.p[res.n++] = deq[head] * deq[tail];
res.n = unique(res.p, res.p + res.n) - res.p;
res.p[res.n] = res.p[];
return true;
} /*******************************************************************************************/ Poly poly;
Line line[MAXN], deq[MAXN];
char str[];
Point pre, cur;
int n; int main() {
line[n++] = Line(Point(, ), Point(, )); line[n - ].makeAg();
line[n++] = Line(Point(, ), Point(, )); line[n - ].makeAg();
line[n++] = Line(Point(, ), Point(, )); line[n - ].makeAg();
line[n++] = Line(Point(, ), Point(, )); line[n - ].makeAg();
pre = Point(, );
double x, y;
while(scanf("%lf%lf%s", &x, &y, str) != EOF) {
cur = Point(x, y);
Point mid = (cur + pre) / ;
if(strcmp(str, "Hotter")) {
Point st = rotate(pre, -PI/, mid);
Point ed = rotate(cur, -PI/, mid);
line[n++] = Line(st, ed); line[n - ].makeAg();
}
if(strcmp(str, "Colder")) {
Point st = rotate(pre, PI/, mid);
Point ed = rotate(cur, PI/, mid);
line[n++] = Line(st, ed); line[n - ].makeAg();
}
bool flag = half_planes_cross(line, n, poly, deq);
printf("%.2f\n", flag * (poly.area() + EPS));
pre = cur;
}
}
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