标签:
Mean:
略
analyse:
把n个矩形的点输入多边形寻找最小覆盖面积矩形的模版代码中就OK,网上套的模板。
Time complexity: O(n)
Source code:
/* * this code is made by crazyacking * Verdict: Accepted * Submission Date: 2015-05-31-23.18 * Time: 0MS * Memory: 137KB */ #include <queue> #include <cstdio> #include <set> #include <string> #include <stack> #include <cmath> #include <climits> #include <map> #include <cstdlib> #include <iostream> #include <vector> #include <algorithm> #include <cstring> #define LL long long #define ULL unsigned long long using namespace std; const double eps = 1e-8; const int N = 4004; int sign(double d) { return d < -eps ? -1 : (d > eps); } struct point { double 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; } void read(){ scanf("%lf%lf", &x, &y); } }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); } //st1-->ed1叉乘st2-->ed2的值 double 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); } double 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); } //多边形类 struct poly { static const int N = 50005; //点数的最大值 point ps[N+5]; //逆时针存储多边形的点,[0,pn-1]存储点 int pn; //点数 poly() { pn = 0; } //加进一个点 void push(point tp) { ps[pn++] = tp; } //第k个位置 int trim(int k) { return (k+pn)%pn; } void clear(){ pn = 0; } }; //返回含有n个点的点集ps的凸包 poly graham(point* ps, int n) { std::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; //注意要赋值给tmp! 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; } //求点p到st->ed的垂足,列参数方程 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; } //next为直线(st,ed)上的点,返回next沿(st,ed)右手垂直方向延伸l之后的点 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; } //求含n个点的点集ps的最小面积矩形,并把结果放在ds(ds为一个长度是4的数组即可,ds中的点是逆时针的)中,并返回这个最小面积。 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; scanf("%d",&t); for(int Cas = 1; Cas <=t; ++Cas) { printf("Case #%d:\n",Cas); int num = 0; scanf("%d",&num); for(int i = 0; i < num ; ++i) { ps[i*4+0].read(); ps[i*4+1].read(); ps[i*4+2].read(); ps[i*4+3].read(); } struct point ds[4]; double ans = getMinAreaRect(ps,num*4,ds); printf("%.0lf\n",ans); } return 0; }
标签:
原文地址:http://www.cnblogs.com/crazyacking/p/4542955.html