Google codejam 2010 Round 2 :: Grazing Google Goats

考试的时候只写了处理两个圆的，最后一刻写完的，交上去WA了。。后来才知道，要用long double

 

看了Google的题解，发现其方法确实很不错。Google提出了两种方法，都是O(n logn)的：

  1、通过inversion变换，转化成半平面求交的问题。inversion变换我以前确实没听说过，开了眼界了。。

  2、由于所有圆过公共点，把圆心按极角排序后，用一个栈维护以Q为原点的极坐标系中，在某个极角区间内最近的圆是哪个。

 

我实现了方法2，程序并不长，但写的时候感到有些纠结，幸好一次AC，要不还没法调……

 

/* * $File: d.cpp * $Date: Sun Jun 06 17:10:33 2010 +0800 */#include <cstdio>#include <cmath>#include <algorithm>using namespace std;namespace Solve{const int NPOINT_MAX = 5005;typedef long double Real_t;struct Point{int x, y;inline int mod()const{return x * x + y * y;}};struct Vector{int x, y;inline Real_t len() const{return sqrt((Real_t)(x * x + y * y));}inline int operator * (const Vector &v) const{return x * v.y - v.x * y;}inline int dot(const Vector &v) const{return x * v.x + y * v.y;}Vector(const Point &p1, const Point &p2) :x(p2.x - p1.x), y(p2.y - p1.y) {}Vector(const Point &p) :x(p.x), y(p.y) {}Vector() :x(0), y(0) {}};Vector rotate_clockwise(const Vector &v);Vector rotate_counterclocksise(const Vector &v);Point point[NPOINT_MAX];int npoint;inline bool point_cmt_angle(const Point &p1, const Point &p2){return Vector(p1) * p2 > 0;}Real_t work();Real_t calc_area(const Point &p0, const Vector &d1, const Vector &d2);Real_t calc_angle(const Vector &v1, const Vector &v2);void solve(FILE *fin, FILE *fout);}void Solve::solve(FILE *fin, FILE *fout){int ncase;fscanf(fin, "%d", &ncase);for (int id = 1; id <= ncase; id ++){int n, m;static Point p0[NPOINT_MAX];fscanf(fin, "%d%d", &n, &m);for (int i = 0; i < n; i ++)fscanf(fin, "%d%d", &p0[i].x, &p0[i].y);fprintf(fout, "Case #%d:", id);for (int i = 0; i < m; i ++){int x0, y0;fscanf(fin, "%d%d", &x0, &y0);npoint = n;for (int j = 0; j < n; j ++)point[j].x = p0[j].x - x0,point[j].y = p0[j].y - y0;fprintf(fout, " %.9Lf", work());}fprintf(fout, "/n");}}Solve::Real_t Solve::work(){struct Stack_node{Vector dir;int p;// p is the point before dir};static Stack_node stack[NPOINT_MAX];// stack is in the clockwise order!sort(point, point + npoint, point_cmt_angle);int n = 0;for (int i = 0; i < npoint; ){point[n] = point[i];i ++;while (i < npoint && Vector(point[i]) * point[i - 1] == 0){if (Vector(point[i]).dot(point[n]) < 0)return 0;if (point[i].mod() < point[n].mod())point[n] = point[i];i ++;}n ++;}int nstack = 2;stack[1].p = 0;stack[0].dir = rotate_counterclocksise(point[0]);stack[1].dir = rotate_clockwise(point[0]);for (int i = 1; i < n; i ++){Vector vs = rotate_clockwise(point[i]), vt = rotate_counterclocksise(point[i]);if (vs * stack[0].dir <= 0 && vt * stack[nstack - 1].dir >= 0)return 0;while (nstack >= 2){Vector tmp = rotate_clockwise(Vector(point[stack[nstack - 1].p], point[i]));if (tmp * stack[nstack - 1].dir >= 0)break;if (tmp * stack[nstack - 2].dir >= 0){stack[nstack - 1].dir = tmp;stack[nstack].dir = vs;stack[nstack].p = i;nstack ++;break;}nstack --;}if (nstack < 2)return 0;}Real_t ans = 0;for (int i = 1; i < nstack; i ++)ans += calc_area(point[stack[i].p], stack[i].dir, stack[i - 1].dir);return ans;}Solve::Real_t Solve::calc_area(const Point &p0, const Vector &d1, const Vector &d2){Real_t a = calc_angle(rotate_clockwise(p0), d1), b = calc_angle(d1, d2);return p0.mod() * (b * 2 + sin(a * 2) - sin(2 * (a + b))) / 2;}Solve::Vector Solve::rotate_clockwise(const Vector &v){Vector ans;ans.x = v.y;ans.y = -v.x;return ans;}Solve::Vector Solve::rotate_counterclocksise(const Vector &v){Vector ans;ans.x = -v.y;ans.y = v.x;return ans;}Solve::Real_t Solve::calc_angle(const Vector &v1, const Vector &v2){Real_t tmp = v1.dot(v2) / v1.len() / v2.len();if (tmp > 1)tmp = 1;if (tmp < -1)tmp = -1;// deal with error.return acos(tmp);}int main(){Solve::solve(stdin, stdout);}

 

顺便说一下比赛经过：

  最开始把第一题理解错了，想了半天觉得不可做，然后把第二题写了，把第三题小点裸了，这时候还有一个多小时。。 想了很久第四题，觉得一个小时肯定实现不了，仔细一看，小点只有两个圆。。 很高兴，但写的时候纠结了…… 最后不到5分钟时写完，过了样例，还没交，先看了下排名，大概四百八九。。 然后我想赌一把，结果不幸WA掉了，排名瞬间跌至506。。 然后不敢动了，过了几秒比赛结束，刷新一下，最后排名460，幸亏前面有人WA了大点……