Problem Statement | |||||||||||||
| Nick likes to draw fractals. For the special occasion of Single Round Match 500, he decided to draw the 500th generation of his favorite fractal. Each generation of the fractal can be described as a set of segments on the plane. Some of these segments are calledfinal and all other are considered to be non-final. In each non-final segment, one of its endpoints is chosen and called theroot of this segment. In pictures below, solid and dotted lines are used to represent final and non-final segments, correspondingly. The first generation consists of one segment with endpoints (0, 0) and (0, 81). This segment is non-final and its root is (0, 0). ![]() The i-th generation, i >= 2, is produced from the (i-1)-th generation as follows. All final segments from the (i-1)-th generation are included into the i-th generation without any changes. For each non-final segment from the (i-1)-th generation, let A and B be its endpoints, with A being its root. The following steps are then done:
![]() Consider a rectangle R on the plane that consists of points (x, y), such that x1 <= x <= x2 and y1 <= y <= y2. Let S be the set of all segments of the 500-th generation of the fractal described above (both final and non-final ones). Return the total length of all parts of segments from S that belong to rectangle R. | |||||||||||||
Definition | |||||||||||||
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Notes | |||||||||||||
| - | The returned value must have an absolute or relative error less than 1e-9. | ||||||||||||
Constraints | |||||||||||||
| - | x1 will be between -100 and 100, inclusive. | ||||||||||||
| - | x2 will be between x1+1 and 100, inclusive. | ||||||||||||
| - | y1 will be between -100 and 100, inclusive. | ||||||||||||
| - | y2 will be between y1+1 and 100, inclusive. | ||||||||||||
Examples | |||||||||||||
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【题解】
我的思路和官方思路不一样。官方思路基于的是矩形切割,分治(貌似)
我的思路是将每个方格包含多少长度统计出来,最后输出答案。
离散化即可(包括点、线段)
【代码】
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
using namespace std;
double s[505][505];
class FractalPicture
{
public:
double getLength(int, int, int, int);
};
int get(int x)
{
return (x+100)*2;
}
int get(int x,int y)
{
return (min(x,y)+100)*2+1;
}
int dir(int x1,int y1,int x2,int y2)
{
return x1==x2;
}
void work(int gg,int x1,int y1,int x2,int y2)
{
int i,len,x,y;
if (gg>500) return;
len=abs(x1-x2)+abs(y1-y2);
if (len>1)
{
int l=len/3;
x=(x1+2*x2)/3;
y=(y1+2*y2)/3;
if (dir(x1,y1,x2,y2)==0)
{
int ll=min(x1,x),rr=max(x1,x);
for (i=ll;i<rr;i++)
s[get(i,i+1)][get(y1)]+=1;
work(gg+1,x,y,x,y-l);
work(gg+1,x,y,x,y+l);
}
else
{
int ll=min(y1,y),rr=max(y1,y);
for (i=ll;i<rr;i++)
s[get(x1)][get(i,i+1)]+=1;
work(gg+1,x,y,x-l,y);
work(gg+1,x,y,x+l,y);
}
work(gg+1,x,y,x2,y2);
}
else
{
if (dir(x1,y1,x2,y2)==0)
{
s[get(x1,x2)][get(y1)]+=1;
s[get(x1,x2)][get(y1)-1]+=double(500-gg)/3;
s[get(x1,x2)][get(y1)+1]+=double(500-gg)/3;
}
else
{
s[get(x1)][get(y1,y2)]+=1;
s[get(x1)-1][get(y1,y2)]+=double(500-gg)/3;
s[get(x1)+1][get(y1,y2)]+=double(500-gg)/3;
}
return;
}
}
double FractalPicture::getLength(int x1, int y1, int x2, int y2)
{
work(1,0,0,0,81);
double ans=0;
int i,j;
for (i=x1;i<x2;i++)
for (j=y1;j<y2;j++)
{
ans+=s[get(i,i+1)][get(j)];
ans+=s[get(i)][get(j,j+1)];
ans+=s[get(i,i+1)][get(j,j+1)];
}
for (i=x1;i<x2;i++)
ans+=s[get(i,i+1)][get(y2)];
for (i=y1;i<y2;i++)
ans+=s[get(x2)][get(i,i+1)];
return ans;
}
//以下的正式比赛是用不上。
int main()
{
int x1,y1,x2,y2;
cin >> x1 >> y1 >> x2 >> y2;
FractalPicture a;
cout << a.getLength(x1,y1,x2,y2);
}

本篇介绍了一个绘制特定分形图案的算法实现,该分形从一个初始线段开始,每一代通过特定规则生成新的线段,并区分最终线段与非最终线段。文章提供了完整的代码实现,用于计算指定矩形区域内第500代分形图案的总线段长度。



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