USACO Spinning Wheels 解题报告

这道题的题目很难懂。。。虽然我自认为英语还不错。。。同样看不懂题目的同学可以看看这里的解释http://www.byvoid.com/blog/usaco-323-spinning-wheels/

同时那里的做法也非常可取，简单明了，对0~359每个角度对每个轮子逐一判断（当然，要具体到每个轮子的每个缺口）。

大神总能写出简单高效的代码http://belbesy.wordpress.com/2012/08/14/usaco-3-2-3-spinning-wheels/。我在慎重考虑自己是不是改行搬砖去。

我的做法和我看到的做法都不一样。用的是整体的角度，先是一个完整的圆，然后逐一减去每个轮子透不过的区域，剩下的就是能透光的区域，如果这个区域和某一个轮子的所有缺口都不重叠，则这一秒没有光通过。

照理说我这种方法相对于每个角度单独考虑会快一些。但写起来麻烦很多，圆上的边是否相交及相交的区域我不知道有没有简洁高效的方法。我的代码中是一个正确的方法，但是根据两条边是否通过360度逐一分情况考虑的，比较繁琐。

/*
ID: thestor1
LANG: C++
TASK: spin
*/
#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <cassert>
#include <string>
#include <algorithm>

using namespace std;

struct Wedge
{
	int angle, extent;
};

struct Wheel
{
	int speed;
	int nWedge;
	vector<Wedge> wedges;
};

bool check(const Wheel* const wheels, int iWheel, const int nWheel, const int intersectAngle, const int intersectExtent)
{
	if(iWheel >= nWheel)
	{
		return true;
	}

	for(int i = 0; i < wheels[iWheel].nWedge; ++i)
	{
		int iangle = wheels[iWheel].wedges[i].angle;
		int iextent = wheels[iWheel].wedges[i].extent;

		int resAngle; 
		int resExtent;

		if(iextent == 359)
		{
			resAngle = intersectAngle;
			resExtent = intersectExtent;
		}
		else if(intersectExtent == 359)
		{
			resAngle = iangle;
			resExtent = iextent;
		}
		else
		{
			int intersectEnd = intersectAngle + intersectExtent;
			int iend = iangle + iextent;
			if(intersectEnd >= 360)
			{
				intersectEnd -= 360;
				if(iend >= 360)
				{
					iend -= 360;
					resAngle = max(iangle, intersectAngle);
					resExtent = (min(iend, intersectEnd) + 360 - resAngle) % 360;
				}
				else
				{
					if(intersectEnd < iangle)
					{
						if(intersectAngle > iend)
						{
							continue;
						}
						resAngle = intersectAngle;
						resExtent = iend - resAngle;
					}
					else
					{
						if(check(wheels, iWheel + 1, nWheel, iangle, intersectEnd - iangle))
						{
							return true;
						}
						if(intersectAngle > iend)
						{
							continue;
						}
						resAngle = intersectAngle;
						resExtent = iend - resAngle;
					}
				}
			}
			else
			{
				if(iend >= 360)
				{
					iend -= 360;
					if(iend < intersectAngle)
					{
						if(iangle > intersectEnd)
						{
							continue;
						}
						resAngle = iangle;
						resExtent = intersectEnd - resAngle;
					}
					else
					{
						if(check(wheels, iWheel + 1, nWheel, intersectAngle, iend - intersectAngle))
						{
							return true;
						}
						if(iangle > intersectEnd)
						{
							continue;
						}
						resAngle = iangle;
						resExtent = intersectEnd - resAngle;
					}
				}
				else
				{
					if(iangle > intersectEnd || iend < intersectAngle)
					{
						continue;
					}
					resAngle = max(iangle, intersectAngle);
					resExtent = min(iend, intersectEnd) - resAngle;
				}
			}
		}
		if(check(wheels, iWheel + 1, nWheel, resAngle, resExtent))
		{
			return true;
		}
	}
	return false;
}

bool check(Wheel *wheels, const int nWheel)
{
	return check(wheels, 0, nWheel, 0, 359);
}

int main()
{
	FILE *fin  = fopen ("spin.in", "r");
	FILE *fout = fopen ("spin.out", "w");
	//freopen("log.txt", "w", stdout);

	const int nWheel = 5;
	Wheel wheels[nWheel];

	for(int i = 0; i < nWheel; ++i)
	{
		fscanf(fin, "%d", &wheels[i].speed);
		fscanf(fin, "%d", &wheels[i].nWedge);
		for(int j = 0; j < wheels[i].nWedge; ++j)
		{
			Wedge wedge;
			//int angle, extent;
			fscanf(fin, "%d%d", &wedge.angle, &wedge.extent);
			wheels[i].wedges.push_back(wedge);
		}
	}

	int t = 360; 
	for(t = 0; t < 360; ++t)
	{
		if(check(wheels, nWheel))
		{
			break;
		}
		for(int i = 0; i < nWheel; ++i)
		{
			for(int j = 0; j < wheels[i].nWedge; ++j)
			{
				wheels[i].wedges[j].angle += wheels[i].speed;
				wheels[i].wedges[j].angle %= 360;
			}
		}
	}
	if(t < 360)
	{
		fprintf(fout, "%d\n", t);
	}
	else
	{
		fprintf(fout, "none\n", t);
	}
	return 0;
}