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;
}