poj2966（有问题）

仍然是多边形与线段求交（不规范），然后加最短路。

边权：如果相交则inf，如果不相交则其直线距离。

不知道为什么错，想出了几个脑残图形，都对了。

对应的测试数据：

1 0 1 4
6
0 0
1 1
2 0
2 4
1 3
0 4

0 0 5 4
7
1 0
5 2
5 4
3 4
1 4
-2 2
-1 0

0 0 2 6
8
2 0
4 2
4 4
2 6
0 4
2 4
0 2
2 2

0 0 5 0
4
1 0 
2 0
3 0
4 0

0 0 2 2
9
2 0 
3 0
5 0
5 1
4 1
3 2
1 1
2 1
3 1

非凸包版本（我认为对了）

#include <iostream>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

#define MAXN 1000
#define offset 10000
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
#define _sign(x) ((x)>eps?1:((x)<-eps?2:0))
#define MAXMAT 200
#define inf 1<<30
#define elem_t double

using namespace std;

struct point
{
	double x, y;
};
struct line
{
	point a, b;
};
double xmult(point p1, point p2, point p0)
{
	return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y);
}
double distance_(point p1, point p2)
{
	return sqrt((p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y));
}
bool opposite_side(point p1, point p2, line l)
{
	return xmult(l.a, p1, l.b)*xmult(l.a, p2, l.b) < -eps;
}
bool intersect_ex(line u, line v)
{
	return opposite_side(u.a, u.b, v) && opposite_side(v.a, v.b, u);
}
int insidepoly(int n, point *p, point a, point b)
{
	for (int i = 0; i <= n; i++)
	{
		for (int j = 0; j <= n; j++)
		{
			line temp, temp2;
			temp.a = p[i], temp.b = p[j];
			temp2.a = a, temp2.b = b;
			if (intersect_ex(temp, temp2))
			{
				return 1;
			}
		}
	}
	return 0;
}

int bellman_ford(int n, elem_t mat [][MAXMAT], int s, elem_t* min, int* pre){
	int v[MAXMAT], i, j, k, tag;
	for (i = 0; i < n; i++)
		min[i] = inf, v[i] = 0, pre[i] = -1;
	for (min[s] = 0, j = 0; j < n; j++){
		for (k = -1, i = 0; i < n; i++)
			if (!v[i] && (k == -1 || min[i] < min[k]))
				k = i;
		for (v[k] = 1, i = 0; i < n; i++)
			if (!v[i] && mat[k][i] >= 0 && min[k] + mat[k][i] < min[i])
				min[i] = min[k] + mat[pre[i] = k][i];
	}
	for (tag = 1, j = 0; tag && j <= n; j++)
		for (tag = i = 0; i < n; i++)
			for (k = 0; k < n; k++)
				if (min[k] + mat[k][i] < min[i])
					min[i] = min[k] + mat[pre[i] = k][i], tag = 1;
	return j <= n;
}

int main()
{
	point a, b;
	cin >> a.x >> a.y >> b.x >> b.y;
	int n;
	cin >> n;
	point p[110];
	p[0] = a;
	for (int i = 1; i <= n; i++)
	{
		cin >> p[i].x >> p[i].y;
	}
	p[++n] = b;

	//for (int i = 0; i <= n; i++)
	{
		//cout << "No " << i << " point is " << p[i].x << ' ' << p[i].y << endl;
	}

	elem_t mat[MAXMAT][MAXMAT];
	for (int i = 0; i <= n; i++)
	{
		for (int j = 0; j <= n; j++)
		{
			if (insidepoly(n, p, p[i], p[j]))
			{
				mat[i][j] = inf;
				//cout << i << ' ' << j << ' ' << mat[i][j] << endl;
			}
			else
			{
				mat[i][j] = distance_(p[i], p[j]);
				//cout << i << ' ' << j << ' ' << mat[i][j] << endl;
			}
		}
	}

	elem_t min[MAXMAT];
	int pre[MAXMAT];

	bellman_ford(n+1, mat, 0, min, pre);

	/*for (int i = 0; i <= n; i++)
	{
		cout << i << ' ' << min[i] << endl;
	}*/

	printf("%.4lf\n", min[n]);
	
	//system("pause");
}

凸包版本

#include <iostream>
#include <stdio.h>
#include <math.h>
#include <stdlib.h>


#define MAXN 1000
#define offset 10000
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
#define _sign(x) ((x)>eps?1:((x)<-eps?2:0))
#define MAXMAT 200
#define inf 1000000000

typedef double elem_t;

struct point{ double x, y; };
struct line{ point a, b; };

double xmult(point p1, point p2, point p0){
	return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y);
}
double distance_(point p1, point p2)
{
	return sqrt((p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y));
}
bool opposite_side(point p1, point p2, line l)
{
	return xmult(l.a, p1, l.b)*xmult(l.a, p2, l.b) < -eps;
}
bool intersect_ex(line u, line v)
{
	return opposite_side(u.a, u.b, v) && opposite_side(v.a, v.b, u);
}
int insidepoly(int n, point *p, point a, point b)
{
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < n; j++)
		{
			line temp, temp2;
			temp.a = p[i], temp.b = p[j];
			temp2.a = a, temp2.b = b;
			if (intersect_ex(temp, temp2))
			{
				return 1;
			}
		}
	}
	return 0;
}
//graham算法顺时针构造包含所有共线点的凸包,O(nlogn)
point p1, p2;
int graham_cp(const void* a, const void* b){
	double ret = xmult(*((point*) a), *((point*) b), p1);
	return zero(ret) ? (xmult(*((point*) a), *((point*) b), p2) > 0 ? 1 : -1) : (ret > 0 ? 1 : -1);
}
void _graham(int n, point* p, int& s, point* ch){
	int i, k = 0;
	for (p1 = p2 = p[0], i = 1; i<n; p2.x += p[i].x, p2.y += p[i].y, i++)
		if (p1.y - p[i].y>eps || (zero(p1.y - p[i].y) && p1.x > p[i].x))
			p1 = p[k = i];
	p2.x /= n, p2.y /= n;
	p[k] = p[0], p[0] = p1;
	qsort(p + 1, n - 1, sizeof(point), graham_cp);
	for (ch[0] = p[0], ch[1] = p[1], ch[2] = p[2], s = i = 3; i < n; ch[s++] = p[i++])
		for (; s>2 && xmult(ch[s - 2], p[i], ch[s - 1]) < -eps; s--);
}
int wipesame_cp(const void *a, const void *b)
{
	if ((*(point *) a).y < (*(point *) b).y - eps) return -1;
	else if ((*(point *) a).y > (*(point *) b).y + eps) return 1;
	else if ((*(point *) a).x < (*(point *) b).x - eps) return -1;
	else if ((*(point *) a).x > (*(point *) b).x + eps) return 1;
	else return 0;
}
int _wipesame(point * p, int n)
{
	int i, k;
	qsort(p, n, sizeof(point), wipesame_cp);
	for (k = i = 1; i < n; i++)
		if (wipesame_cp(p + i, p + i - 1) != 0) p[k++] = p[i];
	return k;
}
//构造凸包接口函数,传入原始点集大小n,点集p(p原有顺序被打乱!)
//返回凸包大小,凸包的点在convex中
//参数maxsize为1包含共线点,为0不包含共线点,缺省为1
//参数clockwise为1顺时针构造,为0逆时针构造,缺省为1
//在输入仅有若干共线点时算法不稳定,可能有此类情况请另行处理!
int graham(int n, point* p, point* convex, int maxsize = 1, int dir = 1)
{
	point* temp = new point[n];
	int s, i;
	n = _wipesame(p, n);
	_graham(n, p, s, temp);
	for (convex[0] = temp[0], n = 1, i = (dir ? 1 : (s - 1)); dir ? (i < s) : i; i += (dir ? 1 : -1))
		if (maxsize || !zero(xmult(temp[i - 1], temp[i], temp[(i + 1)%s])))
			convex[n++] = temp[i];
	delete []temp;
	return n;
}
int bellman_ford(int n, elem_t mat [][MAXMAT], int s, elem_t* min, int* pre){
	int v[MAXMAT], i, j, k, tag;
	for (i = 0; i < n; i++)
		min[i] = inf, v[i] = 0, pre[i] = -1;
	for (min[s] = 0, j = 0; j < n; j++){
		for (k = -1, i = 0; i < n; i++)
			if (!v[i] && (k == -1 || min[i] < min[k]))
				k = i;
		for (v[k] = 1, i = 0; i < n; i++)
			if (!v[i] && mat[k][i] >= 0 && min[k] + mat[k][i] < min[i])
				min[i] = min[k] + mat[pre[i] = k][i];
	}
	for (tag = 1, j = 0; tag && j <= n; j++)
		for (tag = i = 0; i < n; i++)
			for (k = 0; k < n; k++)
				if (min[k] + mat[k][i] < min[i])
					min[i] = min[k] + mat[pre[i] = k][i], tag = 1;
	return j <= n;
}
int main()
{
	point a, b;
	std::cin >> a.x >> a.y >> b.x >> b.y;
	int n;
	std::cin >> n;
	point p[MAXMAT];
	p[0] = a;
	for (int i = 1; i <= n; i++)
	{
		std::cin >> p[i].x >> p[i].y;
	}
	p[++n] = b;
	point convex[MAXMAT];
	int convexsize = graham(n+1, p, convex, 1, 0);
	convex[convexsize++] = b;
	
	/*for (int i = 0; i < convexsize; i++)
	{
		std::cout <<"no." <<i << " point is "<<convex[i].x << ' ' << convex[i].y << std::endl;
	}
	for (int i = 0; i <= n; i++)
	{
		std::cout << "no." << i << " point is " << p[i].x << ' ' << p[i].y << std::endl;
	}
	std::cout << convexsize << std::endl;
	std::cout << n << std::endl;*/
	elem_t mat[MAXMAT][MAXMAT];

	for (int i = 0; i < convexsize; i++)
	{
		for (int j = 0; j < convexsize; j++)
		{
			if (insidepoly(convexsize, convex, convex[i], convex[j]))
			{
				mat[i][j] = inf;
				///std::cout << i << ' ' << j << ' ' << mat[i][j] << std::endl;
			}
			else if (i == j)
			{
				mat[i][j] = 0.0;
				///std::cout << i << ' ' << j << ' ' << mat[i][j] << std::endl;
			}
			else
			{
				mat[i][j] = distance_(convex[i], convex[j]);
				///std::cout << i << ' ' << j << ' ' << mat[i][j] << std::endl;
			}
			
		}
	}
	/*
	for (int i = 0; i < convexsize; i++)
	{
		for (int j = 0; j < convexsize; j++)
		{
			std::cout << i << ' ' << j << ' ' << mat[i][j] << std::endl;
		}
	}*/

	elem_t min[MAXN];
	int pre[MAXN];
	int iii = bellman_ford(convexsize, mat, 0, min, pre);
/*for (int i = 0; i < convexsize; i++)
	{
		std::cout << min[i] << std::endl;
	}
	for (int i = 1; i < 10; i++)
	{
		std::cout << pre[i] << '\t';
	}
	printf("\n");*/
	printf("%.4f\n", min[convexsize - 1]);
	//system("pause");
}