【BZOJ 2541】【Vijos 1366】【CTSC 2000】冰原探险

http://www.lydsy.com/JudgeOnline/problem.php?id=2541

https://vijos.org/p/1366

loli秘制大爆搜_(:з」∠)_坑了好久啊QAQ一上午花了2h+写这道题，最后WA了2个点，调了一下午多。

在矩形一条边上的所有位置都是等效的，所以把每个矩形的四条边拆开，表示为点。每个点只会连出去一条边，暴力找边建图，最后跑堆优dij。

时间复杂度\(O(n^2)\)（附带大常数16一脸不可过？不过最后竟然过了）



一开始认为有环爆搜不可做，便建图跑了最短路。后来xyx0711跟我说直接bfs不走环，因为正确的路不会走环，后来想想也是。。。但是懒得改了。



恶心经历：冰块一次推进洞真心没想到，改完之后还WA第8个点，后来发现判断和T的连边时少写了一个条件，快速写上过了那个点，再评测发现第一个点突然又WA了，查了好久发现因为之前写得太急把坐标打反了（坐标打反了都能放过我9个点，这数据。。。）

改第8个点改了一下午TWT，自己画了一下原图，还手动模拟出了正确答案QAQ



起点是最左上角的点，终点是最靠右边的点，这个是离散过坐标轴后画出来的图

真心代码题

#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int in() {
	int k = 0, fh = 1; char c = getchar();
	for (; c < '0' || c > '9'; c = getchar())
		if (c == '-') fh = -1;
	for (; c >= '0' && c <= '9'; c = getchar())
		k = k * 10 + c - 48;
	return k * fh;
}

const int N = 4003;
const int jie[4][2] = {3, 1, 2, 0, 3, 1, 2, 0};

int n, xs, xt, ys, yt, xa[N], ya[N], xb[N], yb[N], num[N][4], to[N][4][2], tot = 0, l, r, up, tt[4];

struct node {int nxt, to;} E[N * 4 * 2 + 100];
int cnt = 0, point[N * 4], dist[N * 4], S, T;
bool inq[N * 4];

void ins(int u, int v) {E[++cnt] = (node) {point[u], v}; point[u] = cnt;}

struct Qnode {
	int id, dist;
	Qnode (int _id = 0, int _dist = 0) : id(_id), dist(_dist) {}
	bool operator < (const Qnode &A) const {
		return dist > A.dist;
	}
};

priority_queue <Qnode> Q;

int main() {
	n = in(); xs = in(); ys = in(); xt = in(); yt = in();
	for (int i = 1; i <= n; ++i) {
		xa[i] = in();
		ya[i] = in();
		xb[i] = in();
		yb[i] = in();
		for (int j = 0; j < 4; ++j)
			num[i][j] = ++tot;
	}

	if (xs == xt) {
		l = ys; r = yt;
		if (l > r) swap(l, r);
		up = 0;
		for (int i = 1; i <= n; ++i)
			if (yb[i] < l || ya[i] > r || xa[i] > xs || xb[i] < xs)
				++up;
		if (up == n) {puts("1"); return 0;}
	}

	if (ys == yt) {
		l = xs; r = xt;
		if (l > r) swap(l, r);
		up = 0;
		for (int i = 1; i <= n; ++i)
			if (yb[i] < ys || ya[i] > ys || xa[i] > r || xb[i] < l)
				++up;
		if (up == n) {puts("1"); return 0;}
	}

	for (int i = 1; i <= n; ++i) {
		l = ya[i]; r = yb[i]; up = xa[i];
		for (int j = 1; j <= n; ++j)
			if (xb[j] < up) {
				if (l <= ya[j] - 1 && ya[j] - 1 <= r) {
					if ((to[j][1][1] == 0) || (xa[to[j][1][1]] > up))
						to[j][1][1] = i;
				}
				if (l <= yb[j] + 1 && yb[j] + 1 <= r) {
					if ((to[j][3][1] == 0) || (xa[to[j][3][1]] > up))
						to[j][3][1] = i;
				}
			}

		l = xa[i]; r = xb[i]; up = ya[i];
		for (int j = 1; j <= n; ++j)
			if (yb[j] < up) {
				if (l <= xa[j] - 1 && xa[j] - 1 <= r) {
					if ((to[j][0][1] == 0) || (ya[to[j][0][1]] > up))
						to[j][0][1] = i;
				}
				if (l <= xb[j] + 1 && xb[j] + 1 <= r) {
					if ((to[j][2][1] == 0) || (ya[to[j][2][1]] > up))
						to[j][2][1] = i;
				}
			}

		l = ya[i]; r = yb[i]; up = xb[i];
		for (int j = 1; j <= n; ++j)
			if (xa[j] > up) {
				if (l <= ya[j] - 1 && ya[j] - 1 <= r) {
					if ((to[j][1][0] == 0) || (xb[to[j][1][0]] < up))
						to[j][1][0] = i;
				}
				if (l <= yb[j] + 1 && yb[j] + 1 <= r) {
					if ((to[j][3][0] == 0) || (xb[to[j][3][0]] < up))
						to[j][3][0] = i;
				}
			}

		l = xa[i]; r = xb[i]; up = yb[i];
		for (int j = 1; j <= n; ++j)
			if (ya[j] > up) {
				if (l <= xa[j] - 1 && xa[j] - 1 <= r) {
					if ((to[j][0][0] == 0) || (yb[to[j][0][0]] < up))
						to[j][0][0] = i;
				}
				if (l <= xb[j] + 1 && xb[j] + 1 <= r) {
					if ((to[j][2][0] == 0) || (yb[to[j][2][0]] < up))
						to[j][2][0] = i;
				}
			}
	}

	for (int i = 1; i <= n; ++i)
		for (int j = 0; j < 4; ++j)
			for (int k = 0; k < 2; ++k)
				if (to[i][j][k])
					ins(num[i][j], num[to[i][j][k]][jie[j][k]]);

	S = ++tot; T = ++tot;

	int x = xs, y = ys;

	for (int i = 1; i <= n; ++i) {
		if (xa[i] > x && ya[i] <= y && y <= yb[i]) {
			if ((tt[0] == 0) || (xa[i] < xa[tt[0]]))
				tt[0] = i;
		}
		if (ya[i] > y && xa[i] <= x && x <= xb[i]) {
			if ((tt[1] == 0) || (ya[i] < ya[tt[1]]))
				tt[1] = i;
		}
		if (xb[i] < x && ya[i] <= y && y <= yb[i]) {
			if ((tt[2] == 0) || (xb[i] > xb[tt[2]]))
				tt[2] = i;
		}
		if (yb[i] < y && xa[i] <= x && x <= xb[i]) {
			if ((tt[3] == 0) || (yb[i] > yb[tt[3]]))
				tt[3] = i;
		}
	}

	for (int i = 0; i < 4; ++i)
		if (tt[i]) ins(S, num[tt[i]][i]);

	x = xt; y = yt;

	for (int i = 1; i <= n; ++i) {
		if (xa[i] - 1 == x) {
			if (y < ya[i] && ((to[i][0][0] == 0 && ya[i] > y) || (to[i][0][0] != 0 && yb[to[i][0][0]] < y)))
				ins(num[i][0], T);
			if (y > yb[i] && ((to[i][0][1] == 0 && yb[i] < y) || (to[i][0][1] != 0 && ya[to[i][0][1]] > y)))
				ins(num[i][0], T);
		}
		if (ya[i] - 1 == y) {
			if (x < xa[i] && ((to[i][1][0] == 0 && xa[i] > x) || (to[i][1][0] != 0 && xb[to[i][1][0]] < x)))
				ins(num[i][1], T);
			if (x > xb[i] && ((to[i][1][1] == 0 && xb[i] < x) || (to[i][1][1] != 0 && xa[to[i][1][1]] > x)))
				ins(num[i][1], T);
		}
		if (xb[i] + 1 == x) {
			if (y < ya[i] && ((to[i][2][0] == 0 && ya[i] > y) || (to[i][2][0] != 0 && yb[to[i][2][0]] < y)))
				ins(num[i][2], T);
			if (y > yb[i] && ((to[i][2][1] == 0 && yb[i] < y) || (to[i][2][1] != 0 && ya[to[i][2][1]] > y)))
				ins(num[i][2], T);
		}
		if (yb[i] + 1 == y) {
			if (x < xa[i] && ((to[i][3][0] == 0 && xa[i] > x) || (to[i][3][0] != 0 && xb[to[i][3][0]] < x)))
				ins(num[i][3], T);
			if (x > xb[i] && ((to[i][3][1] == 0 && xb[i] < x) || (to[i][3][1] != 0 && xa[to[i][3][1]] > x)))
				ins(num[i][3], T);
		}
	}

	memset(dist, 127, sizeof(dist));
	dist[S] = 0;
	Q.push(Qnode(S, 0));
	Qnode u;
	while (!Q.empty()) {
		u = Q.top(); Q.pop();
		if (inq[u.id]) continue;
		inq[u.id] = true;
		for (int i = point[u.id]; i; i = E[i].nxt)
			if (dist[u.id] + 1 < dist[E[i].to]) {
				dist[E[i].to] = dist[u.id] + 1;
				Q.push(Qnode(E[i].to, dist[E[i].to]));
			}
	}

	printf("%d\n", dist[T] == dist[0] ? 0 : dist[T]);
	return 0;
}