bzoj 1018 堵塞的交通traffic 线段树

Posted 2022-09-22 pkgunboat

题意：有一个n * 2的网格图，有3种操作：给两个相邻的点加上一条边，断开相邻的两个点连着的边，询问两个点的连通性。

思路：直接看博客就行了，https://blog.csdn.net/roll_keyboard/article/details/81185535，在纸上画一画来确定4个顶点之间的更新关系。有一个需要注意的细节是有可能通过绕远路的方式可以到达，所以需要考虑前面和后面的部分对询问区间的影响。

代码：

#include <bits/stdc++.h>
#define ls (o << 1)
#define rs (o << 1 | 1)
using namespace std;
const int maxn = 100010;
struct node 
	bool l, r, u, d, x1, x2, U, D; 
;
node tr[maxn * 4];
node init() 
	node ans;
	ans.l = ans.r = ans.D = ans.U = ans.x1 = ans.x2 = 0;
	ans.u = ans.d = 1;
	return ans;

node merge(node a1, node a2) 
	node ans;
	ans.l = (a1.l | (a1.u & a1.U & a2.l & a1.D & a1.d));
	ans.r = (a2.r | (a2.u & a1.U & a1.r & a1.D & a1.d));
	ans.u = ((a1.u & a1.U & a2.u) | (a1.x1 & a1.D & a2.x2));
	ans.d = ((a1.d & a1.D & a2.d) | (a1.x2 & a1.U & a2.x1));
	ans.x1 = ((a1.u & a1.U & a2.x1) | (a1.x1 & a1.D & a2.d));
	ans.x2 = ((a1.x2 & a1.U & a2.u) | (a1.d & a1.D & a2.x2));
	ans.U = a2.U;
	ans.D = a2.D;
	return ans; 

void build(int o, int l, int r) 
	if(l == r) 
		tr[o] = init();
		return;
	
	int mid = (l + r) >> 1;
	build(ls, l, mid);
	build(rs, mid + 1, r);
	tr[o] = merge(tr[ls], tr[rs]);

void update(int o, int l, int r, int p, int type) 
	if(l == r) 
		if(type >> 2) 
			tr[o].l = tr[o].r = tr[o].x1 = tr[o].x2 = (type & 1);
			return;	
		 else if (type >> 1) 
			tr[o].U = (type & 1);
		 else 
			tr[o].D = (type & 1);
		
		return; 
	
	int mid = (l + r) >> 1;
	if(p <= mid) update(ls, l, mid, p, type);
	else update(rs, mid + 1, r, p, type);
	tr[o] = merge(tr[ls], tr[rs]);

node query(int o, int l, int r, int ql, int qr) 
	if(l >= ql && r <= qr) 
		return tr[o];
	
	int mid = (l + r) >> 1;
	node ans = init();
	ans.U = ans.D = 1;
	if(ql <= mid) ans = merge(ans, query(ls, l, mid, ql, qr));
	if(qr > mid) ans = merge(ans, query(rs, mid + 1, r, ql, qr));
	return ans;

void out(bool flag) 
	if(flag) printf("Y\n");
	else printf("N\n");

char s[10];
int main() 
	int n;
	scanf("%d", &n);
	int x1, y1, x2, y2;
	build(1, 1, n);
	while(1) 
		scanf("%s", s + 1);
		if(s[1] == ‘E‘) break;
		scanf("%d%d%d%d", &x1, &y1, &x2, &y2);
		if(y1 > y2) 
			swap(x1, x2);
			swap(y1, y2); 
		
		if(s[1] == ‘A‘) 
			node ans1, ans2, ans3;
			if(y1 > 1) ans1 = query(1, 1, n, 1, y1 - 1);
			ans2 = query(1, 1, n, y1, y2);
			if(y2 < n) ans3 = query(1, 1, n, y2 + 1, n);
			if(y1 > 1 && (ans1.r && ans1.U && ans1.D)) 
				ans2.l |= 1;
				ans2.x1 |= (ans2.l & ans2.d);
				ans2.x2 |= (ans2.l & ans2.u);
				ans2.d |= (ans2.x1 & ans2.l);
				ans2.u |= (ans2.l & ans2.x2);
			
			if(y2 < n && (ans2.U && ans3.l && ans2.D)) 
				ans2.r |= 1;
				ans2.x1 |= (ans2.u & ans2.r);
				ans2.x2 |= (ans2.d & ans2.r);
				ans2.d |= (ans2.x2 & ans2.r);
				ans2.u |= (ans2.x1 & ans2.r);
			
			if(x1 == 1 && x2 == 1) 
				out(ans2.u);
			 else if(x1 == 1 && x2 == 2) 
				out(ans2.x1);
			 else if(x1 == 2 && x2 == 1) 
				out(ans2.x2);
			 else 
				out(ans2.d);
			
		 else 
			int type = 0;
			if(y1 == y2) 
				type |= (1 << 2);
				if(s[1] == ‘O‘) type |= 1;
			 else 
				if(x1 == 1) type |= (1 << 1);
				if(s[1] == ‘O‘) type |= 1;
			
			update(1, 1, n, y1, type);