计算几何+2sat：1020T3

本文搬运自本人高中时期CSDN博客，若图片加载不出来，可到原文查看：https://blog.csdn.net/zhangtingxiqwq/article/details/133943270

http://cplusoj.com/d/senior/p/SS231019C

我们进行这样的转化

在这里插入图片描述

则0/1必选一个，2/3必选一个

那么就变成一个2sat问题

两三角形有交，则一个选，一个不能选

对角三角形一个选，一个不选。一个不选，一个选

三角形不合法，则选向不选连边，代表必须不选

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// 5.3k
#include<bits/stdc++.h>
using namespace std;
#define int long long
inline int read(){int x=0,f=1;char ch=getchar(); while(ch<'0'||
ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){
x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
//mt19937 rand(time(0));
//mt19937_64 rand(time(0));
//srand(time(0));
#define N 200010
//#define M
//#define mo
#define eps 1e-4
double H, W, X[N], Y[N]; 
struct Point {
	double x, y; 
	Point operator - (const Point &A) const {
		Point B; B.x=x-A.x; B.y=y-A.y; 
		return B; 
	}
	double operator ^ (const Point &A) const {
		return x * A.y - y * A.x; 
	}
	bool check() {
//		printf("Checking %lf %lf\n", x, y); 
		if(x < 0 || x > W) return false; 
		if(y < 0 || y > H) return false; 
		return true; 
	}
};
namespace Cross {
	bool Line_cross(Point p1, Point p2, Point p3, Point p4) {
		double a1 = (p1 - p2) ^ (p3 - p2); 
		double a2 = (p1 - p2) ^ (p4 - p2); 
		if(a1 * a2 >= 0) return false; 
		return true; 
	}
	bool cross(Point p1, Point p2, Point p3, Point p4) {
//		printf("(%lf %lf) (%lf %lf) || (%lf %lf) (%lf %lf)\n", p1.x, p1.y, p2.x, p2.y, p3.x, p3.y, p4.x, p4.y); 
		bool t1 = Line_cross(p1, p2, p3, p4); 
		bool t2 = Line_cross(p3, p4, p1, p2); 
		return t1 && t2; 
	}
}
struct node {
	Point a[3]; 
	void make_node(int i, int j, double k) {
		a[0] = {X[i], Y[i]}; 
		if(j == 0 || j == 3) a[1] = {X[i], Y[i] + k}; 
		if(j == 3 || j == 1) a[2] = {X[i] + k, Y[i]}; 
		if(j == 1 || j == 2) a[1] = {X[i], Y[i] - k}; 
		if(j == 2 || j == 0) a[2] = {X[i] - k, Y[i]}; 
	}
	bool check() {
		if(a[0].check() == false) return false; 
		if(a[1].check() == false) return false; 
		if(a[2].check() == false) return false; 
		return true; 
	}
	void print() {
		printf("%lf %lf\n", a[0].x, a[0].y); 
		printf("%lf %lf\n", a[1].x, a[1].y); 
		printf("%lf %lf\n", a[2].x, a[2].y); 
		printf(">> %lld\n", check()); 
	}
	bool operator ^(const node &A) const {
//		; A.print(); 
		int f0, f1, g0, g1; 
		for(f0 = 0; f0 <= 2; ++f0) 
			for(f1 = f0+1; f1 <= 2; ++f1)
				for(g0 = 0; g0 <= 2; ++g0)
					for(g1 = g0+1; g1<=2; ++g1) {
						if(Cross::cross(a[f0], a[f1], A.a[g0], A.a[g1])) 
							return true; 
					}
		return false; 
	}
	
}p[N]; 
int n, m, i, j, k, T;
namespace Graph {
	int make_node(int i, int j) { 
		return j * n + i; 
	}
	struct two_sat {
		int dfn[N], low[N], vis[N], col[N], tot, i; 
		vector<int>G[N]; 
		stack<int>z; 
		void clear() {
			tot = 0; 
			while(!z.empty()) z.pop(); 
			memset(dfn, 0, sizeof(dfn)); 
			memset(low, 0, sizeof(low)); 
			memset(vis, 0, sizeof(vis)); 
			memset(col, 0, sizeof(col)); 
			for(i=0; i<N; ++i) G[i].clear(); 
		}
		void add_edge(int u,  int v) {
//			printf("%lld  %lld\n", u, v); 
			G[u].pb(v); 
		}
		void dfs(int x) {
			dfn[x] = low[x] = ++tot; 
			z.push(x); vis[x] = 1; 
			for(auto y : G[x]) {
				if(vis[y] == -1) continue; 
				if(!vis[y]) dfs(y), low[x] = min(low[x], low[y]); 
				else low[x] = min(low[x], low[y]); 
			}
//			printf("\t %lld : %lld %lld\n", x, dfn[x], low[x]); 
			if(dfn[x] == low[x]) {
				while(z.top() != x) col[z.top()] = x, vis[z.top()] = -1, z.pop(); 
				col[x] = x; z.pop(); vis[x] = -1; 
			}
//			vis[x] = -1; 
		}
		void tarjan() {
			for(i=1; i<=8*n; ++i) 
				if(!vis[i]) dfs(i); 
//			for(i=1; i<=8*n; ++i) printf("%3lld", i); 
//			printf("\n"); 
//			for(i=1; i<=8*n; ++i) printf("%3lld", col[i]); 
//			printf("\n"); 
		}
		int pan(int u, int v) {
			return col[u] == col[v]; 
		}
	}Sat;
}
using namespace Graph; 
double l, r, mid, ans; 

bool check(double k) {
//	printf("# Now is %.3lf\n", k); 
	int i, j, x, y, u, v; 
	Sat.clear(); 
	for(i=1; i<=n; ++i) {
		for(j=0; j<=3; ++j) {
			u = make_node(i, j); 
			v = make_node(i, j^1); 
			Sat.add_edge(u, v + 4*n); 
			Sat.add_edge(v + 4*n, u ); 
			p[u].make_node(i, j, k); 
//			p[u].print(); 
			if(p[u].check() == false) 
				Sat.add_edge(u, u + 4*n);
//				 Sat.add_edge(u + 4*n, u); 
		}
//		printf("-----------\n"); 
	}
		
	for(i=1; i<=n; ++i) 
		for(j=i+1; j<=n; ++j) 
			for(x=0; x<=3; ++x) 
				for(y=0; y<=3; ++y) {
//					if(i == j) continue; 
					u = make_node(i, x); 
					v = make_node(j, y); 
					if(p[u] ^ p[v]) {
//						printf("%lld %lld || %lld %lld\n", i, j, x, y); 
						Sat.add_edge(u, v + 4*n); 
						Sat.add_edge(v, u + 4*n); 
					}
				}
	Sat.tarjan(); 
	for(i=1; i<=n; ++i) 
		for(j=0; j<=3; ++j) {
			u = make_node(i, j); 
			v = make_node(i, j^1); 
//			printf("%lld | %lld %lld %lld\n", i, j, u, u+4*n) ; 
//				u+4*n, v+4*n); 
			if(Sat.pan(u, u + 4*n)) return false; 
//			if(Sat.pan(u + 4*n, v + 4*n)) return false; 
		}
//	printf("\t ok\n"); 
	return true; 
	
}

signed main()
{
//	freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
		freopen("city.in", "r", stdin);
	freopen("city.out", "w", stdout);	
//	T=read();
//	while(T--) {
//
//	}
	scanf("%lf%lf%lld", &W, &H, &n); 
	for(i=1; i<=n; ++i) {
		scanf("%lf%lf", &X[i], &Y[i]); 
	}
	l = 0; r = max(H, W); 
	while(r - l > eps){
		mid = (l + r) / 2; 
		if(check(mid)) l = mid, ans = mid; 
		else r = mid; 
	}
	printf("%.2lf", ans*2); 
	return 0;
}