1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
| #include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;
inline const int Get_Int() {
int num=0,bj=1;
char x=getchar();
while(!isdigit(x)) {
if(x=='-')bj=-1;
x=getchar();
}
while(isdigit(x)) {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
const int maxn=100005,K=18;
struct Node {
int n,x,y,x2,y2,xy;
Node():Node(0,0) {n=0;}
Node(int x,int y):n(1),x(x),y(y),x2(x*x),y2(y*y),xy(x*y) {}
Node(int n,int x,int y,int x2,int y2,int xy):n(n),x(x),y(y),x2(x2),y2(y2),xy(xy) {}
Node operator + (const Node& b) {return Node(n+b.n,x+b.x,y+b.y,x2+b.x2,y2+b.y2,xy+b.xy);}
Node operator - (const Node& b) {return Node(n-b.n,x-b.x,y-b.y,x2-b.x2,y2-b.y2,xy-b.xy);}
void operator += (const Node& b) {*this=*this+b;}
double avg_x() {return 1.0*x/n;}
double avg_y() {return 1.0*y/n;}
double A() {return x2-2*avg_x()*x+n*avg_x()*avg_x();}
double B() {return 2*avg_y()*x+2*avg_x()*y-2*xy-2*n*avg_x()*avg_y();}
double C() {return y2-2*avg_y()*y+n*avg_y()*avg_y();}
double delta() {
if(n==1)return 0;
double a=A(),b=B(),c=C(),d=sqrt(a*a+b*b+c*c-2*a*c);
return (a+c-d)/2;
}
} a[maxn];
int n,m,Depth[maxn],p[maxn][K];
vector<int> edges[maxn];
void AddEdge(int x,int y) {edges[x].push_back(y);}
int LCA(int a,int b) {
if(Depth[a]<Depth[b])swap(a,b);
for(int i=K-1; i>=0; i--)if(Depth[a]-(1<<i)>=Depth[b])a=p[a][i];
if(a==b)return a;
for(int i=K-1; i>=0; i--)if(p[a][i]!=p[b][i])a=p[a][i],b=p[b][i];
return p[a][0];
}
namespace Tree {
void Dfs(int Now,int fa,int depth) {
Depth[Now]=depth;
p[Now][0]=fa;
for(int i=1; i<K; i++)p[Now][i]=p[p[Now][i-1]][i-1];
for(int Next:edges[Now]) {
if(Next==fa)continue;
a[Next]+=a[Now];
Dfs(Next,Now,depth+1);
}
}
void solve() {
Dfs(1,0,1);
int q=Get_Int();
while(q--) {
int x=Get_Int(),y=Get_Int(),lca=LCA(x,y);
printf("%0.5lf\n",(a[x]+a[y]-a[lca]-a[p[lca][0]]).delta());
}
}
}
namespace Circle {
vector<int> cir;
int step=0,top=0,Dfn[maxn],Lowlink[maxn],Stack[maxn],Color[maxn];
bool inCircle[maxn];
void Tarjan(int Now,int fa) {
Dfn[Now]=Lowlink[Now]=++step;
Stack[++top]=Now;
for(int Next:edges[Now]) {
if(Next==fa)continue;
if(!Dfn[Next]) {
Tarjan(Next,Now);
Lowlink[Now]=min(Lowlink[Now],Lowlink[Next]);
} else Lowlink[Now]=min(Lowlink[Now],Dfn[Next]);
}
if(Dfn[Now]==Lowlink[Now]&&cir.empty()) {
int y;
do {
y=Stack[top--];
cir.push_back(y);
} while(y!=Now);
if(cir.size()>1)for(int x:cir)inCircle[x]=1;
else cir.clear();
}
}
void Dfs(int Now,int fa,int color,int depth) {
Color[Now]=color;
Depth[Now]=depth;
p[Now][0]=fa;
for(int i=1; i<K; i++)p[Now][i]=p[p[Now][i-1]][i-1];
for(int Next:edges[Now]) {
if(Next==fa||inCircle[Next])continue;
a[Next]+=a[Now];
Dfs(Next,Now,color,depth+1);
}
}
int num[maxn];
Node val[maxn<<1];
void solve() {
Tarjan(1,0);
int cnt=0;
for(int x:cir)Dfs(x,0,x,1),num[x]=++cnt;
cir.insert(cir.end(),cir.begin(),cir.end());
for(int i=0; i<cir.size(); i++)val[i+1]=val[i]+a[cir[i]];
int q=Get_Int();
while(q--) {
int x=Get_Int(),y=Get_Int();
if(Color[x]==Color[y]) {
int lca=LCA(x,y);
printf("%0.5lf\n",(a[x]+a[y]-a[lca]-a[p[lca][0]]).delta());
} else {
int fx=Color[x],fy=Color[y];
Node tx=a[x]-a[fx],ty=a[y]-a[fy];
if(num[fx]>num[fy])swap(fx,fy);
Node cx=val[num[fy]]-val[num[fx]-1],cy=val[num[fx]+cnt]-val[num[fy]-1];
printf("%0.5lf\n",min((tx+cx+ty).delta(),(tx+cy+ty).delta()));
}
}
}
}
int main() {
n=Get_Int();
m=Get_Int();
for(int i=1; i<=n; i++) {
int x=Get_Int(),y=Get_Int();
a[i]=Node(x,y);
}
for(int i=1; i<=m; i++) {
int x=Get_Int(),y=Get_Int();
AddEdge(x,y);
AddEdge(y,x);
}
if(m==n-1)Tree::solve();
else Circle::solve();
return 0;
}
|
