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| #include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int maxn = 1e+5 + 5;
const double eps = 1e-7;
struct edge {
int to, nxt;
}e[maxn << 1];
int n, m, ptr, lnk[maxn];
int F[maxn][19], inc[maxn], dep[maxn], w[maxn];
double x[maxn], y[maxn];
struct data
{
int n;
double x, y, x2, y2, xy;
data() {
n = 0;
x = y = x2 = y2 = xy = 0;
}
data(double x_, double y_) {
n = 1;
x = x_; y = y_;
x2 = x * x; y2 = y * y;
xy = x * y;
}
data(int n_, double x_, double y_, double x2_, double y2_, double xy_) {
n = n_; x = x_; y = y_; x2 = x2_; y2 = y2_; xy = xy_;
}
data operator + (const data &rhs) {
return data(n + rhs.n, x + rhs.x, y + rhs.y, x2 + rhs.x2, y2 + rhs.y2, xy + rhs.xy);
}
data operator - (const data &rhs) {
return data(n - rhs.n, x - rhs.x, y - rhs.y, x2 - rhs.x2, y2 - rhs.y2, xy - rhs.xy);
}
inline double AVGx() {
return x / (double)n;
}
inline double AVGy() {
return y / (double)n;
}
inline double A() {
double ax = AVGx();
return x2 - 2.0 * ax * x + n * ax * ax;
}
inline double B() {
double ax = AVGx(), ay = AVGy();
return 2.0 * ay * x + 2.0 * ax * y - 2.0 * xy - 2.0 * n * ax * ay;
}
inline double C() {
double ay = AVGy();
return y2 - 2.0 * ay * y + n * ay * ay;
}
inline double sigma() {
if (n == 1) return 0;
double a = A(), b = B(), c = C();
double sq = sqrt(a * a + b * b + c * c - 2 * a * c);
double sig1 = (a + c + sq) / 2, sig2 = (a + c - sq) / 2;
if (sig1 > sig2) swap(sig1, sig2);
return sig1 > -eps ? sig1 : sig2;
}
}d[maxn];
inline void add(int bgn, int end) {
e[++ptr] = (edge){end, lnk[bgn]};
lnk[bgn] = ptr;
}
inline int rd() {
register int x = 0, f = 0, c = getchar();
while (!isdigit(c)) {
if (c == '-') f = 1;
c = getchar();
}
while (isdigit(c)) x = x * 10 + (c ^ 48), c = getchar();
return f ? -x : x;
}
namespace SolveTree {
void dfs(int x) {
dep[x] = dep[F[x][0]] + 1;
for (int i = 1; i <= 17; ++i)
F[x][i] = F[F[x][i - 1]][i - 1];
for (int p = lnk[x]; p; p = e[p].nxt) {
int y = e[p].to;
if (y == F[x][0]) continue;
d[y] = d[y] + d[x];
F[y][0] = x;
dfs(y);
}
}
inline int lca(int x, int y) {
if (dep[x] > dep[y]) swap(x, y);
for (int i = 17; ~i; --i)
if (dep[F[y][i]] >= dep[x]) y = F[y][i];
if (x == y) return x;
for (int i = 17; ~i; --i)
if (F[y][i] ^ F[x][i]) y = F[y][i], x = F[x][i];
return F[x][0];
}
void main() {
dfs(1);
int Q = rd(), u, v;
while (Q--) {
u = rd(); v = rd(); int LCA = lca(u, v);
data res = d[u] + d[v] - d[LCA] - d[F[LCA][0]];
printf("%.5lf\n", res.sigma());
}
}
}
namespace SolveCycle {
int cyc[maxn << 1], cptr, dfn, rev[maxn];
int cid[maxn << 1];
data cyd[maxn << 1];
bool findloop(int x, int fa) {
rev[++dfn] = x; inc[x] = 1;
for (int p = lnk[x]; p; p = e[p].nxt) {
int y = e[p].to;
if (y == fa) continue;
if (inc[y]) {
while (rev[dfn] != y) {
cyc[++cptr] = rev[dfn];
cid[rev[dfn]] = cptr;
--dfn;
}
cyc[++cptr] = y;
cid[y] = cptr;
return true;
} else if (findloop(y, x)) return true;
}
dfn--;
return (inc[x] = false);
}
void dfs(int x, int bel) {
w[x] = bel;
dep[x] = dep[F[x][0]] + 1;
for (int i = 1; i <= 17; ++i)
F[x][i] = F[F[x][i - 1]][i - 1];
for (int p = lnk[x]; p; p = e[p].nxt) {
int y = e[p].to;
if (y != F[x][0] && !cid[y]) {
d[y] = d[y] + d[x];
F[y][0] = x;
dfs(y, bel);
}
}
}
inline int lca(int x, int y) {
if (dep[x] > dep[y]) swap(x, y);
for (int i = 17; ~i; --i)
if (dep[F[y][i]] >= dep[x]) y = F[y][i];
if (x == y) return x;
for (int i = 17; ~i; --i)
if (F[y][i] ^ F[x][i]) y = F[y][i], x = F[x][i];
return F[x][0];
}
void main() {
findloop(1, 0);
for (int i = 1; i <= cptr; ++i) dfs(cyc[i], cyc[i]);
for (int i = 1; i <= cptr; ++i) cyc[i + cptr] = cyc[i];
for (int i = 1; i <= 2 * cptr; ++i) cyd[i] = cyd[i - 1] + d[cyc[i]];
int Q = rd(), u, v;
while (Q--) {
u = rd(); v = rd();
if (w[u] == w[v]) {
int LCA = lca(u, v);
data res = d[u] + d[v] - d[LCA] - d[F[LCA][0]];
printf("%.6lf\n", res.sigma());
} else {
int anu = w[u], anv = w[v];
data resu = d[u] - d[anu], resv = d[v] - d[anv];
if (cid[anu] > cid[anv]) swap(anu, anv);
data pre1 = cyd[cid[anv]] - cyd[cid[anu] - 1];
data pre2 = cyd[cid[anu] + cptr] - cyd[cid[anv] - 1];
printf("%.5lf\n", min((resu + resv + pre1).sigma(), (resu + resv + pre2).sigma()));
}
}
}
}
int main() {
n = rd(); m = rd();
for (int i = 1; i <= n; ++i) {
x[i] = rd();
y[i] = rd();
d[i] = data(x[i], y[i]);
}
int u, v;
for (int i = 1; i <= m; ++i) {
u = rd(); v = rd();
add(u, v);
add(v, u);
}
if (m == n - 1) {
SolveTree::main();
} else {
SolveCycle::main();
}
return 0;
}
|
