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Cod sursa(job #93409)
#include <cstdio>
#include <vector>
#include <algorithm>
#include <cmath>
#include <memory.h>
#include <queue>
using namespace std;
const char iname[] = "adapost.in";
const char oname[] = "adapost.out";
#define MAX_N 400
#define sqr(z) ((z) * (z))
int n;
double S[MAX_N][2], A[MAX_N][2], D[MAX_N][MAX_N];
vector <double> V;
vector <int> G[MAX_N], H[MAX_N * 2 + 5];
queue <int> Q;
int l[MAX_N], r[MAX_N], u[MAX_N];
int C[MAX_N * 2 + 5][MAX_N * 2 + 5];
void read_in(void)
{
scanf("%d", &n);
for (int i = 0; i < n; ++ i)
scanf("%lf %lf", &S[i][0], &S[i][1]);
for (int i = 0; i < n; ++ i)
scanf("%lf %lf", &A[i][0], &A[i][1]);
}
int pairup(int n)
{
if (u[n] != -1)
return 0;
u[n] = 1;
vector <int>::iterator it;
for (it = G[n].begin(); it != G[n].end(); ++ it) {
if (l[*it] == -1) {
l[*it] = n;
r[n] = *it;
return 1;
}
}
for (it = G[n].begin(); it != G[n].end(); ++ it) {
if (pairup(l[*it])) {
l[*it] = n;
r[n] = *it;
return 1;
}
}
return 0;
}
int solve(const double max_cost)
{
int cnt = 0;
for (int i = 0; i < n; ++ i) {
l[i] = r[i] = u[i] = -1;
vector <int> ().swap(G[i]);
}
for (int s = 0; s < n; ++ s) {
for (int a = 0; a < n; ++ a) if (max_cost >= D[s][a])
G[s].push_back(a);
}
for (int i = 0; i < n; ++ i) {
if (!pairup(i)) {
memset(u, -1, sizeof(u));
cnt += pairup(i);
} else
cnt ++;
}
return cnt;
}
double bellman_ford(const double max_cost)
{
for (int s = 0; s < n; ++ s) {
for (int a = 0; a < n; ++ a)
if (::D[s][a] <= max_cost) {
H[s + 1].push_back(n + a + 1);
H[n + a + 1].push_back(s + 1);
C[s + 1][n + a + 1] = 1;
}
}
for (int s = 1; s <= n; ++ s)
H[0].push_back(s), C[0][s] = 1;
for (int a = n + 1; a <= 2 * n; ++ a)
H[a].push_back(2 * n + 1), C[a][2 * n + 1] = 1;
double D[2 * MAX_N + 5];
int T[2 * MAX_N + 5];
for (int stp = 1; stp <= n; ++ stp) {
for (int i = 1; i <= 2*n+1; ++ i) {
D[i] = 1e9;
T[i] = -1;
}
D[0] = 0;
Q.push(0);
while (!Q.empty()) {
int x = Q.front();
Q.pop();
for (size_t i = 0; i < H[x].size(); ++ i) {
int y = H[x][i];
if (C[x][y] != 1)
continue ;
double cost_of_edge;
if (!x || y == 2*n+1)
cost_of_edge = 0;
else if (x <= n)
cost_of_edge = ::D[x - 1][y - n - 1];
else if (x >= n + 1)
cost_of_edge = -(::D[y - 1][x - n - 1]);
if (D[y] > D[x] + cost_of_edge) {
D[y] = D[x] + cost_of_edge;
T[y] = x;
Q.push(y);
}
}
}
for (int x = 2*n+1; x != 0; x = T[x]) {
if (T[x] == 0 || x == 2*n+1)
C[T[x]][x] = 0;
else {
C[T[x]][x] = C[T[x]][x] == 1 ? 0 : 1;
C[x][T[x]] = C[x][T[x]] == 1 ? 0 : 1;
}
}
}
double res = 0;
for (int x = 1; x <= n; ++ x) {
for (size_t i = 0; i < H[x].size(); ++ i) {
int y = H[x][i];
res += ::D[x - 1][y - n - 1] * (1 - C[x][y]);
}
}
return res;
}
int main(void)
{
freopen(iname, "r", stdin);
freopen(oname, "w", stdout);
read_in();
for (int i = 0; i < n; ++ i) {
for (int j = 0; j < n; ++ j) {
D[i][j] = sqrt(sqr(S[i][0] - A[j][0]) + sqr(S[i][1] - A[j][1]));
V.push_back(D[i][j]);
}
}
sort(V.begin(), V.end());
int delta, k;
for (delta = 1; delta < n * n; delta <<= 1) ;
for (k = 0; delta; delta >>= 1) {
if ((k + delta) < n * n && solve(V[k + delta]) < n)
k += delta;
}
if (solve(V[k]) < n)
k ++;
printf("%.5lf %.5lf", V[k], bellman_ford(V[k]));
return 0;
}