挑战程序竞赛系列（93）：3.6凸包（4）

挑战程序竞赛系列（93）：3.6凸包（4）

传送门：POJ 3608: Bridge Across Islands

题意：

跨岛大桥：在两个凸包小岛之间造桥，求最小距离？



思路：

旋转卡壳法，两个凸包分别记作P和Q，对于P中的每一条边，计算和Q中的每个点对应的最小面积，在最小面积的情况下，计算两条边之间的最短距离，或者点到直线的最短距离。



一开始以为给定凸包的点是无序，实际上已经按照凸包排好序了，所以拿过来直接旋转卡壳求解即可。

代码如下：

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main{

String INPUT = "./data/judge/201710/P3608.txt";

public static void main(String[] args) throws IOException {
new Main().run();
}

static final int INF = 0x3f3f3f3f;
static final double EPS = 1e-8;

class P implements Comparable<P>{

double x;
double y;

P(double x, double y){
this.x = x;
this.y = y;
}

P sub(P a) {
return new P(x - a.x, y - a.y);
}

double det(P a) {
return x * a.y - y * a.x;
}

@Override
public int compareTo(P o) {
return Double.compare(x, o.x) == 0 ? Double.compare(y, o.y) : Double.compare(x, o.x);
}

@Override
public String toString() {
return x + "," + y;
}
}

int N, M;
P[] p;
P[] q;

double dist(P a, P b) {
double dx = a.x - b.x;
double dy = a.y - b.y;
return Math.sqrt(dx * dx + dy * dy);
}

// ab 垂直 ac
double verticle(P a, P b, P c) {
return (b.x - a.x) * (c.x - a.x) + (b.y - a.y) * (c.y - a.y);
}

double cross(P a, P b, P c) {
return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}

// 点c到直线ab的最短距离
double min(P a, P b, P c) {
if (dist(a, b) < EPS) return dist(b, c);
if (verticle(a, b, c) < EPS) return dist(a, c);
if (verticle(b, a, c) < EPS) return dist(b, c);
return Math.abs(cross(a, b, c) / dist(a, b));
}

double min(P a, P b, P c, P d) {
return Math.min(Math.min(min(a, b, c), min(a, b, d)), Math.min(min(c, d, a), min(c, d, b)));
}

double solve(P[] a, P[] b, int n, int m) {

P[] ps = new P[n + 1];
P[] qs = new P[m + 1];
System.arraycopy(a, 0, ps, 0, n);
System.arraycopy(b, 0, qs, 0, m);

ps
= ps[0];
qs[m] = qs[0];

int ymin = 0;
int ymax = 0;

for (int i = 0; i < n; ++i) if (ps[i].y < ps[ymin].y) ymin = i;
for (int i = 0; i < m; ++i) if (qs[i].y > qs[ymax].y) ymax = i;

double ans = INF;
double tmp = 0.0;
for (int i = 0; i < n; ++i) {

while ((tmp = cross(ps[ymin + 1], qs[ymax + 1], ps[ymin]) - cross(ps[ymin + 1], qs[ymax], ps[ymin])) > EPS) {
ymax = (ymax + 1) % m;
}
if (tmp + EPS < 0) ans = Math.min(ans, min(ps[ymin], ps[ymin + 1], qs[ymax]));
else ans = Math.min(ans, min(ps[ymin], ps[ymin + 1], qs[ymax], qs[ymax + 1]));
ymin = (ymin + 1) % n;
}

return ans;
}

void read() {
while (true) {
N = ni();
M = ni();

if (N + M == 0) break;

p = new P
;
q = new P[M];

for (int i = 0; i < N; ++i) {
p[i] = new P(nd(), nd());
}

for (int i = 0; i < M; ++i) {
q[i] = new P(nd(), nd());
}

out.printf("%.5f\n", Math.min(solve(p, q, N, M), solve(q, p, M, N)));

}
}

FastScanner in;
PrintWriter out;

void run() throws IOException {
boolean oj;
try {
oj = ! System.getProperty("user.dir").equals("F:\\oxygen_workspace\\Algorithm");
} catch (Exception e) {
oj = System.getProperty("ONLINE_JUDGE") != null;
}

InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
in = new FastScanner(is);
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
read();
out.flush();
if (!oj){
System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");
}
}

public boolean more(){
return in.hasNext();
}

public int ni(){
return in.nextInt();
}

public long nl(){
return in.nextLong();
}

public double nd(){
return in.nextDouble();
}

public String ns(){
return in.nextString();
}

public char nc(){
return in.nextChar();
}

class FastScanner {
BufferedReader br;
StringTokenizer st;
boolean hasNext;

public FastScanner(InputStream is) throws IOException {
br = new BufferedReader(new InputStreamReader(is));
hasNext = true;
}

public String nextToken() {
while (st == null || !st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (Exception e) {
hasNext = false;
return "##";
}
}
return st.nextToken();
}

String next = null;
public boolean hasNext(){
next = nextToken();
return hasNext;
}

public int nextInt() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Integer.parseInt(more);
}

public long nextLong() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Long.parseLong(more);
}

public double nextDouble() {
if (next == null){
hasNext();
}
String more = next;
next = null;
return Double.parseDouble(more);
}

public String nextString(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more;
}

public char nextChar(){
if (next == null){
hasNext();
}
String more = next;
next = null;
return more.charAt(0);
}
}
}