挑战程序竞赛系列（91）：3.6凸包（2）

挑战程序竞赛系列（91）：3.6凸包（2）

传送门：POJ 1113: Wall

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题意参考hankcs：
http://www.hankcs.com/program/algorithm/poj-1113-wall.html

题意：

墙：有个愚蠢的皇帝要你造墙将城堡围起来，城堡的顶点有N个，墙必须离城堡的边至少L单位远，并且墙的总长度尽量小。求此长度？

所以求最大凸包把所有的点都围起来即可，但是为了保证围墙的距离最少，拐点用半径为L的圆包围起来，此题巧妙之处在于，凸包的所有踵点的周长实际就是一个圆的周长。

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.Arrays;import java.util.StringTokenizer;public class Main{    String INPUT = "./data/judge/201709/P1113.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    static final int MAX_N = 1000 + 16;    static final double PI = Math.acos(-1.0);    class P implements Comparable<P>{        int x;        int y;        P(int x, int y){            this.x = x;            this.y = y;        }        P sub(P a) {            return new P(x - a.x, y - a.y);        }        int det(P a) {            return x * a.y - y * a.x;        }        int dot(P a) {            return x * a.x + y * a.y;        }        @Override        public int compareTo(P o) {            return this.x != o.x ? this.x - o.x : this.y - o.y;        }    }    int N, L;    P[] ps;    double dist(P a, P b) {        return Math.sqrt(a.sub(b).dot(a.sub(b)));    }    P[] convexHull() {        Arrays.sort(ps);        P[] qs = new P[N * 2];        int k = 0;        for (int i = 0; i < N; qs[k++] = ps[i++]) {            while (k > 1 && qs[k - 1].sub(qs[k - 2]).det(ps[i].sub(qs[k - 1])) <= 0) k --;        }        for (int i = N - 2, t = k; i >= 0; qs[k++] = ps[i--]) {            while (k > t && qs[k - 1].sub(qs[k - 2]).det(ps[i].sub(qs[k - 1])) <= 0) k --;        }        P[] res = new P[k - 1];        System.arraycopy(qs, 0, res, 0, k - 1);        return res;    }    void solve() {        P[] qs = convexHull();        double res = 0;        int n = qs.length;        for (int i = 0; i < n; ++i) {            res += dist(qs[i], qs[(i + 1) % n]);        }        out.printf("%.0f\n", 2 * PI * L + res);    }    void read() {        N = ni();        L = ni();        ps = new P[N];        for (int i = 0; i < N; ++i) {            ps[i] = new P(ni(), ni());        }        solve();    }    FastScanner in;    PrintWriter out;    void run() throws IOException {        boolean oj;        try {            oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");        } 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);        }    }}