挑战程序竞赛系列（85）：3.6极限情况（2）

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/P1418.txt";

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

    static final double PI  = Math.acos(-1);
    static final double EPS = 5E-13;
    static final int MAX_N  = 102;

    class P{

        double x;
        double y;

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

    P[]   o = new P[MAX_N];                 // 圆心坐标
    double[] r = new double[MAX_N];         // 圆半径
    boolean[] visible = new boolean[MAX_N]; // 对应圆是否可见
    int N;

    double[] angle = new double[2 * MAX_N];
    int tot;

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

    double norm(double ang) {
        while (ang < 0) {
            ang += 2 * PI;
        }
        while (ang > 2 * PI) {
            ang -= 2 * PI;
        }
        return ang;
    }

    void solve() {
        Arrays.fill(visible, false);
        for (int i = 0; i < N; ++i) {
            tot = 0;
            angle[tot++] = 0;
            angle[tot++] = 2 * PI;

            for (int j = 0; j < N; ++j) {
                if (i == j) continue;
                double d = distance(o[i], o[j]);
                if (r[i] + r[j] < d || d < r[i] - r[j] || d < r[j] - r[i]) continue; // 包含或者不相交
                double phi = Math.atan2(o[j].y - o[i].y, o[j].x - o[i].x);
                double the = Math.acos((r[i] * r[i] + d * d - r[j] * r[j]) / (2 * r[i] * d));
                angle[tot++] = norm(phi - the);
                angle[tot++] = norm(phi + the);
            }

            Arrays.sort(angle, 0, tot);

            for (int j = 0; j < tot - 1; ++j) {
                double mid = (angle[j] + angle[j + 1]) / 2;

                double nx = 0; 
                double ny = 0;

                for (int t = -1; t < 2; t += 2) {
                    nx = o[i].x + (r[i] + t * EPS) * Math.cos(mid);
                    ny = o[i].y + (r[i] + t * EPS) * Math.sin(mid);

                    P np = new P(nx, ny);

                    int k = 0;
                    for (k = N - 1; k >= 0; --k) {
                        if (distance(np, o[k]) < r[k]) {
                            break;
                        }
                    }
                    if (k != -1)
                        visible[k] = true;
                }
            }
        }

        int ans = 0;
        for (int i = 0; i < N; ++i) {
            if (visible[i]) ans ++;
        }
        out.println(ans);
    }

    void read() {
        while (true) {
            N = ni();
            if (N == 0) break;

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

            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);
        }
    }
}