ACPC2016 Day2 G : Star
解法
正 N 角形から小さい二等辺三角形を N 個除けば良い。
コード
import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.NoSuchElementException; /* _ooOoo_ o8888888o 88" . "88 (| -_- |) O\ = /O ____/`---'\____ .' \\| |// `. / \\||| : |||// \ / _||||| -:- |||||- \ | | \\\ - /// | | | \_| ''\---/'' | | \ .-\__ `-` ___/-. / ___`. .' /--.--\ `. . __ ."" '< `.___\_<|>_/___.' >'"". | | : `- \`.;`\ _ /`;.`/ - ` : | | \ \ `-. \_ __\ /__ _/ .-` / / ======`-.____`-.___\_____/___.-`____.-'====== `=---=' ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ pass System Test! */ public class G { private static class Task { void solve(FastScanner in, PrintWriter out) throws Exception { int N = in.nextInt(); int K = in.nextInt(); Point a = new Point(1.0, 0.0); Point b = new Point(Math.cos(Math.PI * 2 / N), Math.sin(Math.PI * 2 / N)); Point pa = new Point(Math.cos(Math.PI * 2 / N * K), Math.sin(Math.PI * 2 / N * K)); Point pb = new Point(Math.cos(Math.PI * 2 / N * (1 - K)), Math.sin(Math.PI * 2 / N * (1 - K))); Point intersection = lineIntersection(a, pa, b, pb); Point ai = a.sub(intersection); Point bi = b.sub(intersection); double S = Math.abs(ai.det(bi)) / 2; double convex = Math.abs(a.det(b)) / 2 * N; out.print(convex - S * N); } private static double EPS = 2e-8; /** * Return the point which is intersection of line p1-p2 and q1-q2 * * @param p1 * @param p2 * @param q1 * @param q2 * @return */ public static Point lineIntersection(Point p1, Point p2, Point q1, Point q2) { double a = (q2.sub(q1)).det(q1.sub(p1)); double b = (q2.sub(q1)).det(p2.sub(p1)); return p1.add((p2.sub(p1)).multiply(a / b)); } /** * Return point p is on segment a-b * * @param a * @param b * @param p * @return */ public static boolean onSegment(Point a, Point b, Point p) { if (Math.abs(a.x - b.x) < EPS) return Math.min(a.y, b.y) <= p.y && p.y <= Math.max(a.y, b.y); double alpha = (b.y - a.y) / (b.x - a.x); double beta = a.y - alpha * a.x; return Math.abs(p.y - (alpha * p.x + beta)) < EPS && Math.min(a.x, b.x) <= p.x && p.x <= Math.max(a.x, b.x); } class Point implements Comparable<Point> { double x, y; Point(double x, double y) { this.x = x; this.y = y; } @Override public int compareTo(Point o) { if (this.x == o.x) return Double.compare(this.y, o.y); return Double.compare(this.x, o.x); } /** * 外戚を計算して返す * * @param p * @return */ public double det(Point p) { return x * p.y - y * p.x; } /** * 内積 * * @param p * @return */ public double dot(Point p) { return x * p.x + y * p.y; } public Point sub(Point p) { return new Point(x - p.x, y - p.y); } public Point add(Point p) { return new Point(x + p.x, y + p.y); } public Point multiply(double d) { return new Point(x * d, y * d); } } } /** * ここから下はテンプレートです。 */ public static void main(String[] args) throws Exception { OutputStream outputStream = System.out; FastScanner in = new FastScanner(); PrintWriter out = new PrintWriter(outputStream); Task solver = new Task(); solver.solve(in, out); out.close(); } private static class FastScanner { private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int bufferLength = 0; private boolean hasNextByte() { if (ptr < bufferLength) { return true; } else { ptr = 0; try { bufferLength = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (bufferLength <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } private void skipUnprintable() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; } boolean hasNext() { skipUnprintable(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } double nextDouble() { return Double.parseDouble(next()); } double[] nextDoubleArray(int n) { double[] array = new double[n]; for (int i = 0; i < n; i++) { array[i] = nextDouble(); } return array; } double[][] nextDoubleMap(int n, int m) { double[][] map = new double[n][]; for (int i = 0; i < n; i++) { map[i] = nextDoubleArray(m); } return map; } public int nextInt() { return (int) nextLong(); } public int[] nextIntArray(int n) { int[] array = new int[n]; for (int i = 0; i < n; i++) array[i] = nextInt(); return array; } public long[] nextLongArray(int n) { long[] array = new long[n]; for (int i = 0; i < n; i++) array[i] = nextLong(); return array; } public String[] nextStringArray(int n) { String[] array = new String[n]; for (int i = 0; i < n; i++) array[i] = next(); return array; } public char[][] nextCharMap(int n) { char[][] array = new char[n][]; for (int i = 0; i < n; i++) array[i] = next().toCharArray(); return array; } public int[][] nextIntMap(int n, int m) { int[][] map = new int[n][]; for (int i = 0; i < n; i++) { map[i] = nextIntArray(m); } return map; } } }