CS Academy Round #34 Point in Kgon

問題

https://csacademy.com/contest/archive/task/point-in-kgon/

解法

これを見ました。
http://kmjp.hatenablog.jp/entry/2017/06/23/0930

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

public class Main {

  private final int MOD = (int) (1e9 + 7);
  private final Combination combination = new Combination(400001, MOD);

  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    int K = in.nextInt();
    long[] X = new long[N * 2];
    long[] Y = new long[N * 2];
    for (int i = 0; i < N; i++) {
      X[i] = in.nextInt();
      Y[i] = in.nextInt();
    }

    int px = in.nextInt();
    int py = in.nextInt();
    for (int i = 0; i < N; i++) {
      X[i] -= px;
      Y[i] -= py;
      X[i + N] = X[i];
      Y[i + N] = Y[i];
    }

    long ans = combination.get(N, K);
    int right = 0;
    for (int left = 0; left < N; left++) {
      right = Math.max(right, left + 1);
      while (right < left + N && X[left] * Y[right] - Y[left] * X[right] >= 0) {
        right++;
      }
      ans += MOD - combination.get(right - left - 1, K - 1);
      ans %= MOD;
    }

    out.println(ans % MOD);
  }

  class Combination {

    private long[] fact;
    private long[] invFact;
    private int MOD;

    public Combination(int max, int MOD) {
      this.MOD = MOD;
      long[] inv = new long[max + 1];
      fact = new long[max + 1];
      invFact = new long[max + 1];
      inv[1] = 1;
      for (int i = 2; i <= max; i++) {
        inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
      }
      fact[0] = invFact[0] = 1;
      for (int i = 1; i <= max; i++) {
        fact[i] = fact[i - 1] * i % MOD;
      }
      for (int i = 1; i <= max; i++) {
        invFact[i] = invFact[i - 1] * inv[i] % MOD;
      }
    }

    public long get(int x, int y) {
      if (x < y || y < 0) {
        return 0;
      }
      return fact[x] * invFact[y] % MOD * invFact[x - y] % MOD;
    }
  }

  public static void main(String[] args) {
    PrintWriter out = new PrintWriter(System.out);
    new Main().solve(new FastScanner(), 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;
    }
  }
}