読者です 読者をやめる 読者になる 読者になる

天下一プログラマーコンテスト2016 予選B C - 天下一プログラマーコンテスト1999

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.NoSuchElementException;

/*
                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
            pass System Test!
*/

public class Main {
  private static class Task {

    void solve(FastScanner in, PrintWriter out) {
      int N = in.nextInt();
      String[] pq = in.next().split("/");
      double p = Double.parseDouble(pq[0]) / Double.parseDouble(pq[1]);
      int[][] A = in.nextIntMap(N, N);

      int[] win = new int[N];
      for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) win[i] += A[i][j];

      // 正しい順位表
      int[] leaderBoard = new int[N];
      {
        ArrayList<int[]> tmp = new ArrayList<>();
        for (int i = 0; i < N; i++) {
          tmp.add(new int[]{win[i], i});
        }
        Collections.sort(tmp, (o1, o2) -> o1[0] == o2[0] ? Integer.compare(o1[1], o2[1]) : -Integer.compare(o1[0], o2[0]));
        Collections.reverse(tmp);
        for (int i = 0; i < N; i++) leaderBoard[i] = tmp.get(i)[1];
      }

      // dp[i][q] := i 番目の人が q 勝利したと記録されている確率
      double[][] dp = new double[N][N + 1];
      for (int i = 0; i < N; i++) {
        double[] dpi = dp[i];
        dpi[0] = 1.0;
        for (int j = 0; j < N; j++) {
          if (i == j) continue;

          double[] next = new double[N + 1];
          for (int winNum = 0; winNum < N; winNum++) {
            if (A[i][j] == 1) {
              next[winNum + 1] += dpi[winNum] * p;
              next[winNum] += dpi[winNum] * (1 - p);
            }
            if (A[i][j] == 0) {
              next[winNum + 1] += dpi[winNum] * (1 - p);
              next[winNum] += dpi[winNum] * p;
            }
          }
          dpi = next;
        }
        dp[i] = dpi;
      }

      // dpWin[x][y] := 下から x までの順位が正しく記録されていて、 x の勝数が y と記録されている確率
      double[][] dpWin = new double[N + 1][N + 1];
      dpWin[leaderBoard[0]] = dp[leaderBoard[0]];
      for (int i = 1; i < N; i++) {
        int pre = leaderBoard[i - 1];
        int cur = leaderBoard[i];

        for (int preWinNum = 0; preWinNum < N; preWinNum++)
          for (int curWinNum = preWinNum; curWinNum < N; curWinNum++) {
            if (preWinNum == curWinNum && cur > pre) continue;
            dpWin[cur][curWinNum] += dpWin[pre][preWinNum] * dp[cur][curWinNum];
          }

      }

      double total = 0.0;
      for (int winNum = 0; winNum < N + 1; winNum++) total += dpWin[leaderBoard[N - 1]][winNum];
      out.println(total);
    }
  }

  /**
   * ここから下はテンプレートです。
   */
  public static void main(String[] args) {
    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 int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }

    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;
    }
  }
}