HackerRank HourRank 11 - LCS Returns

問題

www.hackerrank.com

文字列 a と b が与えられる。a と b の LCS を増やすように a の好きな場所に好きな文字を 1 文字だけ挿入するような場所と文字の組み合わせはいくつあるか。

解法

A[i] と A[i+1] の間に文字 c を挿入することを考える。この時、LCS が増えるためには LCS(A[0..i], B[0..p-1]) + LCS(A[i+1..N-1], B[p+1..M-1]) = LCS であり、かつ、B[p] が c と同じ文字でなければならない。

コード

package hackerrank.hourrank11;

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 B {
  private static class Task {

    //文字列を62進数に変える
    int[] string2IntArray(String a) {
      int N = a.length();
      int[] A = new int[N];
      for (int i = 0; i < N; i++) {
        char c = a.charAt(i);
        if (c >= 'a' && c <= 'z') A[i] = c - 'a';
        else if (c >= 'A' && c <= 'Z') A[i] = c - 'A' + 26;
        else A[i] = c - '0' + 52;
      }
      return A;
    }

    void solve(FastScanner in, PrintWriter out) {
      String a = in.next();
      String b = in.next();
      int N = a.length();
      int M = b.length();
      int[] A = string2IntArray(a);
      int[] B = string2IntArray(b);

      int[][] dpl = new int[N + 1][M + 1];//左からのLCS
      int[][] dpr = new int[N + 1][M + 1];//右からのLCS

      //左からLCSを求めるDP
      for (int i = 0; i < N; i++)
        for (int j = 0; j < M; j++) {
          if (A[i] == B[j]) {
            dpl[i + 1][j + 1] = Math.max(dpl[i + 1][j + 1], dpl[i][j] + 1);
          }
          dpl[i + 1][j + 1] = Math.max(dpl[i + 1][j + 1], dpl[i][j + 1]);
          dpl[i + 1][j + 1] = Math.max(dpl[i + 1][j + 1], dpl[i + 1][j]);
        }

      int LCS = dpl[N][M];

      //右からLCSを求めるDP
      for (int i = N - 1; i >= 0; i--)
        for (int j = M - 1; j >= 0; j--) {
          if (A[i] == B[j]) {
            dpr[i][j] = Math.max(dpr[i][j], dpr[i + 1][j + 1] + 1);
          }
          dpr[i][j] = Math.max(dpr[i][j], dpr[i + 1][j]);
          dpr[i][j] = Math.max(dpr[i][j], dpr[i][j + 1]);
        }

      assert LCS == dpr[0][0];

      long ans = 0;
      //A[i] と A[i+1] の間に c を挿入する
      //左側はA[i] と B[p-1] までのLCS
      //右側はA[i+1] と B[p+1] までの LCS
      for (int i = -1; i < N; i++) {
        for (int c = 0; c < 62; c++) {
          //LCS を更新するかどうかチェック
          for (int p = 0; p < M; p++) {
            if (c != B[p]) continue;
            if (dpl[i + 1][p] + dpr[i + 1][p + 1] == LCS) {
              ans++;
              break;
            }
          }
        }
      }

      out.println(ans);

    }
  }

  /**
   * テンプレート
   */
  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 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;
    }
  }
}