AOJ 2644 Longest Match

問題

Longest Match | Aizu Online Judge

解法

SuffixArray を作ると、Sに含まれる a の SuffixArray 上での lower_bound と upper_bound を求めることができます。その中で最も前のものを求めたいですが、これはRMQで持っておけば良いです。

b については上記の問題をすべて反転させた文字列で行えば同じ問題になります。

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

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

public class Main {
  private static class Task {

    void solve(FastScanner in, PrintWriter out) throws Exception {
      String S = in.next();
      SuffixArray sa = new SuffixArray(S);
      SuffixArray reverseSA = new SuffixArray(new StringBuilder(S).reverse().toString());

      int N = S.length();
      RMQ rmq = new RMQ(N + 1);
      RMQ reverseRMQ = new RMQ(N);
      for (int i = 0; i <= N; i++) {
        rmq.update(i, sa.sa[i]);
        reverseRMQ.update(i, reverseSA.sa[i]);
      }

      int Q = in.nextInt();
      for (int q = 0; q < Q; q++) {
        String x = in.next();
        String y = new StringBuilder(in.next()).reverse().toString();

        int low = sa.lowerBound(x);
        if (low == -1) {
          out.println(0);
          continue;
        }
        int up = sa.upperBound(x);

        int reverseLow = reverseSA.lowerBound(y);
        if (reverseLow == -1) {
          out.println(0);
          continue;
        }
        int reverseUp = reverseSA.upperBound(y);

        long s = rmq.query(low, up);
        long t = N - reverseRMQ.query(reverseLow, reverseUp);
        if (s + x.length() <= t && s <= t - y.length()) {
          out.println(t - s);
        } else {
          out.println(0);
        }

      }
    }

    class RMQ {
      private long INF = (long) 1e18;
      private int N;
      private long[] seg;

      RMQ(long[] array) {
        N = Integer.highestOneBit(array.length) * 2;
        seg = new long[N * 2];
        Arrays.fill(seg, INF);
        for (int i = 0; i < array.length; i++) update(i, array[i]);
      }

      RMQ(int M) {
        N = Integer.highestOneBit(M) * 2;
        seg = new long[N * 2];
        Arrays.fill(seg, INF);
      }

      void update(int k, long value) {
        seg[k += N - 1] = value;
        while (k > 0) {
          k = (k - 1) / 2;
          seg[k] = Math.min(seg[k * 2 + 1], seg[k * 2 + 2]);
        }
      }

      //[a, b)
      long query(int a, int b) {
        return query(a, b, 0, 0, N);
      }

      long query(int a, int b, int k, int l, int r) {
        if (r <= a || b <= l) return INF;
        if (a <= l && r <= b) return seg[k];
        long x = query(a, b, k * 2 + 1, l, (l + r) / 2);
        long y = query(a, b, k * 2 + 2, (l + r) / 2, r);
        return Math.min(x, y);
      }
    }

    class SuffixArray {
      String S;
      int N, K;
      Integer[] sa;
      int[] rank;
      public SuffixArray(String S) {
        this.S = S;
        build();
      }

      private void build() {
        N = S.length();
        rank = new int[N + 1];
        sa = new Integer[N + 1];
        for (int i = 0; i <= N; i++) {
          sa[i] = i;
          rank[i] = i < N ? S.charAt(i) : -1;
        }

        int[] tmp = new int[N + 1];
        for (int _k = 1; _k <= N; _k *= 2) {
          final int k = _k;
          Arrays.sort(sa, new Comparator<Integer>() {
            @Override
            public int compare(Integer i, Integer j) {
              return compareNode(i, j, k);
            }
          });
          tmp[sa[0]] = 0;
          for (int i = 1; i <= N; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + ((compareNode(sa[i - 1], sa[i], k) < 0) ? 1 : 0);
          }
          for (int i = 0; i <= N; i++) {
            rank[i] = tmp[i];
          }
        }
      }

      private int compareNode(int i, int j, int k) {
        if (rank[i] != rank[j]) {
          return rank[i] - rank[j];
        } else {
          int ri = i + k <= N ? rank[i + k] : -1;
          int rj = j + k <= N ? rank[j + k] : -1;
          return ri - rj;
        }
      }

      public int lowerBound(String t) {
        int a = -1, b = S.length();
        while (b - a > 1) {
          int c = (a + b) / 2;
          String sub = S.substring(sa[c], Math.min(t.length() + sa[c], S.length()));
          if (sub.compareTo(t) < 0)
            a = c;
          else
            b = c;
        }
        String sub = S.substring(sa[b], Math.min(t.length() + sa[b], S.length()));
        return sub.compareTo(t) == 0 ? b : -1;
      }

      public int upperBound(String t) {
        int a = -1, b = S.length() + 1;
        while (b - a > 1) {
          int c = (a + b) / 2;
          String sub = S.substring(sa[c], Math.min(t.length() + sa[c], S.length()));
          if (sub.compareTo(t) <= 0)
            a = c;
          else
            b = c;
        }
        return b;
      }
    }
  }

  /**
   * 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;
    }
  }
}