Codecraft-17 and Codeforces Round #391 (Div. 1 + Div. 2, combined) D. Felicity's Big Secret Revealed

問題

http://codeforces.com/contest/757/problem/D

0と1からなるn文字の文字列が与えられます。この文字列の好きな位置（先頭や末尾も含むN+1個）に仕切りを入れることができます。仕切りはいくつ入れても構いませんが、同じ位置に2個以上入れることはできません。仕切りを入れ終わったら、仕切りに挟まれている数字を10進数になおし、setに入れます。setの最大の数字をmとした時に、setに1〜mが全て含まれているような仕切りの入れ方をvalidとします。validな仕切りの入れ方をmod 1e9+7 で答えてください。

解法

nが75以下なので、mは最大でも20であることが分かります。

次のようなbitDPを考えます。

dp[pos][status] := pos文字目まで見た時に、[1, 20] の数字を含む状態のbitが status であるような組合せ

どこから始めても良いので初期状態は dp[i][0]=1 (0<=i

コード

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

public class D {
  private final int MOD = (int) (1e9 + 7);
  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    String S = in.next();
    int M = 1 << 20;
    int[][] dp = new int[N + 1][M];
    for (int pos = 0; pos < N; pos++) {
      dp[pos][0] = 1;
    }
    for (int pos = 0; pos < N; pos++) {
      int cur = 0;
      for (int end = pos + 1; end <= N; end++) {
        cur = cur * 2 + (S.charAt(end - 1) - '0');
        if (cur > 20) break;
        if (cur == 0) continue;
        for (int state = 0; state < M; state++) {
          int next = state | (1 << (cur - 1));
          dp[end][next] += dp[pos][state];
          dp[end][next] %= MOD;
        }
      }
    }

    long ans = 0;
    for (int end = 0; end <= N; end++) {
      for (int h = 1; h <= 20; h++) {
        int state = (1 << h) - 1;
        ans += dp[end][state];
        ans %= MOD;
      }
    }
    out.println(ans);
  }

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