Character Recognition

This problem requires you to write a program that performs character recognition.

Each ideal character image has 20 lines of 20 digits. Each digit is a '0' or a '1'. See Figure 1a (way below) for the layout of character images in the file.

The file font.in contains representations of 27 ideal character images in this order:

_abcdefghijklmnopqrstuvwxyz

where _ represents the space character. Each ideal character is 20 lines long.

The input file contains one or more potentially corrupted character images. A character image might be corrupted in these ways:

• at most one line might be duplicated (and the duplicate immediately follows)
• at most one line might be missing
• some 0's might be changed to 1's
• some 1's might be changed to 0's.

No character image will have both a duplicated line and a missing line. No more than 30% of the 0's and 1's will be changed in any character image in the evaluation datasets.

In the case of a duplicated line, one or both of the resulting lines may have corruptions, and the corruptions may be different.

Write a program to recognize the sequence of one or more characters in the image provided in the input file using the font provided in file font.in.

Recognize a character image by choosing the font character images that require the smallest number of overall changed 1's and 0's to be corrupted to the given font image, given the most favourable assumptions about duplicated or omitted lines. Count corruptions in only the least corrupted line in the case of a duplicated line. You must determine the sequence of characters that most closely matches the input sequence (the one that requires the least number of corruptions). There is a unique best solution for each evaluation dataset.

A correct solution will use precisely all of the data supplied in the input file.

PROGRAM NAME: charrec

INPUT FORMAT (both input files)

Both input files begin with an integer N (19 <= N < 1200) that specifies the number of lines that follow:

N
(digit1)(digit2)(digit3) ... (digit20)
(digit1)(digit2)(digit3) ... (digit20)
...

Each line of data is 20 digits wide. There are no spaces separating the zeros and ones.

The file font.in describes the font. It will always contain 541 lines. It may differ for each evaluation dataset.

SAMPLE INPUT (file charrec.in)

• Incomplete sample showing the beginning of font.in (space and a).

  540
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000011100000000000
  00000111111011000000
  00001111111001100000
  00001110001100100000
  00001100001100010000
  00001100000100010000
  00000100000100010000
  00000010000000110000
  00000001000001110000
  00001111111111110000
  00001111111111110000
  00001111111111000000
  00001000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000000000000000000
  

  Figure 1a: font.in

• Sample charrec.in, showing an a corrupted

  19
  00000000000000000000
  00000000000000000000
  00000000000000000000
  00000011100000000000
  00100111011011000000
  00001111111001100000
  00001110001100100000
  00001100001100010000
  00001100000100010000
  00000100000100010000
  00000010000000110000
  00001111011111110000
  00001111111111110000
  00001111111111000000
  00001000010000000000
  00000000000000000000
  00000000000001000000
  00000000000000000000
  00000000000000000000
  

  Figure 1b: charrec.in

OUTPUT FORMAT

Your program must produce an output file that contains a single string of the characters recognized. Its format is a single line of ASCII text. The output should not contain any separator characters. If your program does not recognize a particular character, it must output a ? in the appropriate position.

SAMPLE OUTPUT (file charrec.out)

a

Note that the 'sample output' formerly displayed a blank followed by an 'a', but that seems wrong now.