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lab11a
ISBN-10

We'll go over the following method with the lab-leader:

  /** Return how many occurrences of `target` occur in `s`.
   * @param s the string to search through
   * @param target the char to count.
   * @return how many occurrences of `target` occur in `s`.
   */
  int countOccurences( String s, char target ) {
    int seenSoFar = 0;
    int i=0;

    while (i < s.length()) {
      if (s.charAt(i) == target) {
         seenSoFar = seenSoFar + 1;
      }
      // else do nothing.

      i = i + 1;
    }
    return seenSoFar;

  }

Ten-digit book numbers — ISBN-10s — have the following “checksum” property:
the digits x₁x₂x₃…x₉x₁₀ have the property that
(1·x₁ + 2·x₂ + 3·x₃ + … + 9·x₉ + 10·x₁₀) % 11 = 0.
This scheme means ¹that if somebody mis-types a digit, or transposes two digits, a computer can recognize that an error has been made.

For example, for the ten digits "0306406152",

(

1·0

2·3

3·0

4·6

5·4

6·0

7·6

8·1

9·5

10·2

)

% 11

(

)

% 11

165 % 11

0 (since 11 goes into 165 fifteen times with remainder 0)

Thus "0306406152" is a valid ISBN-10.

Test case for you to try by hand, to understand what our code will have to do:
Which of these is a valid ISBN-10?

"0020300004"
"0010300007"
"0000000000"
"1000000000"
"1000000001"

By the way, mathemeticians have a concise way of writing this sum:

	10
(	Σ	i·x_i	)	mod 11 = 0
	i=1

You'll see this summation-notation if you look on (say) Wikipedia. Don't be intimidated; whenever you see a high-falutin’ “Σ”, just think about writing it out as a summation in your head. (In fact, you can think of math as being a programming-language that has a convenient syntax for loops that add.)

Write the following method:
class ISBNChecker { boolean isValidISBN10( String isbn ) { return false; // stub. } }
- From the countOccurences above, we see how to have a loop look at each character individually.
- Remember, though, that the third digit, x₃, occurs at index 2 of the string. Similarly, x₄ occurs at index 3. In general, the ith digit x_i of a string s is s.charAt( ).
- One thing we need to do in this problem is to convert a char into an int from 0..9. Here is a helper method you can use, to make your code more readable:
  int charToInt( char digit ) { return Integer.parseInt( Character.toString(digit) ); }

You'll be checked off on isValidISBN10 only. Here are some tests.

class ISBNCheckerTester {

  public static void main( String[] args ) {
    ISBNChecker looper = new ISBNChecker();
    System.out.println( "\nTest some okay (but contrived) ISBNs: " );
    checkExpect( looper.isValidISBN10("0000000000"), true  );
    checkExpect( looper.isValidISBN10("1000000001"), true  );
    checkExpect( looper.isValidISBN10("0100000002"), true  );
    checkExpect( looper.isValidISBN10("0010000003"), true  );
    checkExpect( looper.isValidISBN10("0001000004"), true  );
    checkExpect( looper.isValidISBN10("0000000019"), true  );
    checkExpect( looper.isValidISBN10("0000000027"), true  );
    checkExpect( looper.isValidISBN10("2000000010"), true  );
    checkExpect( looper.isValidISBN10("4000000020"), true  );
    checkExpect( looper.isValidISBN10("5000000080"), true  );
    System.out.println( "\nTest some real and incorrect ISBNs: " );
    checkExpect( looper.isValidISBN10("0306406152"), true  );
    checkExpect( looper.isValidISBN10("0306406162"), false );
    checkExpect( looper.isValidISBN10("0306406154"), false );
    checkExpect( looper.isValidISBN10("0553565699"), true  );
    checkExpect( looper.isValidISBN10("1553565699"), false );
  }

  static void checkExpect( boolean actual, boolean expected ) {
    if (actual == expected) {
      System.out.print(".");
    }
    else {
      System.out.println("failed test: expected " + expected + ", got " + actual );
    }
  }

}

Extra challenge: Actually, sometimes the check-digit works out to be 10. Since that won't fit into a single digit, in that case the letter 'X' is used (reminiscent of the roman numeral).

Fix your code above so that ISBN-10s ending in the letter 'X' are also recognized. (Hint: put your change inside charToInt.)

    System.out.println( "\nTest some X-digit ISBNs: " );
    checkExpect( looper.isValidISBN10("000000000X"), false );
    checkExpect( looper.isValidISBN10("050000000X"), true  );
    checkExpect( looper.isValidISBN10("000020000X"), true  );
    checkExpect( looper.isValidISBN10("300000002X"), true  );

Extra extra challenge: ISBN-10s are created by using 9 digits of “real” data, and then constructing the 10th digit so that the above property holds. The formula to compute the tenth digit ² is

That is, compute

Your task: Write char createCheckDigit( String isbnPart ).
Extra extra extra challenge: Can you modify isValidISBN10 so that it is much much shorter, by having it call createCheckDigit as a helper?
Extra extra extra extra challenge: Read about ISBN-13, and implement a verifier isValidISBN13 for that as well.
Then, write isValidISBN which can take a 10-digit or a 13-digit input, and return isValidISBN10 or isValidISBN13 as appropriate.

¹ In ITEC122, you'll learn why this is true. ↩

² You might wonder why this formula works; from what we saw above, shouldn't x₁₀ be the negative of that sum, so that ten times it will have the last digit cancel out the first nine? Yes! But in mod 11 (where we can subract a multiple of 11 without changing anything), ten times a number is equivalent to negative-one times that number. More on modular arithmetic in ITEC122. ↩

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©2009, Ian Barland, Radford University
Last modified 2009.Apr.07 (Tue) Please mail any suggestions
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lab11a ISBN-10

lab11a
ISBN-10