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This syntax, with its multiple sets of square brackets, fits right in with the syntax used to declare and construct the array of arrays So why is an array of arrays sometimes called a jagged array Figure 7-4 shows the various objects you would end up with if you called the method in Example 7-20, passing the events from Example 7-10, asking for five days of events starting from July 11 The figure is laid out to show each child array as a row, and as you can see, the rows are not all the same length the first couple of days have two items per row, the third day has one, and the last two are empty (ie, they are zero-length arrays) So rather than looking like a neat rectangle of objects, the rows form a shape with a somewhat uneven or jagged righthand edge.

This jaggedness can be either a benefit or a problem, depending on your goals In this example, it s helpful we used it to handle the fact that the number of events in our calendar may be different every day, and some days may have no events at all But if you re working with information that naturally fits into a rectangular structure (eg, pixels in an image), rows of differing lengths would constitute an error it would be better to use a data structure that doesn t support such things, so you don t have to work out how to handle such an error Moreover, jagged arrays end up with a relatively complicated structure there are a lot of objects in Figure 7-4.

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Each array is an object distinct from the objects its element refers to, so we ve ended up with 11 objects: the five events, the five per-day arrays (including two zero-length arrays), and then one array to hold those five arrays In situations where you just don t need this flexibility, there s a simpler way to represent multiple rows: a rectangular array..

A rectangular array lets you store multidimensional data in a single array, rather than needing to create arrays of arrays. They are more regular in form than jagged arrays in a two-dimensional rectangular array, every row has the same width.

In Advances in Cryptology CRYPTO 95: 15th Annual International Cryptology Conference, Santa Barbara, California, USA, August 1995, Proceedings (LNCS 963), ed Don Coppersmith, 197 207 Berlin: Springer-Verlag Long, Johnny 2004 Google hacking for penetration testers Rockland, MA: Syngress Publishing Lunt, Teresa F 1988 Automated audit trail analysis and intrusion detection: A survey In Proceedings of the 11th National Computer Security Conference, Baltimore, Maryland 1993 A survey of intrusion detection techniques Computers and Security 12 (4): 405 418 Malkhi, Dahlia, and Michael K Reiter 1997 Byzantine quorum systems In Proceedings of the 29th Annual ACM Symposium on Theory of Computing, 569 578 New York: ACM Press Maor, Ofer, and Amichai Shulman 2003 Blind SQL injection Imperva, September wwwimpervacom/application_defense_center/white_papers/blind_sql_server_injection html..

Rectangular arrays are also sometimes called multidimensional arrays, but that s a slightly confusing name, because jagged arrays also hold multidimensional data.

Rectangular arrays tend to suit different problems than jagged arrays, so we need to switch temporarily to a different example. Suppose you were writing a simple game in which a character runs around a maze. And rather than going for a typical modern 3D game rendered from the point of view of the player, imagine something a bit more retro a basic rendering of a top-down view, and where the walls of the maze all fit neatly onto a grid. If you re too young to remember this sort of thing, Figure 7-5 gives a rough idea of what passed for high-tech entertainment back when your authors were at school.

We don t want to get too hung up on the details of the game play, so let s just assume that our code needs to know where the walls are in order to work out where the player can or can t move next, and whether she has a clean shot to take out the baddies chasing her through the maze. We could represent this as an array of numbers, where 0 represents a gap and 1 represents a wall, as Example 7-21 shows. (We could also have used bool instead of int as the element type, as there are only two possible options: a wall or no wall. However, using true and false would have prevented each row of data from fitting on a single row in this book, making it much harder to see how Example 7-21 reflects the map in Figure 7-5. Moreover, using numbers leaves open the option to add exciting game features such as unlockable doors, squares of instant death, and other classics.)

int[,] walls = { { 1, 1, 1, { 0, 0, 1, { 1, 0, 1, { 1, 0, 0, { 1, 0, 1, { 1, 0, 1, { 1, 0, 1, { 1, 0, 1, { 1, 0, 1, { 1, 0, 1, { 1, 0, 0, { 1, 1, 1, }; new int[,] 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1 1 1 1 1 0 1 1 1 1 1 1 }, }, }, }, }, }, }, }, }, }, }, }

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