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54 Exploring Abstractions: Information Structures Exercises 1. ••• Express the idea of a list such as we constructed using [.... ] from an abstract point of view, along the lines of how we described an abstract array. 2. •••• A stack is an abstraction with a behavior informally described as follows: A stack is a repository for data items. When the stack is first created, the stack contains no items. Item are inserted one at a time using the push method and removed one at a time using the pop method.

This is the so-called binary representation (not to be confused with binary relations). Each bit in a binary representation represents a specific power of 2 and the number itself is derived by summing the various powers of two. e. 32 +0 +0 + 4 +0 + 1 The appeal of the binary representation is that it is complete: every natural number can be represented in this way, and it is simple: a choice of one of two values for each power of two is all that is necessary. An enumeration of the binary numerals for successive natural numbers reveals a pleasing pattern: 0 1 2 3 4 5 6 7 8 0 1 10 11 100 101 110 111 1000 ...

An image will not usually be homogeneous, but will instead consist of regions that are largely black or largely white. Let us use the following 16-by-16 pixel image of a familiar icon as an example: Figure 20: 16 x 16 pixel image of yin-yang icon The quad-tree is formed by recursively sub-dividing the image into four quadrants, subdividing those quadrants into sub-quadrants, and so on, until a quadrant contains only black or only white pixels. The sub-divisions of a region are the four sub-trees of a tree representing the entire region.

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Computer science: abstraction to implementation by Keller R.

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