By Franklin Mendivil

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**Extra resources for Fractals, Graphs, and Fields**

**Example text**

We will systematically blur the distinction between items and containers. The previous paragraph was the first step. We write “a point has an x-coordinate” instead of the more verbose “a point refers to a container which stores an x-coordinate” and “a dic item has a key” instead of the more verbose “a dic item refers to a container that stores a key”. We also say “a dic item which is part of a dictionary D” instead of the more verbose “a dic item that refers to a container that is part of a dictionary D”.

The access to a key of a dictionary container is read-only. , one of the dangers of pointers is avoided. The wish to have the efficiency of pointer access without its dangers was our main motivation for introducing items into the signatures of operations on complex data types. 30 Foundations Let us next see some operations involving items. We use dictionaries as a typical example. change inf (it, j ). Note that only the first operation involves a search in the data structure realizing D and that the other two operations access the item directly.

The cost of passing a reference parameter is bounded by a constant and the cost of passing a value parameter is the cost of copying the argument. We follow the custom to account for parameter passing at the place of call. Similarly, the space bound does not include the extra space needed for the elements contained in the set, it only accounts for the space required by the data structure that realizes the set. The extra space needed for an element is zero if the element fits into one machine word and is the space requirement of the element otherwise.