150 lines
4.2 KiB
Text
150 lines
4.2 KiB
Text
.NH 2
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Representation of complex data structures in a sequential file
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.PP
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Most programmers are quite used to deal with
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complex data structures, such as
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arrays, graphs and trees.
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There are some particular problems that occur
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when storing such a data structure
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in a sequential file.
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We call data that is kept in
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main memory
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.UL internal
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,as opposed to
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.UL external
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data
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that is kept in a file outside the program.
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.sp
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We assume a simple data structure of a
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scalar type (integer, floating point number)
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has some known external representation.
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An
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.UL array
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having elements of a scalar type can be represented
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externally easily, by successively
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representing its elements.
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The external representation may be preceded by a
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number, giving the length of the array.
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Now, consider a linear, singly linked list,
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the elements of which look like:
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.DS
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record
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data: scalar_type;
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next: pointer_type;
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end;
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.DE
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It is significant to note that the "next"
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fields of the elements only have a meaning within
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main memory.
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The field contains the address of some location in
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main memory.
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If a list element is written to a file in
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some program,
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and read by another program,
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the element will be allocated at a different
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address in main memory.
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Hence this address value is completely
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useless outside the program.
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.sp
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One may represent the list by ignoring these "next" fields
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and storing the data items in the order they are linked.
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The "next" fields are represented \fIimplicitly\fR.
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When the file is read again,
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the same list can be reconstructed.
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In order to know where the external representation of the
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list ends,
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it may be useful to put the length of
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the list in front of it.
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.sp
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Note that arrays and linear lists have the
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same external representation.
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.PP
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A doubly linked, linear list,
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with elements of the type:
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.DS
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record
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data: scalar_type;
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next,
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previous: pointer_type;
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end
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.DE
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can be represented in precisely the same way.
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Both the "next" and the "previous" fields are represented
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implicitly.
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.PP
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Next, consider a binary tree,
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the nodes of which have type:
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.DS
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record
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data: scalar_type;
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left,
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right: pointer_type;
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end
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.DE
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Such a tree can be represented sequentially,
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by storing its nodes in some fixed order, e.g. prefix order.
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A special null data item may be used to
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denote a missing left or right son.
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For example, let the scalar type be integer,
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and let the null item be 0.
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Then the tree of fig. 3.1(a)
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can be represented as in fig. 3.1(b).
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.DS
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.ft 5
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4
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/ \e
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9 12
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/ \e / \e
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12 3 4 6
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/ \e \e /
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8 1 5 1
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.ft R
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Fig. 3.1(a) A binary tree
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.ft 5
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4 9 12 0 0 3 8 0 0 1 0 0 12 4 0 5 0 0 6 1 0 0 0
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.ft R
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Fig. 3.1(b) Its sequential representation
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.DE
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We are still able to represent the pointer fields ("left"
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and "right") implicitly.
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.PP
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Finally, consider a general
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.UL graph
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, where each node has a "data" field and
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pointer fields,
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with no restriction on where they may point to.
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Now we're at the end of our tale.
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There is no way to represent the pointers implicitly,
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like we did with lists and trees.
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In order to represent them explicitly,
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we use the following scheme.
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Every node gets an extra field,
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containing some unique number that identifies the node.
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We call this number its
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.UL id.
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A pointer is represented externally as the id of the node
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it points to.
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When reading the file we use a table that maps
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an id to the address of its node.
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In general this table will not be completely filled in
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until we have read the entire external representation of
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the graph and allocated internal memory locations for
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every node.
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Hence we cannot reconstruct the graph in one scan.
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That is, there may be some pointers from node A to B,
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where B is placed after A in the sequential file than A.
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When we read the node of A we cannot map the id of B
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to the address of node B,
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as we have not yet allocated node B.
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We can overcome this problem if the size
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of every node is known in advance.
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In this case we can allocate memory for a node
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on first reference.
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Else, the mapping from id to pointer
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cannot be done while reading nodes.
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The mapping can be done either in an extra scan
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or at every reference to the node.
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