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A primary data structure is a data structure that is created without the use of other data structures, whereas a secondary data structure relies on a primary data structure. A data structure is an organized collection of data elements.
[NOTE: Be careful not to confuse the term data structure with the term data type. It is a common mistake. This answer addresses dat structures. Often people who ask about primary data structures or primitive data structures are really asking about primitve data types.]
Here is an example where an array is a primary data structure and a binary tree is a secondary data structure based on the array:
An array is a primary data structure -- it is a set of sequentially numbered data elements, such as an array of integers or an array of names -- name0, name, name2, ...
A binary tree is a data structure where each element (called a node) has a data component and pointers to it's left and right sub-trees. [Think of a directory of folders, but each folder can only have two sub-folders.] We can create an and store an array of nodes to set up the tree in languages like C++ or Java.
The root of the tree could be node 1 in the array, it would point to nodes 2 and 3. node 2 would point to nodes 4 and 5, while node 3 would point to nodes 6 and 7 .. and so on. generally node n point to nodes 2n and 2n+1. (You can start with node 0, but the math is a little easier if you start with node 1.)
The binary tree in this case is the secondary data structure, while the undelying array is the primary data structure.
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