10.4 Introduction to Abstract Data Types (ADT) (3)
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1.
Define what an Abstract Data Type (ADT) is. Your answer should clearly explain the relationship between data and the operations performed on that data. Provide a simple example to illustrate your definition.
An Abstract Data Type (ADT) is a theoretical model of data and its associated operations. It defines a set of data types and a set of operations that can be performed on those data types, without specifying how the data is physically stored or implemented. The key concept is separation of what the data represents and what can be done with it.
Essentially, an ADT describes the behavior of a data structure. It focuses on the logical properties of the data and the operations that manipulate it. This abstraction allows for flexibility in implementation; the ADT can be implemented using various underlying data structures (e.g., arrays, linked lists, trees) without affecting the interface or behavior of the ADT itself.
Example: Consider a Stack ADT. The data type is a collection of items. The operations are typically: push (adding an item to the top), pop (removing the top item), peek (viewing the top item), and isEmpty (checking if the stack is empty). The ADT defines *what* a stack does (LIFO - Last In, First Out), but it doesn't specify *how* it's implemented (e.g., using an array or a linked list).
2.
Question 1: Define what an Abstract Data Type (ADT) is. Explain, using examples of a stack, a queue, and a linked list, why these data structures are considered ADTs. Specifically address the distinction between the what (the behaviour) and the how (the implementation) of an ADT.
An Abstract Data Type (ADT) is a mathematical model of a data structure that specifies the logical properties of the data structure, without specifying how it is implemented. It defines a set of operations that can be performed on the data, and the expected behavior of those operations. Crucially, an ADT separates the what (the abstract behavior) from the how (the concrete implementation).
A stack, queue, and linked list are examples of ADTs because they are defined by their logical properties and the operations that can be performed on them. For example:
- Stack: An ADT with operations like push (add an element to the top), pop (remove the top element), and peek (view the top element). The implementation could be an array or a linked list, but the stack ADT defines the behaviour – Last-In, First-Out (LIFO).
- Queue: An ADT with operations like enqueue (add an element to the rear), dequeue (remove the element from the front), and peek (view the front element). The implementation could be an array (circular queue) or a linked list, but the queue ADT defines the behaviour – First-In, First-Out (FIFO).
- Linked List: An ADT with operations like insert (add a new node), delete (remove a node), search (find a node), and traverse (visit nodes in sequence). The implementation uses nodes with data and pointers to the next node, but the linked list ADT defines the behaviour – a sequence of elements where each element points to the next.
The key distinction is that the ADT focuses on the interface (the operations) and the properties of the data, while the implementation details (e.g., using arrays or linked lists) are hidden. This allows for flexibility – the same ADT can be implemented using different underlying data structures.
3.
Question 2: Consider a stack ADT. Describe the key operations that are typically associated with a stack. Explain how each of these operations would be implemented using a linked list as the underlying data structure. Include a diagram illustrating the stack's state after performing a 'push' and a 'pop' operation.
The key operations associated with a stack ADT are:
- Push: Adds an element to the top of the stack.
- Pop: Removes the element from the top of the stack.
- Peek: Returns the element at the top of the stack without removing it.
- isEmpty: Checks if the stack is empty.
Here's how these operations can be implemented using a linked list:
- Push: A new node is created containing the data to be added. This new node's 'next' pointer is set to point to the current top of the stack (the previous top node). The top of the stack is then updated to point to this new node.
- Pop: The top node is removed from the stack. The 'next' pointer of the previous top node is updated to skip the removed node, effectively making the previous top node the new top. If the stack is empty, an error condition (e.g., underflow) is signaled.
- Peek: The data in the top node is accessed, but the node itself is not removed.
- isEmpty: The stack is empty if the top node's 'next' pointer is null.
Diagram:
Before Push: Data: 10 -> Next: null |
After Push: Data: 10 -> Next: Data: 5 |
Before Pop: Data: 10 -> Next: Data: 5 |
After Pop: Data: 5 -> Next: null |