4.2 Data structures Flashcards
What is an array?
How are items accessed in an array?
- A collection of items with a fixed size
- Arrays use index numbers to access individuals elements of the array
What is an abstract data type?
A theoretical description of a way of organising a collection of data, with particular features and access restrictions, that is independent of any particular data structure.
What is a data structure?
The concrete realisation of an abstract data type in code.
What is a static data structure?
A data structure that reserves a fixed amount of memory, specified by the programmer in advance of its use
What is a dynamic data structure?
Data structures that have no fixed size. The memory used grows and shrinks as items are added/removed
2 advantages of static data structures over dynamic data structures
- Data is quicker to access directly, with minimal overhead
- No additional memory is needed to store all of the pointers
2 advantages of dynamic data structures
- There is no wasted memory
- There is no theoretical limit on the number of items that can be added
Queue: FIFO or LIFO?
FIFO (First in first out)
Queue: Four key operations
- Enqueue - adds item to rear of the queue
- Dequeue - removes item and returns item from the front of the queue
- IsEmpty - checks if the queue is empty
- IsFull - checks is the queue is full
Describe briefly the data structures and pointers used by a linear queue
- Linear queues are implemented with arrays (or lists)
- They use a front and rear pointers to point to:
- front → the next item to dequeue
- rear → last item enqueued
Disadvantages of linear queues if you
1. Don’t shuffle down the items
2. If you do
- There is a limit on the number of items that can be added and removed (maxSize)
- Implementing a linear queue where you “shuffle” the items down each time an item is dequeued is very processing intensive
Key difference of circular queue from linear queue?
- Circular queues virtually connect the end to the start of the array
- This overcomes the problem of reusing spaces in the array
What happens to the rear pointer when enqueuing an item to a circular queue?
rear ← (rear + 1) % maxSize
What is a priority queue? How does enqueuing work?
- A queue where each element in the queue has a priority
- When new elements are enqueued, they are inserted ahead of those of lower priority and behind elements of equal or greater priority
Name an algorithm that can be implemented with a priority queue
Dijkstra’s Algorithm
Stack: FIFO or LIFO?
LIFO (Last in first out)
Stack: Five core operations
- Push - adding to top of stack
- Pop - removing from top of stack and returning
- Peek - returns top item without removing it
- IsEmpty - checking if stack is empty
- IsFull - checking if stack is full (only relevant when stored in a static structure)
Describe implementation of a stack
- Using an array or list to store the items
- Initialise a pointer variable that points to the current top item
- The pointer is initialised as -1
- The pointer is incremented if an item is pushed, and vice versa
- The pointer will be -1 if stack is empty.
Graph: Static or dynamic?
Dynamic, they can grow and shrink in size
What is a graph?
Graphs are sets of vertices (nodes) and the edges (arcs) that connect them
What is a graph with a high ratio of edges to vertices called?
Dense
What is a graph with a low ratio of edges to vertices called?
Sparse
What is a weighted graph?
A graph that has weights (number values) on each edge
What is a connected graph?
A graph where there is a path between each pair of vertices
Suggest three things that graphs could be used to model
- Social networking: the nodes could be individual people. An edge could represent that two people are acquaintances.
- Transport networks: the nodes could be towns. An edge could represent that a train line connects two towns.
- The internet: the nodes could be routers. An edge could represent that two routers are connected.
2 ways to represent graphs
Adjacency matrix and adjacency list
How do you represent no edge for a weighted graph?
“-” or “∞” (can’t use zero)
How could an adjacency list be implemented if graph is 1. weighted 2. unweighted?
- List of dictionaries if weighted
- List of lists if unweighted
Advantage of adjacency matrix
Adding new edges / checking for presence of edges is simple and quick as 2D static arrays can be used
2 advantages of adjacency lists
- Adjacency lists are very space efficient, as no memory is needed to store the empty spaces
- It is easy to add / delete nodes
Disadvantage of adjacency list
Slow to query (e.g. to check the presence of an edge), as each item in the list must be searched sequentially until the desired edge is found
2 disadvantages of adjacency matrices
- If the graph is sparse, then there are lots of empty spaces, which is wasted memory
- It can be hard to add / delete nodes if a 2D static array is used
What is a tree?
A connected, undirected graph with no cycles
What is a rooted tree? (3*)
- A tree in which one vertex has been designated as the root
- Rooted trees have parent-child relationships between adjacent nodes
- The root is the only node with no parent. All other nodes are descendants of the root
What is an internal node?
A node in a rooted tree which has a parent and at least one child
What is a leaf node?
A node in a rooted tree that has a parent but is not the parent of other nodes (no child nodes)
Suggest a use for rooted trees
A game tree, where edges represent moves, and nodes represent all possible positions in the game
What is a binary tree?
A rooted tree in which each node has at most two child nodes
Name a common application of binary trees
Binary search trees
What is an ordered binary tree? (3*)
- A type of binary tree where the data items are in a particular order
- Items left of a node have a value less than the node
- Items right of a node have a value greater than the node
What is a hash table?
A data structure that creates a mapping between keys and values
What is the purpose of a hash table? (2•)
- To provide a way of storing a list of values in which a key is used to locate values in the list without searching through all other values
- They are used so that records can be retrieved quickly
What does a hash function/algorithm do in a hash table?
Computes the array index for the value to be stored or retrieved
What is hashing?
Hashing is the irreversible process of converting data of arbitrary length into data of a fixed length.
When does a collision occur (hashing)?
When two or more keys hash to the same index
When are collisions unavoidable (hashing)?
When the number of possible keys is larger than the number of available spaces
What is a dictionary? (2•)
- A collection of key-value pairs in which the value is accessed via the associated key
- There can be no duplicate keys
Name an application of dictionaries
Dictionary based compression
What is the meaning of the symbol ↦ ?
Maps to
What is important about the components of a vector?
That they are all drawn from the same field of values, e.g Reals or Rationals
4 ways vectors be represented
- A list of values
- A one-dimensional array
- A dictionary (if the vector can be considered to represent a function)
- Visually (using an arrow)
How can a vector be represented in code if the vector is viewed as a function?
A dictionary
What does vector addition achieve?
Translation
What does scalar-vector multiplication achieve?
Scaling
What is another name for dot product?
Scalar product
What is a convex combination of vectors u and v?
αu + βv
such that α , β >= 0
and α + β = 1
What is an application of the dot product?
Finding the angle between two vectors
In a convex combination of u and v, what is the significance of α = β = 0.5?
The resultant vector is the midpoint of the position vectors u and v
Describe the steps involved in adding a record to a hash table
- Hash algorithm applied to key, which returns the location (often an array index) in table where the record should be stored
- If location is not empty, a collision has occurred
– Open addressing is used (the next free location is used, wrapping round at the end of the array)
– Or rehashing occurs (starting from scratch with a larger array)
– Or chaining is used (a pointer to a list is stored at each location a collision has occurred)
When might it be appropriate to represent a vector using a dictionary?
If the vector is used to represent a function
Describe the steps involved in rehashing (2•)
- A larger hash table is created
- Each value in the existing table is inserted into the new table in a position determined by a new hashing algorithm
Name three methods of collision handling (for a hash table)
- Rehashing
- Chaining
- Open addressing
How are collisions resolved with chaining?
A pointer to a list is stored at each location that points to a list of items that have collided at that location
How are collisions resolved with open addressing?
The item is stored in the next available location in the hash table (wrapping around at the end)
