34 Questions
What happens when you call dequeue on an empty queue?
It throws a runtime error
In a linked list implementation, what happens to the old head when dequeuing?
It is garbage collected or cleaned up manually
What is the purpose of the front and end indices in an array-based implementation?
To check if the queue is full or empty
What is the purpose of using modular arithmetic in a circular array implementation?
To map the index to a position in the array
What problem does the array-based implementation have?
It does not handle overflow correctly
What is the purpose of using a circular array in the array-based implementation?
To handle overflow correctly
What is the purpose of a distance function?
To measure the dissimilarity between two elements in a set
What is the name of the book recommended for further reading?
Introduction to Algorithms
What is the approximate distance between the points (1, 2) and (6, 10)?
9.4
What is Euclidian distance an example of?
A distance function
What is a distance function also known as?
A metric
What is 𝑑(lion, cat) an example of?
A distance function
What is the time complexity of the algorithm described?
O(V + E)
What happens when a vertex is removed from the queue?
It is visited immediately
What is the purpose of the queue in the algorithm?
To manage the order in which vertices are processed
What happens to a vertex that has never been enqueued?
It is added to the queue
Why is the time complexity O(V + E) in a dense graph?
Because the number of edges is close to V
What is the purpose of the constant-time check-and-enqueue operation?
To add adjacent vertices to the queue
What is the cost of transforming the last characters of two strings in Case 3?
1
What is the condition for Case 3?
The two strings have different last characters and x > |y|
What is the general formula for Lev(x_i, y_j) in Case 3?
Lev(x_i-1, y_j) + 1
What is the purpose of the Levenshtein distance?
To find the minimum cost to transform one string into another
What is the general formula for Lev(x_i, y_j) in all cases?
min(Lev(x_i-1, y_j) + 1, Lev(x_i, y_j-1) + 1, Lev(x_i-1, y_j-1) + k)
What is the condition for Case 4?
The two strings have different last characters and x < |y|
What is the cost of transforming the last characters of two strings in Case 4?
1
What is the general formula for Lev(x_i, y_j) in Case 4?
Lev(x_i, y_j-1) + 1
What is the value of 𝐿𝐶 when 𝐸𝐶 is maximized?
7
What is the relationship between 𝐸𝐶 and 𝐿𝐶?
𝐿𝐶 is a function of 𝐸𝐶
What is the maximal value of 𝐸𝐶& in the given scenario?
7
What is the purpose of defining 𝐿𝐶 for each event vertex 𝑣?
To track the latest completion times for each event
What is the value of 𝐸𝐶 when 𝐶 = 4 and 𝐸𝐶! = 3?
7
What is the vertex label in the diagram corresponding to 𝑣 = 2 and 𝑤 = 4?
b
What is the relationship between 𝐸𝐶! and 𝐸𝐶& in the given scenario?
𝐸𝐶& is a function of 𝐸𝐶!
What is the purpose of maximizing 𝐸𝐶?
To maximize the latest completion times
Study Notes
Queue Operations
- IsEmpty: checks if the queue is empty by checking if the head is null
- Enqueue: creates a new tail (appends at the end) by setting newTail.NextItem to null and tail.NextItem to newTail
- Dequeue: removes the head by setting result to head.Value and head to head.NextItem
Array-Based Implementation
- Uses an index to the front element and the end element
- Initializes front and end to 0
- If front == end, the queue is empty; if end == sizeOfArray, the queue is full
- To enqueue: adds item at end and increments end
- To dequeue: item is array[front], and increments front
Modular Arithmetic
- Uses modular arithmetic to solve the problem of array-based implementation
- Example: 0%5 = 0, 1%5 = 1, ..., 5%5 = 0, ...
Circular Array
- Uses front and end pointers like before and initializes them to zero
- Solves the problem of array-based implementation using modular arithmetic
Time Complexity
- Time complexity of operations depends on the implementation
- Linked list implementation: O(1) for IsEmpty, Enqueue, and Dequeue
- Array-based implementation: O(1) for IsEmpty, Enqueue, and Dequeue
Distance Function
- A distance function defines the distance between two elements in a set
- Examples: Euclidian distance, String distance (Levenshtein distance)
Levenshtein Distance
- Measures the minimum number of operations to transform one string to another
- Operations: insertion, deletion, substitution
- Cases:
- Case 1: x[i] == y[j]
- Case 2: x[i] != y[j] and x is longer than y
- Case 3: x[i] != y[j] and x is shorter than y
- Case 4: x[i] != y[j] and x and y have different lengths
- Formula: Lev(x[i], y[j]) = min(Lev(x[i-1], y[j-1]) + k, Lev(x[i-1], y[j]) + 1, Lev(x[i], y[j-1]) + 1)
Graph Traversal
- Time complexity: O(V + E)
- Component 1: constant-time dequeue and visit
- Component 2: constant-time check-and-enqueue for every adjacent vertex
Examples
- Graph traversal example with vertices and edges
- Example of calculating the maximum distance between vertices
Learn about queue operations such as enqueue, dequeue, and checking if the queue is empty. Understand the implementation of a linked list queue.
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