Question

Q 1: Write a function to measure the amortized cost of appending for Python’s list class.

Q 2: Write functions for two primary operations in the Queue enqueue ( ) and dequeue ( ).

Answer 1

The amortized cost of appending for Python's list class is O(1). Enqueue and dequeue functions can be implemented using a list in Python.

Step-by-step explanation:

Q 1: Amortized Cost of Appending for Python's list class

The amortized cost of appending for Python's list class is O(1). This means that the average time complexity of appending an element to a list is constant, regardless of the number of elements already in the list.

Python's list class uses a dynamic array structure, which automatically resizes the underlying array when necessary to accommodate additional elements. The resizing process occurs by allocating a new array with a larger capacity and copying the existing elements to the new array. Since this resizing happens infrequently, the cost is amortized over multiple appends.

Q 2: Enqueue and Dequeue Functions for a Queue

Enqueue and dequeue are the two primary operations in a queue. In Python, you can implement these operations using a list.

def enqueue(queue, item):
queue.append(item)

def dequeue(queue):
return queue.pop(0)

The enqueue function appends an item to the end of the queue, and the dequeue function removes and returns the item from the front of the queue. By using the built-in list methods append() and pop(), we can effectively simulate a queue in Python.

Answer 2

Q 1:

import time

def measure_amortized_cost_of_appending(num_iterations):

# Create an empty list

lst = []

# Start a timer

start_time = time.perf_counter()

# Append num_iterations elements to the list

for i in range(num_iterations):

lst.append(i)

# End the timer

end_time = time.perf_counter()

# Calculate and return the amortized cost of appending

return (end_time - start_time) / num_iterations

This function creates an empty list, starts a timer, appends num_iterations elements to the list, and ends the timer. It then calculates and returns the amortized cost of appending by dividing the elapsed time by the number of iterations.

Q 2:

class Queue:

def __init__(self):

self.items = []

def enqueue(self, item):

self.items.append(item)

def dequeue(self):

return self.items.pop(0)

This implementation of the Queue class uses a Python list to store the items in the queue. The enqueue method appends an item to the end of the list, and the dequeue method removes and returns the item at the front of the list (index 0).