Lecture 5 Finger Exercise

Question 1. Implement a function walk(n, leftbound, rightbound, leftbias) that meets the specification below. You do not need to import random; the server will import it for you. You also should not call random.seed(); the server will ignore any lines containing that text.

def walk(num_steps, leftbound, rightbound, leftbias=0.5):
    """
    Perform a random walk along the real number line, starting from 0.

    Parameters:
        num_steps (int): The number of steps to run the random walk.
        leftbound (int): A negative number location that the walk may not go past.
        rightbound (int): A positive number location that the walk may not go past.
        leftbias (float): A value between 0 and 1 inclusive.

    Each step attempts to go either one unit left (-1) with probability
    leftbias, or one unit right (+1) otherwise.

    The walk may go up to, but not beyond, leftbound or rightbound.
    Attempting to go left while at leftbound leaves the location unchanged;
    similarly for going right at rightbound. Each time step for which
    the walk reaches or remains at either bound counts as a wall hit.

    After completing num_steps steps, return a two-element list, where
    the first element is the total number of wall hits, and the second
    is the final location.
    """
    # your code here

For example, consider a scenario where leftbound = -1 and rightbound = 1. Suppose a walk of n = 4 steps results in the sequence of locations 0 → -1 → -1 → 0 → 1. This would count as three wall hits, with a final location of 1.

Question 2. Implement a function reorder_using_index(sequence, func). This function allows you to sort a list using a rule that cares about both the value of the item and its original position in the list. You may assume that there will be no need for a tiebreaker.

def reorder_using_index(sequence, func):
    """
    Reorder a sequence based on a scoring function that takes a list
    of the form [index, element] as an input.

    Parameters:
        sequence (list): A list of elements.
        func (function): A function that takes a list of the form
            [index, element] and returns a number to be used as a
            sorting key.

    Return a new list containing the original elements of the sequence,
    reordered in increasing order of the scores produced by func.
    """
    # your code here

For example, suppose sequence = [10, 2, 8] and func returns 2 * index + element. The elements are scored as: 10 → 10, 2 → 4, and 8 → 12. Sorting by these scores in increasing value results in the final list [2, 10, 8].