Lecture 12 Finger Exercise

Question 1. Implement a function next_char_frequencies() that satisfies the following docstring.

def next_char_frequencies(phrases, target_char):
    """
    Find which characters follow a given character and how often.

    Parameters:
        phrases (list): A collection of strs containing only lower-case
            characters, no spaces.
        target_char (str): A single lower-case character.

    Return a dict that maps lower-case characters (str) to ints. The
    values are the total number of times each character immediately
    follows target_char across all strings in phrases. If a character
    never follows target_char, it does not appear as a key.
    """

For example:

• When words = ["an", "ana", "banana"]
next_char_frequencies(words, "a") should evaluate to {"n": 4}.

• When titles = ["greeneggsandham", "catinthehat", "hortonhearsawho"]
next_char_frequencies(titles, "e") should evaluate to {"a": 1, "e": 1, "g": 1, "h": 1, "n": 1}.

Question 2. Given an m x n grid representing a geographic map, a cell value of 1 represents land, and a cell value of 0 represents water. An island is a group of contiguous 1s that are connected horizontally, vertically, or diagonally.

Given a starting location (i, j) in the grid, implement the following function to compute the area of the island containing the location, which is the number of contiguous 1s connected to (i, j).

def island_area(grid, start):
    """
    Determine the area of an island that contains a given location.

    Parameters:
        grid (list): A list of lists of ints. The ints are either 1
            (representing land) or 0 (representing water).
        start (tuple): The (row, col) indices of a start location within
            the grid.

    Return the number of cells in grid for the island that the start
    location is on. If the start location is in water, return 0.
    """

For example, if the input grid is the following

grid = [
    [0, 1, 1, 0],
    [0, 1, 0, 0],
    [1, 1, 0, 1],
    [0, 0, 0, 1],
]

and the start location is (0, 1), then the island its on has size 5.

Hint 1: If you run BFS to completion from a start node, it will visit all the nodes that are reachable from the start. Thus, to identify all the locations of an island, is there a certain collection in our BFS implementation whose size would be relevant?

Hint 2: In class, we used explicit dictionaries to represent graphs. Here, the edge relationships are implicitly a cell's neighboring 1s in the supplied grid. We suggest making a helper function to compute this.

Hint 3: This is not strictly necessary, but note that because we are not returning a path, we may not have to store paths in our BFS frontiers. Instead, maybe just storing the newly discovered nodes would be sufficient.