**π‘ Problem Formulation:** You are given a binary matrix (a 2D list) where each row contains zeros and ones. The challenge is to write a Python program using the map function to identify the row that has the maximum number of one’s (1s). For instance, given a matrix [[0,1,1], [1,1,1], [0,0,1]], the desired output is 1, representing the second row, which contains three 1s β the maximum in this matrix.

## Method 1: Using map with a Custom Function

This method involves creating a custom function that counts the number of ones in a row and then mapping this function across all rows of the matrix. The max function is then used to identify the row with the highest count. This method is straightforward and lets you encapsulate row counting logic easily.

Here’s an example:

def count_ones(row): return row.count(1) matrix = [[0,1,1], [1,1,1], [0,0,1]] max_row = max(range(len(matrix)), key=lambda x: count_ones(matrix[x])) print(max_row)

Output:

1

In this snippet, the `count_ones()`

function counts the ones in a single row. The `max()`

function then finds the row index with the maximum count of ones. The use of `lambda x: count_ones(matrix[x])`

as the key for max applies our custom logic across the matrix.

## Method 2: Using map with the sum Function

By leveraging Python’s built-in `sum()`

function, this method simplifies the process by directly adding up the values in each row. It does not require an explicit counting function. The sum works since the rows contain binary values, and the result is equivalent to counting ones.

Here’s an example:

matrix = [[0,1,1], [1,1,1], [0,0,1]] max_row = max(range(len(matrix)), key=lambda x: sum(matrix[x])) print(max_row)

Output:

1

This code uses the `sum()`

function inside a `lambda`

to count the ones for each row passed by `map()`

. The `max()`

function is then used with this sum as the criterion to find the row index that has the maximum number of ones.

## Method 3: Using map with List Comprehension

In this approach, a list comprehension generates a list of one counts for each row. Then the `map()`

function is not explicitly called, as list comprehension handles the mapping step implicitly. Lastly, the index of the max value is found.

Here’s an example:

matrix = [[0,1,1], [1,1,1], [0,0,1]] one_counts = [sum(row) for row in matrix] max_row = one_counts.index(max(one_counts)) print(max_row)

Output:

1

The list comprehension `[sum(row) for row in matrix]`

creates a new list containing the sums (equivalent to the number of ones) for each row. The `max()`

function locates the maximum count while `index()`

returns its position, which corresponds to the row with the most ones.

## Method 4: Using map with the Count Method

This method combines the use of the `map()`

function with each row’s `count()`

method to tally the ones. It showcases Python’s functional programming capabilities by transforming each row to its one count and then finding the row with the maximum one’s count.

Here’s an example:

matrix = [[0,1,1], [1,1,1], [0,0,1]] one_counts = list(map(lambda x: x.count(1), matrix)) max_row = one_counts.index(max(one_counts)) print(max_row)

Output:

1

In this snippet, we use `map()`

to apply a lambda function that invokes the `count`

method on each row. After converting the map object to a list, we then use `max()`

and `index()`

to find the row index corresponding to the maximum number of ones.

## Bonus One-Liner Method 5: The Power of the Max Function’s Key Argument

This sleek one-liner takes full advantage of Python’s `max()`

function by directly using it with a custom key function to determine the row with the most ones. It demonstrates Python’s ability to perform complex tasks in a compact, readable manner.

Here’s an example:

matrix = [[0,1,1], [1,1,1], [0,0,1]] max_row = max(matrix, key=lambda x: x.count(1)) print(matrix.index(max_row))

Output:

1

Instead of working with indices, this snippet finds the row with the highest count of ones directly using `max()`

. Then, the `index()`

method retrieves the index of this max row, giving the same end result in a more concise format.

## Summary/Discussion

**Method 1:**Custom Function with map. Easy to understand. Extra code for a custom function is necessary.**Method 2:**sum with lambda Function. Streamlined with built-in functions. Lacks the clarity of a named function.**Method 3:**List Comprehension. Integrates well with Pythonic style. Less explicit about the mapping process.**Method 4:**map with count Method. Clearly functional programming style. Conversion to a list may seem redundant.**Method 5:**Max Function with Key Argument. Most concise. Less explicit, could be harder to read for beginners.