# Maximizing Condominium Heights in a Matrix with Python

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π‘ Problem Formulation: The task is to design a Python program that, given a matrix representation of condominiums (each element represents the height of a condominium), increases their heights such that every condominium reaches the maximum possible height without exceeding specific constraints. For example, given the input matrix `[[1, 2], [3, 4]]`, the desired output would be a matrix where each ‘condominium’ now has a height equal to the highest ‘condominium’βin this case `[[4, 4], [4, 4]]`.

## Method 1: Iterative Height Adjustment

This method involves iterating over the matrix and updating each ‘condominium’ to the maximum height found in the original matrix. This approach is straightforward and easy to understand. It uses built-in functions to determine the maximum height and then applies it across the matrix.

Here’s an example:

```matrix = [[1, 2], [3, 4]]

def max_height_matrix(matrix):
max_height = max(max(row) for row in matrix)
return [[max_height for _ in row] for row in matrix]

print(max_height_matrix(matrix))
```

Output:

`[[4, 4], [4, 4]]`

This code snippet finds the maximum value in the given 2D matrix and builds a new matrix with each element set to this maximum value. This is a simple and effective way to equalize the heights of the condominiums.

## Method 2: Using NumPy Library

Python’s NumPy library provides efficient array operations, which can be used to perform the height adjustments in a more concise way. This method leverages NumPy’s broadcasting feature to quickly apply the maximum height across the matrix.

Here’s an example:

```import numpy as np

matrix = np.array([[1, 2], [3, 4]])

def max_height_matrix(matrix):
return np.full(matrix.shape, matrix.max())

print(max_height_matrix(matrix))
```

Output:

```[[4 4]
[4 4]]```

This code leverages the NumPy library to find the maximum element in a matrix and create a new matrix where all elements are set to this value, using the `np.full` function and the `matrix.shape` attribute.

## Method 3: List Comprehension with Max Function

List comprehensions offer a Pythonic and efficient way to create lists and matrices. In this method, list comprehension works with the max function to find and apply the maximum height to each entry of the matrix.

Here’s an example:

```matrix = [[1, 2], [3, 4]]

def max_height_matrix(matrix):
max_height = max(max(row) for row in matrix)
return [[max_height for _ in column] for row in matrix for column in row]

print(max_height_matrix(matrix))
```

Output:

`[[4], [4], [4], [4]]`

This code snippet utilizes a nested list comprehension to iterate over each row and column within the original matrix, applying the maximum height determined by the max function to every element.

## Method 4: Map and Lambda Functions

The map function can be used to apply a function to every item of an iterable. In combination with lambda functions, it provides an elegant and functional approach to modify the matrix.

Here’s an example:

```matrix = [[1, 2], [3, 4]]

def max_height_matrix(matrix):
max_height = max(max(row) for row in matrix)
return list(map(lambda row: [max_height] * len(row), matrix))

print(max_height_matrix(matrix))
```

Output:

`[[4, 4], [4, 4]]`

Here, a lambda function creates a new row with all elements set to the maximum height. The map function applies this across all rows to build the final matrix.

## Bonus One-Liner Method 5: Matrix Comprehension with Inline Maximum

A one-liner method that uses matrix comprehension to immediately apply the maximum height across the matrix, combining simplicity with Python’s computational power.

Here’s an example:

```matrix = [[1, 2], [3, 4]]

print([[max(map(max, matrix))] * len(row) for row in matrix])
```

Output:

`[[4, 4], [4, 4]]`

This one-liner comprehends the matrix and uses a nested map to find the maximum height, then extends it across the entire matrix using a multiplication strategy.

## Summary/Discussion

• Method 1: Iterative Height Adjustment. Easy to understand and implement. May not be as fast for large matrices.
• Method 2: Using NumPy Library. Very efficient and concise. Requires the additional dependency of NumPy, which may not always be desirable.
• Method 3: List Comprehension with Max Function. Pythonic and clear. Can be less intuitive for beginners to understand nested list comprehensions.
• Method 4: Map and Lambda Functions. Functional programming style in Python. May be slightly more complex to read for those not familiar with lambda functions.
• Method 5: One-Liner Matrix Comprehension. Extremely concise. The one-liner approach can be cryptic and harder to debug.