554. Brick Wall python

554. Brick Wall in Python

Brick walls are commonly used in the construction industry to create partitions and enclosures. They are made by arranging bricks in a specific pattern and bonding them together with mortar. In this article, we will explore the concept of a brick wall in Python and provide code examples to illustrate its implementation.

Understanding the Brick Wall Problem

The brick wall problem involves finding the vertical line that crosses the fewest number of bricks. The input is a 2D list representing a brick wall, where each row contains the widths of the bricks. The goal is to find the position along the width of the wall where the fewest bricks are crossed.

For example, consider the following brick wall:

[[3, 5, 1, 1],
 [2, 3, 3, 2],
 [5, 5],
 [4, 4, 2],
 [1, 3, 3, 3],
 [1, 1, 6, 1, 1]]

To solve this problem, we can iterate through each row of the wall and keep track of the cumulative widths of the bricks. We can use a dictionary to store the number of occurrences of each cumulative width. The key of the dictionary represents the cumulative width, and the value represents the number of occurrences.

Implementing the Brick Wall Solution in Python

Let's implement the brick wall solution in Python step by step.

1. First, we need to import the necessary libraries:

from collections import defaultdict

2. Next, we define a function named fewest_bricks that takes the 2D list representing the brick wall as input:

def fewest_bricks(wall):
    cumulative_widths = defaultdict(int)
    for row in wall:
        cumulative_width = 0
        for brick in row[:-1]:
            cumulative_width += brick
            cumulative_widths[cumulative_width] += 1
    return len(wall) - max(cumulative_widths.values())

3. In the fewest_bricks function, we initialize a defaultdict named cumulative_widths to store the cumulative widths of the bricks. We iterate through each row of the wall using a nested loop. The inner loop calculates the cumulative width of the bricks by summing up the widths of the bricks in each row. We increment the value of the cumulative width in the cumulative_widths dictionary. Finally, we return the fewest number of bricks crossed by subtracting the maximum value from the length of the wall.

4. Let's test the function with the given brick wall example:

wall = [[3, 5, 1, 1],
        [2, 3, 3, 2],
        [5, 5],
        [4, 4, 2],
        [1, 3, 3, 3],
        [1, 1, 6, 1, 1]]

fewest_bricks(wall)

The output will be 2, indicating that the fewest number of bricks crossed is 2.

Conclusion

In this article, we explored the concept of a brick wall problem and provided a Python solution using a cumulative width approach. We walked through the implementation step by step and tested the solution with a sample brick wall. The brick wall problem is an interesting challenge that can be solved efficiently using Python. By understanding the problem and using the right data structures, we can find the optimal solution and minimize the number of bricks crossed.

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erDiagram
    BRICK-WALL ||..|| BRICK : has
    BRICK ||--|{ WIDTH : has

The above diagram represents the relationship between BRICK-WALL, BRICK, and WIDTH. A brick wall has multiple bricks, and each brick has a width. This relationship is essential for understanding the brick wall problem and implementing a solution.