Approaching Google Style Coding Interview Problems

In this article, we will walk through a step-by-step approach to solving a typical Google-style coding interview problem. We'll cover asking clarifying questions, thinking through the approach, coming up with an algorithm, communicating our thinking clearly, and analyzing the complexity at the end.

The Problem Statement

Given a 2D matrix of size H x W where each cell contains a number, write a function to find the maximum square submatrix that sums up to zero. You may modify the input array in-place.

Asking Clarifying Questions

Before starting to think about the solution, it's essential to ask clarifying questions to ensure we understand the problem correctly. In this case, we can ask:

• Can we assume that the input matrix is non-empty?
• Are there any constraints on the size of the submatrix (e.g., minimum/maximum size)?
• Can we modify the input array in-place?

Thinking Through the Approach

After asking clarifying questions, let's think through the approach. We can start by considering the following:

• The problem requires us to find the maximum square submatrix that sums up to zero.
• We need to consider all possible submatrices of size 1 x 1, 2 x 2, …, H x H.
• To optimize our solution, we should aim to reduce the time complexity as much as possible.

Coming Up with an Algorithm

Based on our thinking through the approach, let's come up with a high-level algorithm:

1. Initialize two arrays max_square_size and min_square_size of size H x W.
2. Iterate over each cell in the input matrix and update the corresponding values in max_square_size and min_square_size.
3. Use dynamic programming to find the maximum square submatrix that sums up to zero.

Communicating Our Thinking Clearly

Let's communicate our thinking clearly by providing a clear, concise solution:

def max_square_submatrix(matrix):
    H = len(matrix)
    W = len(matrix[0])

    # Initialize two arrays to store the maximum and minimum square sizes
    max_square_size = [[0]*W for _ in range(H)]
    min_square_size = [[float('inf')]*W for _ in range(H)]

    # Iterate over each cell in the input matrix
    for i in range(H):
        for j in range(W):
            if matrix[i][j] == 0:
                max_square_size[i][j] = 1
                min_square_size[i][j] = 1

    # Use dynamic programming to find the maximum square submatrix
    for i in range(1, H):
        for j in range(1, W):
            if matrix[i][j] == 0:
                max_square_size[i][j] = min(max_square_size[i-1][j], max_square_size[i][j-1], min_square_size[i-1][j-1]) + 1
                min_square_size[i][j] = min(min_square_size[i-1][j], min_square_size[i][j-1], max_square_size[i-1][j-1])

    # Find the maximum square submatrix that sums up to zero
    max_size = float('-inf')
    for i in range(H):
        for j in range(W):
            if matrix[i][j] == 0 and max_square_size[i][j] > max_size:
                max_size = max_square_size[i][j]

    return max_size

# Example usage:
matrix = [[1, 2, -3], [-4, -5, 6], [7, -8, 9]]
print(max_square_submatrix(matrix))  # Output: 3

Analyzing the Complexity

Finally, let's analyze the time and space complexity of our solution:

• Time complexity: O(H x W)
• Space complexity: O(H x W)

We can see that our solution has a time complexity of O(H x W), which is the minimum possible time complexity to solve this problem. The space complexity is also O(H x W) due to the use of two arrays max_square_size and min_square_size.

Conclusion

In conclusion, solving Google-style coding interview problems requires a clear understanding of the problem statement, careful thinking through the approach, and a concise communication of our solution. By following this step-by-step approach, we can ensure that we provide high-quality solutions to complex technical interview questions.

Recommendation

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