Introduction

In this blog post, we will explore how to solve the LeetCode problem "1727" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given a binary matrix matrix of size m x n, and you are allowed to rearrange the columns of the matrix in any order. Return the area of the largest submatrix within matrix where every element of the submatrix is 1 after reordering the columns optimally. Example 1: Input: matrix = [[0,0,1],[1,1,1],[1,0,1]] Output: 4 Explanation: You can rearrange the columns as shown above. The largest submatrix of 1s, in bold, has an area of 4. Example 2: Input: matrix = [[1,0,1,0,1]] Output: 3 Explanation: You can rearrange the columns as shown above. The largest submatrix of 1s, in bold, has an area of 3. Example 3: Input: matrix = [[1,1,0],[1,0,1]] Output: 2 Explanation: Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2. Constraints: m == matrix.length n == matrix[i].length 1 <= m * n <= 105 matrix[i][j] is either 0 or 1.

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• High-level approach:

  • For each row, transform the matrix in place such that each element matrix[i][j] stores the length of consecutive 1s ending at that position in the original matrix.
  • For each row, sort the row in non-decreasing order. This simulates the optimal column arrangement.
  • Calculate the area for each sorted row and keep track of the maximum area encountered.

• Complexity:

  • Runtime: O(m n log(n)), where m is the number of rows and n is the number of columns. This is dominated by the sorting within the loop.
  • Storage: O(1) - in-place modification.

Code

    def largestSubmatrix(matrix):
    """
    Calculates the area of the largest submatrix of 1s after optimally rearranging columns.

    Args:
        matrix: A list of lists representing the binary matrix.

    Returns:
        The area of the largest submatrix of 1s.
    """
    m = len(matrix)
    n = len(matrix[0])
    max_area = 0

    for i in range(1, m):
        for j in range(n):
            if matrix[i][j] == 1:
                matrix[i][j] += matrix[i - 1][j]

    for i in range(m):
        matrix[i].sort(reverse=True)
        for j in range(n):
            max_area = max(max_area, matrix[i][j] * (j + 1))

    return max_area