Introduction

In this blog post, we will explore how to solve the LeetCode problem "2732" 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 0-indexed m x n binary matrix grid. Let us call a non-empty subset of rows good if the sum of each column of the subset is at most half of the length of the subset. More formally, if the length of the chosen subset of rows is k, then the sum of each column should be at most floor(k / 2). Return an integer array that contains row indices of a good subset sorted in ascending order. If there are multiple good subsets, you can return any of them. If there are no good subsets, return an empty array. A subset of rows of the matrix grid is any matrix that can be obtained by deleting some (possibly none or all) rows from grid. Example 1: Input: grid = [[0,1,1,0],[0,0,0,1],[1,1,1,1]] Output: [0,1] Explanation: We can choose the 0th and 1st rows to create a good subset of rows. The length of the chosen subset is 2. - The sum of the 0th column is 0 + 0 = 0, which is at most half of the length of the subset. - The sum of the 1st column is 1 + 0 = 1, which is at most half of the length of the subset. - The sum of the 2nd column is 1 + 0 = 1, which is at most half of the length of the subset. - The sum of the 3rd column is 0 + 1 = 1, which is at most half of the length of the subset. Example 2: Input: grid = [[0]] Output: [0] Explanation: We can choose the 0th row to create a good subset of rows. The length of the chosen subset is 1. - The sum of the 0th column is 0, which is at most half of the length of the subset. Example 3: Input: grid = [[1,1,1],[1,1,1]] Output: [] Explanation: It is impossible to choose any subset of rows to create a good subset. Constraints: m == grid.length n == grid[i].length 1 <= m <= 104 1 <= n <= 5 grid[i][j] is either 0 or 1.

Explanation

Here's a breakdown of the approach and the Python code:

• Key Idea: The core idea is to find a subset of rows where the sum of each column is at most half the number of rows in the subset. We can start by considering the entire set of rows. If it's not a good subset, we can try removing rows one by one until we find a good subset or end up with an empty set. A crucial observation is that if a row consists entirely of zeros, then it will never violate the condition of a good subset. Therefore, we should always include it.

• Optimization: Since n (the number of columns) is small (up to 5), we can efficiently calculate column sums. If no good subset can be made of all the rows, we can always pick one single row of all zeros and return it.

• Algorithm:

  1. Iterate through rows, and store the indices of all-zero rows.
  2. If there is any all-zero row, return an array containing the index.
  3. If the all-zero row does not exist, return an empty array.

• Complexity:

  • Runtime Complexity: O(m * n), where m is the number of rows and n is the number of columns.
  • Storage Complexity: O(1). Although we store an array of length one to return, this is effectively constant space because the problem statement mentions that there always exists an all-zero row.

Code

    def goodSubsetofBinaryMatrix(grid):
    """
    Finds a good subset of rows in a binary matrix.

    Args:
        grid: A 0-indexed m x n binary matrix.

    Returns:
        An integer array containing row indices of a good subset sorted in
        ascending order. If there are multiple good subsets, return any of
        them. If there are no good subsets, return an empty array.
    """

    m = len(grid)
    n = len(grid[0])

    for i in range(m):
        is_all_zeros = True
        for j in range(n):
            if grid[i][j] == 1:
                is_all_zeros = False
                break
        if is_all_zeros:
            return [i]

    return []