How do you solve Find a Good Subset of the Matrix on LeetCode?

Find a Good Subset of the Matrix (LeetCode #2732) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: A good subset can be a single row of all zeros.

What is the brute force solution for Find a Good Subset of the Matrix?

The brute force approach for Find a Good Subset of the Matrix is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks all possible subsets of rows to see if they meet the criteria for being a good subset. This means we will evaluate every combination of rows, which can be inefficient as the number of rows increases. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find a Good Subset of the Matrix?

Find a Good Subset of the Matrix uses the following concepts: Array, Hash Table, Bit Manipulation, Matrix. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find a Good Subset of the Matrix?

Start with a brute force approach to demonstrate understanding. Clearly explain your thought process and reasoning. Be ready to optimize your solution and justify the changes.

What are common mistakes when solving Find a Good Subset of the Matrix?

Not checking for single rows first. Overlooking the condition of column sums.

#2732

Find a Good Subset of the Matrix

Hard

ArrayHash TableBit ManipulationMatrixHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal solution leverages the insight that we only need to check for rows with all zeros or pairs of rows. This reduces the complexity significantly by avoiding the need to check all combinations.

⚙️

Algorithm

2 steps

1Step 1: Check each row to see if it contains only zeros. If found, return that row's index.
2Step 2: If no single row is valid, check pairs of rows to see if their combined column sums meet the criteria.

solution.py11 lines

1def findGoodSubset(grid):
2    m = len(grid)
3    for i in range(m):
4        if all(x == 0 for x in grid[i]):
5            return [i]
6    for i in range(m):
7        for j in range(i + 1, m):
8            col_sums = [grid[i][k] + grid[j][k] for k in range(len(grid[0]))]
9            if all(col_sum <= 1 for col_sum in col_sums):
10                return [i, j]
11    return []

ℹ

Complexity note: This complexity is O(n) because we only check each row once for zeros and then at most n pairs of rows, making it linear in terms of the number of rows.

1A good subset can be a single row of all zeros.
2If no single row exists, check pairs of rows.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.