Is Remove All Ones With Row and Column Flips easy or hard?

The problem is rated Medium because the implementation is simple but the insight about row complements is not immediately obvious. Once you realize every row must match the first row or its inverse, the solution becomes a straightforward O(m*n) scan.

Remove All Ones With Row and Column Flips Python/Java solution

Implement the normalization approach: for each row, flip the bits logically if the first element is 1, then compare the transformed row with a reference row. The same logic works across Python, Java, C++, Go, TypeScript, and Rust because it only requires iteration and simple bit checks.

How to solve Remove All Ones With Row and Column Flips in O(n)?

For an m x n matrix, the best achievable complexity is O(m*n) because every element must be inspected. Normalize each row by XORing with its first element so the row starts with 0. After normalization, verify that every row matches the same pattern as the first row.

What is the best approach for Remove All Ones With Row and Column Flips?

The optimal solution normalizes each row relative to its first element and checks whether all rows share the same normalized pattern. A row that starts with 1 is inverted so it matches the form of rows starting with 0. If every normalized row is identical, column flips can align them and row flips can remove remaining ones. This runs in O(m*n) time.

Is Remove All Ones With Row and Column Flips asked at Google/Amazon/Meta?

Matrix pattern and flip transformation problems appear in interviews at companies like Google, Amazon, and Meta. This problem specifically tests recognition of row complement patterns and efficient matrix traversal, both common interview themes.

What data structure is used in Remove All Ones With Row and Column Flips?

The common implementation uses a hash set or direct pattern comparison. Rows are normalized into a canonical form and stored or compared, making the hash table useful for quickly verifying that all patterns are identical.

What is the time complexity of Remove All Ones With Row and Column Flips?

The optimal algorithm scans each cell once while normalizing row patterns, giving O(m*n) time complexity for an m by n matrix. Space complexity is O(n) to store the reference row pattern or hash representation.

Description Hints 5 Solution Video 13:42

2128. Remove All Ones With Row and Column Flips

Medium76.2% acceptance1 companyPremium elsewhere, free here

You are given an m x n binary matrix grid.

In one operation, you can choose any row or column and flip each value in that row or column (i.e., changing all 0's to 1's, and all 1's to 0's).

Return true if it is possible to remove all 1's from grid using any number of operations or false otherwise.

Example 1:

Input: grid = [[0,1,0],[1,0,1],[0,1,0]]
Output: true
Explanation: One possible way to remove all 1's from grid is to:
- Flip the middle row
- Flip the middle column

Example 2:

Input: grid = [[1,1,0],[0,0,0],[0,0,0]]
Output: false
Explanation: It is impossible to remove all 1's from grid.

Example 3:

Input: grid = [[0]]
Output: true
Explanation: There are no 1's in grid.

Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 300
grid[i][j] is either 0 or 1.

Asked at 1 company

Google

Topics

Hints open one at a time

Hint 1

Does the order, in which you do the operations, matter?

Hint 2

No, it does not. An element will keep its original value if the number of operations done on it is even and vice versa. This also means that doing more than 1 operation on the same row or column is unproductive.

Hint 3

Try working backward, start with a matrix of all zeros and try to construct grid using operations.

Hint 4

Start with operations on columns, after doing them what do you notice about each row?

Hint 5

Each row is the exact same. If we then flip some rows, that leaves only two possible arrangements for each row: the same as the original or the opposite.

13:42

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