Is Flip Columns For Maximum Number of Equal Rows easy or hard?

Flip Columns For Maximum Number of Equal Rows is classified as a Medium difficulty problem. The challenge is identifying that rows and their complements behave the same after column flips. Once this insight is recognized, the implementation using hashing is straightforward.

Flip Columns For Maximum Number of Equal Rows Python/Java solution

Python and Java solutions typically build a normalized row pattern and store it in a dictionary or HashMap. Each row is converted into a string or tuple representation after adjusting for the first element. The maximum frequency of any stored pattern is returned as the result.

How to solve Flip Columns For Maximum Number of Equal Rows in O(n)?

The problem can be solved in linear time relative to the matrix size using row pattern hashing. Normalize each row so that rows and their inverses share the same representation, then store the pattern in a hash map. The highest frequency pattern represents the maximum number of rows that can become identical after column flips.

What is the best approach for Flip Columns For Maximum Number of Equal Rows?

The most effective approach is row pattern normalization using a HashMap. Convert each row into a canonical pattern by XORing values relative to the first element so rows and their complements become identical patterns. Counting these patterns in a hash map gives the maximum number of rows that can be made equal. The algorithm runs in O(m*n) time with O(m*n) space.

Is Flip Columns For Maximum Number of Equal Rows asked at Google/Amazon/Meta?

This problem follows common interview patterns used by companies like Google, Amazon, and Meta. It tests recognition of invariants, hashing techniques, and matrix processing. Variations of pattern grouping and row normalization frequently appear in coding interviews.

What data structure is used in Flip Columns For Maximum Number of Equal Rows?

The main data structure is a hash table (HashMap or dictionary). It stores normalized row patterns as keys and counts how many rows share the same pattern. Arrays or matrices are used for the input structure, while the hash table enables constant-time frequency updates.

What is the time complexity of Flip Columns For Maximum Number of Equal Rows?

The optimal solution runs in O(m*n) time, where m is the number of rows and n is the number of columns. Each row is scanned once to build a normalized pattern, and the pattern is stored in a hash map for frequency counting. Space complexity is also O(m*n) because patterns may be stored for each row.

Description Hints 1 Solution Video 11:58

1072. Flip Columns For Maximum Number of Equal Rows

Medium78.5% acceptance4 companies

You are given an m x n binary matrix matrix.

You can choose any number of columns in the matrix and flip every cell in that column (i.e., Change the value of the cell from 0 to 1 or vice versa).

Return the maximum number of rows that have all values equal after some number of flips.

Example 1:

Input: matrix = [[0,1],[1,1]]
Output: 1
Explanation: After flipping no values, 1 row has all values equal.

Example 2:

Input: matrix = [[0,1],[1,0]]
Output: 2
Explanation: After flipping values in the first column, both rows have equal values.

Example 3:

Input: matrix = [[0,0,0],[0,0,1],[1,1,0]]
Output: 2
Explanation: After flipping values in the first two columns, the last two rows have equal values.

Constraints:

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

Asked at 4 companies

Google Amazon Microsoft Bloomberg

Topics

Hints open one at a time

Hint 1

Flipping a subset of columns is like doing a bitwise XOR of some number K onto each row. We want rows X with X ^ K = all 0s or all 1s. This is the same as X = X^K ^K = (all 0s or all 1s) ^ K, so we want to count rows that have opposite bits set. For example, if K = 1, then we count rows X = (00000...001, or 1111....110).

11:58

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def maxEqualRowsAfterFlips(self, matrix: List[List[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[[0,1],[1,1]]

Input

[[0,1],[1,0]]

Input

[[0,0,0],[0,0,1],[1,1,0]]

Your code is saved on this device.Solution