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.lengthn == matrix[i].length1 <= m, n <= 300matrix[i][j] is either 0 or 1.By considering identical or opposite binary patterns within rows, the task reduces to finding the maximum similar pattern. If row 'A' can be made equal to row 'B', they must have the same or opposite pattern for all columns.
Transform each row into a consistent pattern using a reference row and check for identical transformations. The transformation involves flipping columns only when required to match the pattern.
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Time Complexity: O(m * m * n) where m is the number of rows and n is the number of columns. Space Complexity: O(n) for the transformation key.
This alternative method evaluates each row by considering both its native and entirely flipped transformations, tallying frequency counts using these dual patterns in order to discover the maximal frequency count of equivalent rows.
This approach introduces a hashing mechanism to efficiently count the occurrences of different row patterns. Two interpretations, original and flipped, are hashed for each row, then comparison pairs are reduced via a single pass lookup.
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Time Complexity: O(m * n), Space Complexity: Usage is reduced because of the hash bucket with a distant hash-field.
| Approach | Complexity |
|---|---|
| Approach 1: Row Pattern Matching using HashMap | Time Complexity: O(m * m * n) where m is the number of rows and n is the number of columns. Space Complexity: O(n) for the transformation key. |
| Approach 2: Row Pattern Counting with Initial Flip Consideration | Time Complexity: O(m * n), Space Complexity: Usage is reduced because of the hash bucket with a distant hash-field. |
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