How do you solve Score After Flipping Matrix on LeetCode?

Score After Flipping Matrix (LeetCode #861) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(m * n) time complexity and O(1) space complexity. Key insight: Maximizing the first bit of each row significantly increases the score.

What is the time complexity of Score After Flipping Matrix?

The optimal solution for Score After Flipping Matrix runs in O(m * n) time and uses O(1) space. The time complexity is linear because we only iterate through the matrix a few times, making it efficient for the given constraints.

What is the brute force solution for Score After Flipping Matrix?

The brute force approach for Score After Flipping Matrix is Brute Force, with O(2^(m+n)) time complexity and O(1) space complexity. In the brute force approach, we can try every possible combination of toggling rows and columns to find the maximum score. This means we will check all possible states of the matrix, which can be quite slow. The optimal Optimal Solution approach improves this to O(m * n).

What algorithm or data structure is used to solve Score After Flipping Matrix?

Score After Flipping Matrix uses the following concepts: Array, Greedy, Bit Manipulation, Matrix. The recommended patterns to study are: Greedy, Bit Manipulation.

What are the interview tips for Score After Flipping Matrix?

Always think about how to maximize the most significant bits first. Consider edge cases, such as all zeros or all ones. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Score After Flipping Matrix?

Not considering the impact of toggling the first column on the entire row. Forgetting to calculate the score after toggling.

#861

Score After Flipping Matrix

Medium

ArrayGreedyBit ManipulationMatrixGreedyBit Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(2^(m+n))	O(m * n)
Space	O(1)	O(1)

💡

Intuition

Time O(m * n)Space O(1)

Instead of toggling every row and column, we can maximize the score by ensuring the first bit of each row is always 1. This can be achieved by toggling rows based on the first column's values.

⚙️

Algorithm

3 steps

1Step 1: For each row, if the first element is 0, toggle the entire row.
2Step 2: For each column, count the number of 1's and 0's. If there are more 0's than 1's, toggle that column.
3Step 3: Calculate the score by interpreting each row as a binary number and summing them up.

solution.py23 lines

1# Full working Python code
2def maxScore(grid):
3    m, n = len(grid), len(grid[0])
4    # Toggle rows to ensure first column is all 1s
5    for i in range(m):
6        if grid[i][0] == 0:
7            for j in range(n):
8                grid[i][j] ^= 1
9    # Toggle columns based on counts
10    for j in range(1, n):
11        count = sum(grid[i][j] for i in range(m))
12        if count < m / 2:
13            for i in range(m):
14                grid[i][j] ^= 1
15    # Calculate the score
16    score = 0
17    for i in range(m):
18        row_value = 0
19        for j in range(n):
20            row_value = (row_value << 1) | grid[i][j]
21        score += row_value
22    return score
23

ℹ

Complexity note: The time complexity is linear because we only iterate through the matrix a few times, making it efficient for the given constraints.

1Maximizing the first bit of each row significantly increases the score.
2Toggling rows based on the first column simplifies the problem.

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