Score After Flipping Matrix Python Solution

LeetCode 861, Medium. Topics: Array, Greedy, Bit Manipulation, Matrix. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 14 parametrized pytest cases, and a playground notebook:

lcpy gen -n 861   # by problem number
lcpy gen -s score_after_flipping_matrix   # by problem name

Problem

You are given an m x n binary matrix grid. A move consists of choosing any row or column and toggling each value in that row or column (i.e., changing all 0’s to 1’s, and all 1’s to 0’s). Every row of the matrix is interpreted as a binary number, and the score of the matrix is the sum of these numbers. Return the highest possible score after making any number of moves (including zero moves).

Examples

Input: grid = [[0,0,1,1],[1,0,1,0],[1,1,0,0]]
Output: 39
Explanation: 0b1111 + 0b1001 + 0b1111 = 15 + 9 + 15 = 39

Input: grid = [[0]]
Output: 1

Constraints

m == grid.length
n == grid[i].length
1 <= m, n <= 20
grid[i][j] is either 0 or 1.

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(m * n)
    # Space: O(1)
    def matrix_score(self, grid: list[list[int]]) -> int:
        m, n = len(grid), len(grid[0])
        score = 0
        for j in range(n):
            # After the optimal row flip, a row's bit at j is 1 exactly when
            # grid[i][j] == grid[i][0] (the leading bit is always set to 1)
            ones = sum(1 for row in grid if row[j] == row[0])
            score += max(ones, m - ones) * (1 << (n - 1 - j))
        return score

Complexity

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

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Score After Flipping Matrix Python Solution

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