Minimum Number of Operations to Satisfy Conditions

Problem Description

You are given a 2D matrix grid of size m x n. In one operation, you can change the value of any cell to any non-negative number. You need to perform some operations such that each cell grid[i][j] is:

• Equal to the cell below it, i.e. grid[i][j] == grid[i + 1][j] (if it exists).
• Different from the cell to its right, i.e. grid[i][j] != grid[i][j + 1] (if it exists).

Return the minimum number of operations needed.

Key Insights

• Each column must have the same value for all rows.
• Each adjacent cell in a row must have different values.
• The solution involves counting the number of changes needed to ensure the above conditions are met.

Space and Time Complexity

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

Solution

To solve the problem, we can use a greedy approach. For each column in the matrix, we need to ensure that all cells in that column are the same. We can do this by determining the most frequent number in each column and calculating how many changes are needed to make all numbers in that column equal to this most frequent number.

After ensuring that each column has the same value, we then need to ensure that adjacent cells in each row are different. We can achieve this by iterating through each row and adjusting values to ensure they alternate.

The algorithm proceeds as follows:

1. For each column, count the frequency of each number.
2. Determine the number that occurs the most and calculate the number of changes needed for that column.
3. After adjusting the columns, iterate through each row to ensure no two adjacent cells are equal, making changes as necessary.

Code Solutions