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Leetcode 3127. Make a Square with the Same Color Sure, I’d be glad to help you with that problem. However, I don’t have the exact problem details from LeetCode. Let’s create a problem statement based on the title and then work through it.

Problem Statement:

Given a 2D grid of size n x n representing a tiled floor, where each cell is represented by either ‘R’ (Red) or ‘B’ (Blue), determine the minimum number of tiles you need to change to form at least one 2 x 2 square of the same color. You can only change the color of one tile at a time.

Clarifying Questions:

  1. Is the grid always a square (n x n)?
    • Yes, the grid is always a square matrix.
  2. Are there any constraints on the size of the grid (e.g., 1 <= n <= 1000)?
    • Let’s assume reasonable constraints such as (1 \leq n \leq 100) for this problem.
  3. What should be the output if the grid is already full of the same color?
    • If the grid is already full of the same color, then 0 changes are required.
  4. What should we consider if the input has mixed colors uniformly?
    • Focus on finding the minimum number of changes to form at least one 2 x 2 square.

With the assumed problem and constraints, let’s proceed with the code and strategy.

Strategy:

  1. Iterate through the grid:
    • Traverse each cell and treat it as the top-left corner of a potential 2 x 2 square.
  2. Evaluate the cost of changing a 2 x 2 square:
    • For each such square, calculate the number of changes needed to make it all ‘R’ or all ‘B’.
    • Keep track of the minimum changes required among all possible 2 x 2 squares.
  3. Output the minimum changes:
    • Once all possible squares are evaluated, the result will be the minimum number of tile changes needed.

Code:

public class MakeSquareSameColor {
    public int minChangesToSquare(char[][] grid) {
        int n = grid.length;
        int minChanges = Integer.MAX_VALUE;

        // Iterate over each cell (i, j) considering it as the top-left corner of a 2x2 square
        for (int i = 0; i < n - 1; i++) {
            for (int j = 0; j < n - 1; j++) {
                // Calculate changes needed to make the 2x2 square all 'R'
                int changesToR = 0;
                int changesToB = 0;

                if (grid[i][j] != 'R') changesToR++;
                if (grid[i][j] != 'B') changesToB++;
                
                if (grid[i][j + 1] != 'R') changesToR++;
                if (grid[i][j + 1] != 'B') changesToB++;
                
                if (grid[i + 1][j] != 'R') changesToR++;
                if (grid[i + 1][j] != 'B') changesToB++;
                
                if (grid[i + 1][j + 1] != 'R') changesToR++;
                if (grid[i + 1][j + 1] != 'B') changesToB++;

                // Take the minimum changes needed for this square
                int changesForThisSquare = Math.min(changesToR, changesToB);
                
                // Update the global minimum changes needed
                minChanges = Math.min(minChanges, changesForThisSquare);
            }
        }

        return minChanges;
    }

    public static void main(String[] args) {
        MakeSquareSameColor solution = new MakeSquareSameColor();
        char[][] grid = {
            {'R', 'B', 'R'},
            {'R', 'B', 'B'},
            {'B', 'R', 'B'}
        };
        System.out.println(solution.minChangesToSquare(grid));  // Output: 1
    }
}

Time Complexity:

This completes the problem solution. If you have any specific requirements or additional clarifications needed, feel free to ask!

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