C# Solution for Largest Local Values In a Matrix Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe intuition behind this C# solution remains the same as the Java solution: iterate ov
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe intuition behind this C# solution remains the same as the Java solution: iterate over every possible 3x3 submatrix in the given grid and find the maximum value within each submatrix.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n\u2022\tThe LargestLocal method iterates over each possible starting position of a 3x3 submatrix in the grid and uses the FindMaxInSubmatrix method to find the maximum value within each submatrix.\n\u2022\tThe FindMaxInSubmatrix method iterates over the 3x3 submatrix starting at the given row and column indices and finds the maximum value.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\u2022\tLet \u2018n\u2019 be the size of the grid.\n\u2022\tThe time complexity of the LargestLocal method is approximately O(n^2) for scanning the grid and O(9) for each call to FindMaxInSubmatrix, resulting in overall O(n^2).\n\u2022\tThe time complexity of the FindMaxInSubmatrix method is O(9), as it iterates over a 3x3 submatrix.\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nThe space complexity is O((n-2) * (n-2)) for storing the output matrix maxLocal, as it\u2019s a matrix of size (n-2) x (n-2), where \u2018n\u2019 is the size of the input grid. Additionally, space is required for the variables used in the methods, which is constant.\n\n# Code\n```\npublic class Solution {\n    public int[][] LargestLocal(int[][] grid) {\n        int n = grid.Length;\n        int[][] maxLocal = new int[n - 2][];\n        \n        for (int i = 0; i < n - 2; i++) {\n            maxLocal[i] = new int[n - 2];\n            for (int j = 0; j < n - 2; j++) {\n                maxLocal[i][j] = FindMaxInSubmatrix(grid, i, j);\n            }\n        }\n        \n        return maxLocal;\n    }\n\n    private int FindMaxInSubmatrix(int[][] grid, int row, int col) {\n        int max = int.MinValue;\n        for (int i = row; i < row + 3; i++) {\n            for (int j = col; j < col + 3; j++) {\n                max = Math.Max(max, grid[i][j]);\n            }\n        }\n        return max;\n    }\n}\n```
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