C# Brute Force with combinatorics
Intuition\n-  Describe your first thoughts on how to solve this problem. When approaching this problem, the first intuition involves systematically identifying 
# Intuition\n- <!-- Describe your first thoughts on how to solve this problem. -->When approaching this problem, the first intuition involves systematically identifying the columns that contribute most to row coverage. A brute-force solution immediately comes to mind due to the following factors: The Problem\'s Small Scale: The constraints make it feasible to generate and evaluate all combinations of columns without hitting performance limits.\n- Need for Exhaustiveness: Since the goal is to maximize coverage, exploring all possible subsets of numSelect columns ensures that we don\'t miss any optimal solution.\n- Row and Column Coverage: The problem inherently links rows to columns based on 1s in the matrix. A key observation is that a row is covered if all its 1s are matched by the selected columns, which can be checked efficiently.\n- Brute-Force Over Combinations: Given that we need to try all possible subsets of columns, generating combinations of columns seems like the natural first step.\n- Using a brute-force approach allows us to understand the problem better and serves as a stepping stone for further optimizations, if needed.\n___\n# Approach\n- <!-- Describe your approach to solving the problem. -->Conbinations Generator: This recursive function generates all possible combinations of numSelect columns using a simple backtracking approach.\n- Check Covered Rows: For a given set of selected columns, this function iterates over all rows and checks whether the row is covered by the selected columns.\n- Brute Force over Combinations: The main loop iterates over all possible column combinations and calculates the number of rows covered for each combination, keeping track of the maximum number of covered rows.\n___\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->O(( n / numSelect) x m x n).\n___\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->O(numSelect).\n___\n# Code\n```csharp []\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution {\n    public int MaximumRows(int[][] matrix, int numSelect) {\n        int m = matrix.Length; // Number of rows\n        int n = matrix[0].Length; // Number of columns\n        int maxCoveredRows = 0;\n\n        // Generate all combinations of numSelect columns\n        IEnumerable<List<int>> Combinations(int start, int count, List<int> current) {\n            if (current.Count == count) {\n                yield return new List<int>(current);\n                yield break;\n            }\n            for (int i = start; i < n; i++) {\n                current.Add(i);\n                foreach (var combination in Combinations(i + 1, count, current)) {\n                    yield return combination;\n                }\n                current.RemoveAt(current.Count - 1);\n            }\n        }\n\n        // Check how many rows are covered for a given set of selected columns\n        int CountCoveredRows(List<int> selectedColumns) {\n            int coveredRows = 0;\n            foreach (var row in matrix) {\n                bool isCovered = true;\n                for (int j = 0; j < n; j++) {\n                    if (row[j] == 1 && !selectedColumns.Contains(j)) {\n                        isCovered = false;\n                        break;\n                    }\n                }\n                if (isCovered) {\n                    coveredRows++;\n                }\n            }\n            return coveredRows;\n        }\n\n        // Iterate through all combinations of columns and find the maximum rows covered\n        foreach (var combination in Combinations(0, numSelect, new List<int>())) {\n            maxCoveredRows = Math.Max(maxCoveredRows, CountCoveredRows(combination));\n        }\n\n        return maxCoveredRows;\n    }\n}\n```
['Array', 'Backtracking', 'Bit Manipulation', 'Matrix', 'Enumeration', 'C#']