C# Solution for Smallest Sufficient Team Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe intuition behind the above solution is to find the smallest team of people who coll
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe intuition behind the above solution is to find the smallest team of people who collectively possess all the required skills. The solution uses a dynamic programming approach to solve the problem.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n- The solution defines a recursive function F that takes a skillsMask as an input, which represents the bitmask of the remaining required skills.\n- If skillsMask is 0, it means all the required skills have been covered, so the function returns 0.\n- If the dp array already has a pre-calculated value for the given skillsMask, the function returns that value.\n- Otherwise, the function iterates through each person and calculates a smallerSkillsMask by removing the skills of that person from the current skillsMask.\n- If smallerSkillsMask is different from skillsMask, it means the current person\'s skills contribute to the remaining required skills.\n- The function recursively calls F with the smallerSkillsMask and ORs the result with a bitmask representing the current person. This bitmask represents the set of people who possess the required skills.\n- If the dp value for the current skillsMask is not set or the newly calculated bitmask has fewer people than the current dp value, the dp value is updated with the newly calculated bitmask.\n- Finally, the function returns the dp value for the given skillsMask.\n- In the SmallestSufficientTeam method:\n\n1. It initializes variables and data structures required for the solution.\n1. It iterates through the people and creates a skillsMaskOfPerson array, where each element represents the bitmask of skills possessed by a person.\n1. It initializes the dp array with -1 to indicate that the values have not been calculated yet.\n1. It calls the F function with the bitmask representing all the required skills to get the bitmask of people with the smallest team.\n1. It converts the bitmask into the final answer array by counting the set bits and storing the corresponding indices in the ans array.\n1. Finally, it returns the ans array, which represents the smallest team of people with all the required skills.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\nThe time complexity of the solution depends on the number of people (n) and the number of required skills (m). Since the solution uses dynamic programming, the time complexity is O(2^m * n), where 2^m represents the number of possible skill combinations and n represents the number of people.\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nThe space complexity of the solution is O(2^m) because of the dp array, which stores the intermediate results for each skill combination. The skillsMaskOfPerson array also contributes O(n) space complexity. Therefore, the overall space complexity is dominated by the dp array.\n\n# Code\n```\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution\n{\n    private int n;\n    private int[] skillsMaskOfPerson;\n    private long[] dp;\n\n    private long F(int skillsMask)\n    {\n        if (skillsMask == 0)\n        {\n            return 0L;\n        }\n\n        if (dp[skillsMask] != -1)\n        {\n            return dp[skillsMask];\n        }\n\n        for (int i = 0; i < n; i++)\n        {\n            int smallerSkillsMask = skillsMask & ~skillsMaskOfPerson[i];\n            if (smallerSkillsMask != skillsMask)\n            {\n                long peopleMask = F(smallerSkillsMask) | (1L << i);\n                if (dp[skillsMask] == -1 || CountBits(peopleMask) < CountBits(dp[skillsMask]))\n                {\n                    dp[skillsMask] = peopleMask;\n                }\n            }\n        }\n\n        return dp[skillsMask];\n    }\n\n    private int CountBits(long value)\n    {\n        int count = 0;\n        while (value != 0)\n        {\n            count += (int)(value & 1);\n            value >>= 1;\n        }\n        return count;\n    }\n\n    public int[] SmallestSufficientTeam(string[] req_skills, IList<IList<string>> people)\n    {\n        n = people.Count;\n        int m = req_skills.Length;\n        Dictionary<string, int> skillId = new Dictionary<string, int>();\n        \n        for (int i = 0; i < m; i++)\n        {\n            skillId[req_skills[i]] = i;\n        }\n\n        skillsMaskOfPerson = new int[n];\n        for (int i = 0; i < n; i++)\n        {\n            foreach (string skill in people[i])\n            {\n                skillsMaskOfPerson[i] |= 1 << skillId[skill];\n            }\n        }\n\n        dp = new long[1 << m];\n        Array.Fill(dp, -1);\n        long answerMask = F((1 << m) - 1);\n        int[] ans = new int[CountBits(answerMask)];\n        int ptr = 0;\n\n        for (int i = 0; i < n; i++)\n        {\n            if (((answerMask >> i) & 1) == 1)\n            {\n                ans[ptr++] = i;\n            }\n        }\n\n        return ans;\n    }\n}\n\n```
['C#']