Efficient C# program to find the largest divisible subset of distinct positive integers.
Intuition\nTo find the largest divisible subset, we need to identify the subset in which every pair of elements satisfies the condition mentioned in the problem
# Intuition\nTo find the largest divisible subset, we need to identify the subset in which every pair of elements satisfies the condition mentioned in the problem statement. This problem can be solved using dynamic programming.\n\n# Approach\n- Sort the given array nums in ascending order.\n- Initialize two arrays: dp to store the length of the largest divisible subset ending at each index, and prevIndex to store the index of the previous element in the subset.\n- Iterate through each element in nums:\n    - For each element nums[i], initialize dp[i] to 1 (minimum subset size) and prevIndex[i] to -1.\n    - For each element nums[i], iterate through all elements before it (nums[j] where j < i):\n        - If nums[i] % nums[j] == 0 and dp[i] < dp[j] + 1, update dp[i] = dp[j] + 1 and prevIndex[i] = j.\n- Find the index maxIndex of the element with the maximum value in dp array.\n- Backtrack from maxIndex using prevIndex to construct the largest divisible subset.\n- Return this subset.\n\n# Complexity\n- Time complexity:\nO(n^2), where n is the length of the input array nums. We have nested loops, one iterating through each element and the other iterating through all elements before it.\n\n- Space complexity:\nO(n), for the dp and prevIndex arrays, each of length n.\n\n# Code\n```\npublic class Solution {\n    public IList<int> LargestDivisibleSubset(int[] nums) {\n        if (nums == null || nums.Length == 0) return new List<int>();\n\n        Array.Sort(nums);\n\n        int n = nums.Length;\n        int[] dp = new int[n];\n        int[] prevIndex = new int[n];\n        int maxIndex = 0;\n\n        for (int i = 0; i < n; i++) {\n            dp[i] = 1;\n            prevIndex[i] = -1;\n            for (int j = i - 1; j >= 0; j--) {\n                if (nums[i] % nums[j] == 0 && dp[i] < dp[j] + 1) {\n                    dp[i] = dp[j] + 1;\n                    prevIndex[i] = j;\n                }\n            }\n            if (dp[i] > dp[maxIndex]) maxIndex = i;\n        }\n\n        List<int> subset = new List<int>();\n        int currentIndex = maxIndex;\n        while (currentIndex >= 0) {\n            subset.Add(nums[currentIndex]);\n            currentIndex = prevIndex[currentIndex];\n        }\n\n        return subset;\n        \n    }\n}\n```
['C#']