C# Solution for Binary Trees with Factors Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe intuition for the above solution is to use dynamic programming to count the number 
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe intuition for the above solution is to use dynamic programming to count the number of binary trees that can be formed from the given array. The key idea is to break down the problem into subproblems and use the previously calculated results to compute the final answer.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n1.\tSort the input array arr to ensure that we process smaller values before larger ones.\n2.\tInitialize an array dp of the same length as arr to keep track of the number of binary trees that can be formed using each element in arr.\n3.\tCreate a dictionary index to map each element in arr to its index in the sorted array.\n4.\tInitialize each element of dp to 1, as a single element can be a binary tree on its own.\n5.\tLoop through the elements in arr. For each element arr[i], iterate through the elements before it (arr[j]). If arr[i] is divisible by arr[j], it means we can use arr[j] as a left child and arr[i] / arr[j] as a right child to form a binary tree. If the complement (arr[i] / arr[j]) is present in the index dictionary, then we update dp[i] by multiplying the count of trees formed by arr[j] and arr[i] / arr[j] and add it to dp[i]. This accounts for the combinations of left and right subtrees.\n6.\tFinally, sum up all the values in the dp array to get the total number of binary trees that can be formed.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\nThe time complexity of this solution is O(n^2) because of the nested loops over the elements in arr. \n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\nThe space complexity is O(n) for the dp array and O(n) for the index dictionary, resulting in a total space complexity of O(n).\n\n# Code\n```\npublic class Solution {\n    public int NumFactoredBinaryTrees(int[] arr) {\n        int MOD = 1000000007;\n        Array.Sort(arr);\n        long[] dp = new long[arr.Length];\n        Dictionary<int, int> index = new Dictionary<int, int>();\n\n        for (int i = 0; i < arr.Length; i++) {\n            dp[i] = 1;\n            index[arr[i]] = i;\n        }\n\n        for (int i = 0; i < arr.Length; i++) {\n            for (int j = 0; j < i; j++) {\n                if (arr[i] % arr[j] == 0) {\n                    int complement = arr[i] / arr[j];\n                    if (index.ContainsKey(complement)) {\n                        int k = index[complement];\n                        dp[i] = (dp[i] + dp[j] * dp[k]) % MOD;\n                    }\n                }\n            }\n        }\n\n        long result = 0;\n        foreach (long count in dp) {\n            result = (result + count) % MOD;\n        }\n\n        return (int)result;\n    }\n}\n```
['C#']