C# Tree Serialization and Hashing
Intuition\n Describe your first thoughts on how to solve this problem. \n- Tree Representation: When given a list of folder paths, we can represent the file str
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n- Tree Representation: When given a list of folder paths, we can represent the file structure as a tree, where each folder is a node, and subfolders are children of that node.\n\n- Duplicate Detection: To detect duplicates, we need a way to uniquely identify the structure of a subtree. A simple idea is to convert the subtree into a string (or other comparable representation) that captures both the folder names and the hierarchical structure. If two folders produce the same string, they must have identical subtrees.\n\n- Serialization: Since the problem involves hierarchical data (subfolders inside folders), it naturally suggests a recursive approach to traverse the structure from the bottom up (post-order traversal), serialize subtrees, and use a dictionary to count occurrences of each subtree.\n\n- Duplicate Pruning: Once we identify subtrees that appear more than once, we can safely prune them, ensuring that any folder containing a duplicate subtree is marked for deletion.\n___\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n- Build the tree as before, where each node represents a folder.\n- Use a recursive serialization function to convert each subtree to a unique string that can be used for comparison.\n- Track subtree occurrences using a map to count how often each serialized subtree occurs.\n- Mark duplicates based on subtree serialization and recursively traverse the tree to identify and delete duplicates.\n- Return valid paths, ensuring only duplicate subtrees are removed.\n___\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->O(L), where \'L\' is the total length of all paths.\n___\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->O(L).\n___\n\n# Code\n```csharp []\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\npublic class Solution {\n    // Node class to represent the tree structure\n    public class Node {\n        public string name;\n        public Dictionary<string, Node> children;\n        public Node(string name) {\n            this.name = name;\n            this.children = new Dictionary<string, Node>();\n        }\n    }\n    \n    public IList<IList<string>> DeleteDuplicateFolder(IList<IList<string>> paths) {\n        // Root of the tree\n        Node root = new Node("/");\n\n        // Build the tree from the given paths\n        foreach (var path in paths) {\n            AddPath(root, path);\n        }\n\n        // Dictionary to store serialized subtree structures and their frequency\n        Dictionary<string, int> subtreeCount = new Dictionary<string, int>();\n        Dictionary<Node, string> nodeToSerialization = new Dictionary<Node, string>();\n        \n        // Post-order traversal to serialize subtrees and count them\n        SerializeSubtree(root, subtreeCount, nodeToSerialization);\n\n        // List to collect remaining paths after removing duplicates\n        IList<IList<string>> remainingPaths = new List<IList<string>>();\n        \n        // Traverse the tree again to collect valid paths\n        CollectPaths(root, new List<string>(), remainingPaths, subtreeCount, nodeToSerialization);\n        \n        return remainingPaths;\n    }\n    \n    // Helper method to add a path to the tree\n    private void AddPath(Node root, IList<string> path) {\n        Node current = root;\n        foreach (var dir in path) {\n            if (!current.children.ContainsKey(dir)) {\n                current.children[dir] = new Node(dir);\n            }\n            current = current.children[dir];\n        }\n    }\n    \n    // Helper method to serialize a subtree and count the frequency of each serialization\n    private string SerializeSubtree(Node node, Dictionary<string, int> subtreeCount, Dictionary<Node, string> nodeToSerialization) {\n        if (node.children.Count == 0) return ""; // Leaf node\n        \n        // Serialize the subtree rooted at this node\n        List<string> serializedChildren = new List<string>();\n        foreach (var child in node.children.Values) {\n            serializedChildren.Add(child.name + "(" + SerializeSubtree(child, subtreeCount, nodeToSerialization) + ")");\n        }\n        \n        serializedChildren.Sort(); // Sort to ensure identical structures have the same serialization\n        string serialized = string.Join(",", serializedChildren);\n        \n        // Count the serialized structure\n        if (subtreeCount.ContainsKey(serialized)) {\n            subtreeCount[serialized]++;\n        } else {\n            subtreeCount[serialized] = 1;\n        }\n        \n        nodeToSerialization[node] = serialized;\n        return serialized;\n    }\n    \n    // Helper method to collect valid paths (those not marked for deletion)\n    private void CollectPaths(Node node, List<string> currentPath, IList<IList<string>> remainingPaths, Dictionary<string, int> subtreeCount, Dictionary<Node, string> nodeToSerialization) {\n        if (node == null) return;\n\n        // Serialize the subtree to check if it has duplicates\n        if (nodeToSerialization.ContainsKey(node)) {\n            string serialized = nodeToSerialization[node];\n\n            // If this subtree occurs more than once, skip this subtree\n            if (subtreeCount.ContainsKey(serialized) && subtreeCount[serialized] > 1) {\n                return;\n            }\n        }\n\n        // Add the current path to remaining paths if not the root node\n        if (!node.name.Equals("/")) {\n            remainingPaths.Add(new List<string>(currentPath));\n        }\n\n        // Recursively collect paths from child nodes\n        foreach (var child in node.children) {\n            currentPath.Add(child.Key);\n            CollectPaths(child.Value, currentPath, remainingPaths, subtreeCount, nodeToSerialization);\n            currentPath.RemoveAt(currentPath.Count - 1);\n        }\n    }\n}\n```
['Array', 'Hash Table', 'String', 'Trie', 'Hash Function', 'C#']