C# Brute Force Solution with Enumeration
Intuition\n Describe your first thoughts on how to solve this problem. To solve the problem of counting subtrees where the maximum distance between any two citi
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->To solve the problem of counting subtrees where the maximum distance between any two cities is equal to \'d\', we can use a brute-force approach given the constraints that n is less than or equal to 15.\n\n___\n\n# Approach\n<!-- Describe your approach to solving the problem. -->//  Graph Initialization: We initialize the graph as an adjacency list.\n//  Mask Enumeration: We enumerate all possible subsets of cities using a bitmask approach. Each bit in the \n//  mask represents whether a city is included in the subset.\n//  Connected Subtrees: We check if a subset of cities forms a connected component using a BFS-based \n//  IsConnected method.\n//  Maximum Distance Calculation: For each connected subtree, we calculate the maximum distance using BFS in\n//  the GetMaxDistance method.\n//  Result Accumulation: We accumulate the count of subtrees with each possible maximum distance.\n___\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->O(2^n x n^2).\n____\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->O(n^2).\n___\n\n# Code\n```csharp []\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\npublic class Solution {\n    public int[] CountSubgraphsForEachDiameter(int n, int[][] edges) {\n        var graph = new List<int>[n + 1];\n        for (int i = 1; i <= n; i++) {\n            graph[i] = new List<int>();\n        }\n\n        foreach (var edge in edges) {\n            graph[edge[0]].Add(edge[1]);\n            graph[edge[1]].Add(edge[0]);\n        }\n\n        int[] result = new int[n - 1];\n\n        for (int mask = 1; mask < (1 << n); mask++) {\n            List<int> nodes = new List<int>();\n            for (int i = 0; i < n; i++) {\n                if ((mask & (1 << i)) != 0) {\n                    nodes.Add(i + 1);\n                }\n            }\n\n            if (IsConnected(graph, nodes)) {\n                int maxDist = GetMaxDistance(graph, nodes);\n                if (maxDist > 0 && maxDist < n) {\n                    result[maxDist - 1]++;\n                }\n            }\n        }\n\n        return result;\n    }\n\n    private bool IsConnected(List<int>[] graph, List<int> nodes) {\n        var visited = new HashSet<int>();\n        Queue<int> queue = new Queue<int>();\n        queue.Enqueue(nodes[0]);\n        visited.Add(nodes[0]);\n\n        while (queue.Count > 0) {\n            int node = queue.Dequeue();\n            foreach (int neighbor in graph[node]) {\n                if (nodes.Contains(neighbor) && !visited.Contains(neighbor)) {\n                    visited.Add(neighbor);\n                    queue.Enqueue(neighbor);\n                }\n            }\n        }\n\n        return visited.Count == nodes.Count;\n    }\n\n    private int GetMaxDistance(List<int>[] graph, List<int> nodes) {\n        int maxDist = 0;\n        foreach (int node in nodes) {\n            var dist = BFS(graph, node, nodes);\n            maxDist = Math.Max(maxDist, dist);\n        }\n        return maxDist;\n    }\n\n    private int BFS(List<int>[] graph, int start, List<int> nodes) {\n        var dist = new Dictionary<int, int>();\n        foreach (int node in nodes) {\n            dist[node] = -1;\n        }\n\n        Queue<int> queue = new Queue<int>();\n        queue.Enqueue(start);\n        dist[start] = 0;\n\n        int maxDist = 0;\n\n        while (queue.Count > 0) {\n            int node = queue.Dequeue();\n            foreach (int neighbor in graph[node]) {\n                if (nodes.Contains(neighbor) && dist[neighbor] == -1) {\n                    dist[neighbor] = dist[node] + 1;\n                    maxDist = Math.Max(maxDist, dist[neighbor]);\n                    queue.Enqueue(neighbor);\n                }\n            }\n        }\n\n        return maxDist;\n    }\n}\n```
['Tree', 'Enumeration', 'C#']