C# BFS Solution
Intuition\n Describe your first thoughts on how to solve this problem. This problem is well-suited for BFS because we want to explore all possible strings gener
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->This problem is well-suited for BFS because we want to explore all possible strings generated by the given operations and find the lexicographically smallest one.\nA queue is used to perform BFS, and a HashSet<string> is used to keep track of the strings that have already been visited to avoid cycles.\n___\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n//  Operations:\n//  *Operation 1: Add a to all odd indices in the string. This operation is performed by converting the \n//  string to a character array, modifying the relevant indices, and then converting it back to a string.\n//  *Operation 2: Rotate the string by b positions. This is implemented using string slicing, where we \n//  concatenate the last b characters with the first n-b characters.\n//  Result Tracking: The result is updated every time we find a lexicographically smaller string during the \n//  BFS traversal.\n//  Termination: The BFS will eventually terminate when all possible strings have been explored, and the \n//  smallest string will be returned.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->O(n * k), where \'n\' is the length of the string and \'k\' is a constant related to the number of distinct strings.\n___\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->O(n * k) for storign the seen strings in the hash set and the queue.\n___\n\n# Code\n```csharp []\nusing System;\nusing System.Collections.Generic;\n\npublic class Solution {\n    public string FindLexSmallestString(string s, int a, int b) {\n        HashSet<string> seen = new HashSet<string>();\n        Queue<string> queue = new Queue<string>();\n        string result = s;\n\n        queue.Enqueue(s);\n        seen.Add(s);\n\n        while (queue.Count > 0) {\n            string current = queue.Dequeue();\n\n            // Update the result to be the lexicographically smallest string found\n            if (string.Compare(current, result) < 0) {\n                result = current;\n            }\n\n            // Apply operation 1: Add \'a\' to all odd indices\n            char[] chars = current.ToCharArray();\n            for (int i = 1; i < chars.Length; i += 2) {\n                chars[i] = (char)((chars[i] - \'0\' + a) % 10 + \'0\');\n            }\n            string newString1 = new string(chars);\n            if (!seen.Contains(newString1)) {\n                seen.Add(newString1);\n                queue.Enqueue(newString1);\n            }\n\n            // Apply operation 2: Rotate the string by \'b\' positions\n            string newString2 = RotateString(current, b);\n            if (!seen.Contains(newString2)) {\n                seen.Add(newString2);\n                queue.Enqueue(newString2);\n            }\n        }\n\n        return result;\n    }\n\n    private string RotateString(string s, int b) {\n        int n = s.Length;\n        b = b % n;\n        return s.Substring(n - b) + s.Substring(0, n - b);\n    }\n}\n```
['String', 'Breadth-First Search', 'C#']