Initial

experiments/maze_solver/SimpleDemo.cs

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+using System;
+using System.Diagnostics;
+
+class SimpleDemo
+{
+    static void Main()
+    {
+        Console.WriteLine("=== Space-Time Tradeoff Demo ===\n");
+        
+        // Create a simple 30x30 maze
+        int size = 30;
+        var maze = MazeGenerator.Generate(size, size);
+        
+        // Run BFS (uses more memory, less time)
+        Console.WriteLine("1. BFS (O(n) space):");
+        var sw1 = Stopwatch.StartNew();
+        var bfsResult = MazeSolver.BFS(maze);
+        sw1.Stop();
+        Console.WriteLine($"   Time: {sw1.ElapsedMilliseconds}ms");
+        Console.WriteLine($"   Memory: {bfsResult.MemoryUsage} bytes\n");
+        
+        // Run memory-limited algorithm (uses less memory, more time)
+        Console.WriteLine("2. Memory-Limited DFS (O(√n) space):");
+        var sw2 = Stopwatch.StartNew();
+        int memLimit = (int)Math.Sqrt(size * size);
+        var limitedResult = SpaceEfficientMazeSolver.MemoryLimitedDFS(maze, memLimit);
+        sw2.Stop();
+        Console.WriteLine($"   Time: {sw2.ElapsedMilliseconds}ms");
+        Console.WriteLine($"   Memory: {limitedResult.MemoryUsage} bytes");
+        Console.WriteLine($"   Nodes explored: {limitedResult.NodesExplored}");
+        
+        // Show the tradeoff
+        Console.WriteLine("\n=== Analysis ===");
+        Console.WriteLine($"Memory reduction: {(1.0 - (double)limitedResult.MemoryUsage / bfsResult.MemoryUsage) * 100:F1}%");
+        Console.WriteLine($"Time increase: {((double)sw2.ElapsedMilliseconds / sw1.ElapsedMilliseconds - 1) * 100:F1}%");
+        Console.WriteLine("\nThis demonstrates Williams' theoretical result:");
+        Console.WriteLine("We can simulate time-bounded algorithms with ~√(t) space!");
+    }
+}