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//Title of this code
//Rextester.Program.Main is the entry point for your code. Don't change it.
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace Rextester
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var tree = new Menu{Text = "Root", 
                                Children = new List<Menu>(){
                                    new Menu{Text="A1", Children = new List<Menu>(){
                                        new Menu{Text="A2"},
                                        new Menu{Text="B1"}
                                    }},   
                                    new Menu{Text="C1", Children = new List<Menu>(){
                                        new Menu{Text="A3", Children = new List<Menu>(){ new Menu{Text="A4" }}},
                                        new Menu{Text="B2"}
                                    }},
                                    new Menu{Text="D1", Children = new List<Menu>(){
                                        new Menu{Text="B3"}
                                    }}
                                }
                               };
            
            Console.WriteLine("Original Tree");
            PrintTree(tree,0);
            
            Console.WriteLine("====================");
            
            
            Console.WriteLine("Filtered Tree");
            Filter(tree, n => n.Text.StartsWith("A") );
            PrintTree(tree,0);
            
                
        }
        
        
        
        private static bool Filter(Menu item, Func<Menu,bool> predicate)
        {
            bool isVisible = predicate(item) ;
            bool isChildrenVisible = (item.Children != null && item.Children.Count(c => Filter(c,predicate))>0);
            item.IsVisible = isVisible || isChildrenVisible;
            return isVisible;
        }
        
        private static void PrintTree(Menu item, int depth)
        {
            if(!item.IsVisible) return;
            Console.WriteLine("{0}{1}", new string(' ',depth*2),item.Text);
            if(item.Children == null) return;
            foreach(var child in item.Children)
            {
                PrintTree(child,depth+1);
            }
        }
    }
    
    public class Menu
    {
        public Menu()
        {
            IsVisible = true;
        }
        public string Text { get; set; }
        public IEnumerable<Menu> Children { get; set; }
        public bool IsVisible{get;set;}
    }
}

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Compilation time: 0.11 sec, absolute running time: 0.08 sec, cpu time: 0.06 sec, average memory usage: 16 Mb, average nr of threads: 4