Study code - https://www.youtube.com/watch?v=fKR1n35Sj8s&t=30s, write down C# code - good idea to follow.

killProcess_StudyCode.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace KillProcess_YuZhou
{
    class Program
    {
        static void Main(string[] args)
        {
        }

        /// <summary>
        /// This solution is to copy the idea from the video shown here:
        /// https://www.youtube.com/watch?v=fKR1n35Sj8s&t=30s         
        /// </summary>
        /// <param name="pid"></param>
        /// <param name="ppid"></param>
        /// <param name="kill"></param>
        /// <returns></returns>
        public static IList<int> KillProcess(IList<int> pid, IList<int> ppid, int kill)
        {
            var dictionary = buildDictionary(pid, ppid);

            return getAllChildren(dictionary, kill); 
        }

        /// <summary>
        /// Find kill id in the pid and its children hashtable, do 
        /// a DFS/ BFS search 
        /// </summary>
        /// <param name="dictionary"></param>
        /// <param name="kill"></param>
        /// <returns></returns>
        private static IList<int> getAllChildren(IDictionary<int, HashSet<int>> dictionary, int kill)
        {
            // Find kill id in the pid and its children hashtable, do 
            // a DFS/ BFS search 
            IList<int> result = new List<int>();
            var queue = new Queue<int>();
            queue.Enqueue(kill);

            while (queue.Count > 0)
            {
                var parent = queue.Dequeue();
                result.Add(parent);

                if (dictionary.ContainsKey(parent))
                {
                    var children = dictionary[parent];
                    foreach (var item in children)
                    {
                        queue.Enqueue(item);
                    }
                }
            }

            return result; 
        }
        
        /// <summary>
        /// Go over each parent id in the array called ppid, add id and its child
        /// to a hash table. 
        /// Go over the sample case,
        ///     3
        ///    / \      
        ///   1   5
        ///      /
        ///    10  
        /// pid = 3 has two children - 1, 5  
        /// pid = 1 has no child. pid = 5 has one child 10. 
        /// </summary>
        /// <param name="pid"></param>
        /// <param name="ppid"></param>
        /// <returns></returns>
        private static IDictionary<int, HashSet<int>> buildDictionary(IList<int> pid, IList<int> ppid)
        {            
            var dictionary = new Dictionary<int, HashSet<int>>();

            for (int i = 0; i < ppid.Count; i++)
            {
                var current = ppid[i];
                var child = pid[i];

                bool isInDict = dictionary.ContainsKey(current);
                if (isInDict)
                {
                    dictionary[current].Add(child);
                }
                else
                {
                    var set = new HashSet<int>();
                    set.Add(child);
                    dictionary.Add(current, set);
                }
            }

            return dictionary; 
        }
    }
}