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Looking for a data structure that is optimized for finding the next closest element

I have two classes, let's call them foo and bar, that both have a DateTime property called ReadingTime.
I then have long lists of these classes, let's say foos and bars, where foos is List<foo>, bars is List<bar>.
My goal is for every element in foos to find the events in bars that happened right before and right after foo.
Some code to clarify:
var foos = new List<foo>();
var bars = new List<bar>();
...
foreach (var foo in foos)
{
bar before = bars.Where(b => b.ReadingTime <= foo.ReadingTime).OrderByDescending(b => b.ReadingTime).FirstOrDefault();
bar after = bars.Where(b => b.ReadingTime > foo.ReadingTime).OrderBy(b => b.ReadingTime).FirstOrDefault();
...
}
My issue here is performance. Is it possible to use some other data structure than a list to speed up the comparisons? In particular the OrderBy statement every single time seems like a huge waste, having it pre-ordered should also speed up the comparisons, right?
I just don't know what data structure is best, SortedList, SortedSet, SortedDictionary etc. there seem so many. Also all the information I find is on lookups, inserts, delets, etc., noone writes about finding the next closest element so I'm not sure if anything is optimized for that.
I'm on .net core 3.1 if that matters.
Thanks in advance!
Edit: Okay so to wrap this up:
First I tried implementing #derloopkat's approach. For this I figured I needed a data type that could save the data in a sorted order so I just left it as IOrderedEnumerable (which is what linq returns). Probably not very smart, as that actually brought things to a crawl. I then tried going with SortedList. Had to remove some duplicates first which was no problem in my case. Thanks for the help #Olivier Rogier! This got me up to roughly 2x the original performance, though I suspect it's mostly the removed linq OrderBys. For now this is good enough, if/when I need more performance I'm going to go with what #CamiloTerevinto suggested.
Lastly #Aldert thank you for your time but I'm too noob and under too much time pressure to understand what you suggested. Still appreciate it and might revisit this later.
Edit2: Ended up going with #CamiloTerevinto's suggestion. Cut my runtime down from 10 hours to a couple of minutes.

You don't need to sort bars ascending and descending on each iteration. Order bars just once before the loop by calling .OrderBy(f => f.ReadingTime) and then use LastOrDefault() and FirstOrDefault().
foreach (var foo in foos)
{
bar before = bars.LastOrDefault(b => b.ReadingTime <= foo.ReadingTime);
bar after = bars.FirstOrDefault(b => b.ReadingTime > foo.ReadingTime);
//...
}
This produces same output you get with your code and runs faster.

For memory performances and to have strong typing, you can use a SortedDictionary, or SortedList but it manipulates objects. Because you compare DateTime you don't need to implement comparer.
What's the difference between SortedList and SortedDictionary?
SortedList<>, SortedDictionary<> and Dictionary<>
Difference between SortedList and SortedDictionary in C#
For speed optimization you can use a double linked list where each item indicates the next and the previous items:
Doubly Linked List in C#
Linked List Implementation in C#
Using a linked list or a double linked list requires more memory because you store the next and the previous reference in a cell that embeed each instance, but you can have sometimes the most faster way to parse and compare data, as well as to search, sort, reorder, add, remove and move items, because you don't manipulate an array, but linked references.
You also can create powerfull trees and manage data in a better way than arrays.

You can use the binary sort for quick lookup. Below the code where bars is sorted and foo is looked up. You can do yourself some reading on binary searches and enhance the code by also sorting Foos. In this case you can minimize the search range of bars...
The code generates 2 lists with 100 items. then sorts bars and does a binary search for 100 times.
using System;
using System.Collections.Generic;
namespace ConsoleApp2
{
class BaseReading
{
private DateTime readingTime;
public BaseReading(DateTime dt)
{
readingTime = dt;
}
public DateTime ReadingTime
{
get { return readingTime; }
set { readingTime = value; }
}
}
class Foo:BaseReading
{
public Foo(DateTime dt) : base(dt)
{ }
}
class Bar: BaseReading
{
public Bar(DateTime dt) : base(dt)
{ }
}
class ReadingTimeComparer: IComparer<BaseReading>
{
public int Compare(BaseReading x, BaseReading y)
{
return x.ReadingTime.CompareTo(y.ReadingTime);
}
}
class Program
{
static private List<BaseReading> foos = new List<BaseReading>();
static private List<BaseReading> bars = new List<BaseReading>();
static private Random ran = new Random();
static void Main(string[] args)
{
for (int i = 0; i< 100;i++)
{
foos.Add(new BaseReading(GetRandomDate()));
bars.Add(new BaseReading(GetRandomDate()));
}
var rtc = new ReadingTimeComparer();
bars.Sort(rtc);
foreach (BaseReading br in foos)
{
int index = bars.BinarySearch(br, rtc);
}
}
static DateTime GetRandomDate()
{
long randomTicks = ran.Next((int)(DateTime.MaxValue.Ticks >> 32));
randomTicks = (randomTicks << 32) + ran.Next();
return new DateTime(randomTicks);
}
}
}

The only APIs available in the .NET platform for finding the next closest element, with a computational complexity better than O(N), are the List.BinarySearch and Array.BinarySearch methods:
// Returns the zero-based index of item in the sorted List<T>, if item is found;
// otherwise, a negative number that is the bitwise complement of the index of
// the next element that is larger than item or, if there is no larger element,
// the bitwise complement of Count.
public int BinarySearch (T item, IComparer<T> comparer);
These APIs are not 100% robust, because the correctness of the results depends on whether the underlying data structure is already sorted, and the platform does not check or enforce this condition. It's up to you to ensure that the list or array is sorted with the correct comparer, before attempting to BinarySearch on it.
These APIs are also cumbersome to use, because in case a direct match is not found you'll get the next largest element as a bitwise complement, which is a negative number, and you'll have to use the ~ operator to get the actual index. And then subtract one to get the closest item from the other direction.
If you don't mind adding a third-party dependency to your app, you could consider the C5 library, which contains the TreeDictionary collection, with the interesting methods below:
// Find the entry in the dictionary whose key is the predecessor of the specified key.
public bool TryPredecessor(K key, out SCG.KeyValuePair<K, V> res);
//Find the entry in the dictionary whose key is the successor of the specified key.
public bool TrySuccessor(K key, out SCG.KeyValuePair<K, V> res)
There are also the TryWeakPredecessor and TryWeakSuccessor methods available, that consider an exact match as a predecessor or successor respectively. In other words they are analogous to the <= and >= operators.
The C5 is a powerful and feature-rich library that offers lots of specialized collections, with its cons being its somewhat idiomatic API.
You should get excellent performance by any of these options.

Is it a principle to always have the most abstract parameters and if so does it have a name?

For example, one might have a method max on an integer array.
public static int Max(int[] ints)
{
var max = ints[0];
foreach(var i in ints)
{
if(i > max)
{
max = i;
}
}
return max;
}
But actually we didn't utilize the fact that were were using an array, just that we could iterate over them, and we didn't need ints, we just needed an object that knows how to compare itself. So a more powerful method might be:
public static T MyMax<T>(IEnumerable<T> ts) where T : IComparable<T>
{
var max = ts.First();
foreach(var i in ts)
{
if(i.CompareTo(max) > 0)
{
max = i;
}
}
return max;
}
And I guess the above discounts the fact that the IEnumerable<T> could be infinite which would cause this to hang indefinitely, but then why are you trying to find the Max fo an infinite iterable in the first place.
The point I'm trying to make is that the second method is much more powerful than the former, as it makes the least assumptions about it's parameters as needed. Is there a name for such a principle? Is this even a thing?
Thanks in advance.

I would call this Programming to an Interface.
The design principle of Programming to an Interface is most commonly mentioned in the context of declaring variables, and that's how the famous Gang of Four book introduced the principle; but it applies equally well to declaring method parameters.
Don't declare variables to be instances of particular concrete classes. Instead, commit only to an interface defined by an abstract class. You will find this to be a common theme of design patterns...
The term variables here can be considered in a broad sense that includes method parameters.

Is there a down side to returning an IEnumerable<T> via an infinite loop yielding elements?

Is the infinite loop here causing any negative impact? Resharper warns me that the..
Function never returns
..but I can't see any downside here.
public static class RandomEntityFactory
{
public static IEnumerable<T> Enumerate<T>() where T : class
{
while (true)
{
yield return Get<T>();
}
}
public static T Get<T>() where T : class
{
if (typeof(T) == typeof(Client)) return CreateRandomClient() as T;
if (typeof(T) == typeof(Font)) return CreateRandomFont() as T;
throw new Exception("unknown type: " + typeof(T).Name);
}
}

Is there a downside?
It depends on the intended usage. As written, some Linq functions - primarily All and Count - will never complete. Linq queries that use deferred execution would be fine so long as the consumer has a way to break the loop at some point. Clients will have to be sure to use deterministic functions such as Take or First (assuming at some point a return value will meet the condition).
If the intended usage is to let clients enumerate with a foreach, breaking the loop at their discretion, then it's reasonable to return items indefinitely.

Having an "infinite" enumerable does not cause any problems by itself. The particular code you have written looks very odd though. I would do it this way instead:
static IEnumerable<long> Iota()
{
long i = 0;
while (true)
{
yield return i;
i++;
}
}
This is the general-purpose sequence 0, 1, 2, ...
If you want to make an endless sequence of random fonts, you can do this:
Iota().Select(_ => CreateRandomFont())
This avoids writing your Get method, which looks bad to me.

C# pointers, iterators and generics

I am greatly stumped
How can I use an iterator in C# like a C++ iterator? I cannot find a Begin() or End() accessor, I cannot even find out how to declare an iterator. I have read about the Ienumerator. My goal is to implement the Merge Function. Here is part of my Merge function written in C++. Mostly, I am looking for the C# equivalent of what is shown, except I will be using a Reference type rather than integers.
void merge(vector<int>::iterator left, vector<int>::iterator right, vector<int>::iterator leftEnd, vector<int>::iterator rightEnd, vector<int>::iterator full)
{
while(left != leftEnd && right!= rightEnd) //compare left and right until the end of the vector is reached
{
if(*right < *left) //right < left so insert right to the output vector and advance the iterators
{
*full++ = *right++;
}
else //left < right so insert left to the output vector and advance the iterators
{
*full++ = *left++;
}
}
while(left != leftEnd) //copy any remaining elements into the output from left
{
*full++ = *left++;
}
}
Also, what collection(s) should I use? (currently I have been trying List<T> and LinkedList<T>).

It sounds like you want something like:
bool leftValid = left.MoveNext();
bool rightValid = right.MoveNext();
while (leftValid && rightValid)
{
if (right.Current < left.Current)
{
full.Add(right.Current);
rightValid = right.MoveNext();
}
else
{
full.Add(left.Current);
leftValid = left.MoveNext();
}
}
while (leftValid)
{
full.Add(left.Current);
leftValid = left.MoveNext();
}
while (rightValid)
{
full.Add(right.Current);
rightValid = right.MoveNext();
}
Here full would need to be some sort of IList<T> - .NET iterators don't let you make changes to the underlying collection.
You shouldn't try to write "bridging" code to let you use .NET iterators like C++ ones; it's much better to try to start thinking in terms of the .NET iterators when you're using .NET.
Note that it's quite rare to pass iterators around in .NET. It would be more natural to make your method to IEnumerable<T> parameters, and do something like:
using (IEnumerable<T> leftIterator = leftSequence.GetEnumerator())
{
using (IEnumerable<T> rightIterator = rightSequence.GetEnumerator())
{
// Code as above, just using leftIterator and rightIterator
// instead of left and right
}
}

.net containers don't support C++ style iterators. The only thing they have is a
simple forward iterator called IEnumerator<T>
which can't modify the collection
isn't random access
can't be copied (some collections have value type iterators which can be copied, but that's tricky business and rarely used)
and on most collections also gets invalidated whenever you modify the collection
Pretty much the only thing they can do is being iterated over in a foreach statement.
You might want to look into the IList<T> interface which allows random access, but is only supported on collections which support fast indexing. On such a collection you could implement in-place merge sort by using indices.
void Merge<T>(IList<T> container,int left, int right, int leftEnd, int rightEnd, int full)
and then use container[left] instead of *left.
Unfortunate consequence of this is, that you can't implement an efficient in-place container agnostic sorting function like C++ has.

I think you want GetEnumerator(), MoveNext(), and Current.
Normally, you can just use foreach to iterate, but your case is special.
If fact, rather than using "full", organize this as an iterator block and merge two enumerables lazily.
IEnumerable<T> Merge<T>(IEnumerable<T> left, IEnumerable<T> right)
{
... yield return Min<T>(left.Current, right.Current); ..,
}

You can use arrays, which have a fixed size, or List<T>, which are also called ArrayLists in other languages. Their items can be accessed through an indexer (list[i]) and items can be appended with list.Add(item);. They grow automatically. LinkedLists cannot be accessed via an indexer and must be traversed.
You would declare the method like this
void merge(IEnumerator<int> left, IEnumerator<int> right,
List<int> full)
{
// Jon Skeet's code goes here
}
You can get an enumerator like this
IEnumerable<int> intEnumerable = ...;
IEnumerator<int> intEnumerator = intEnumerable.GetEnumerator();
IEnumerable<T> is implemented by most generic collection types. Non generic collections usually implement IEnumerable.
(Edited in response to #CodeInChaos's comment).

Why do we need iterators in c#?

Can somebody provide a real life example regarding use of iterators. I tried searching google but was not satisfied with the answers.

You've probably heard of arrays and containers - objects that store a list of other objects.
But in order for an object to represent a list, it doesn't actually have to "store" the list. All it has to do is provide you with methods or properties that allow you to obtain the items of the list.
In the .NET framework, the interface IEnumerable is all an object has to support to be considered a "list" in that sense.
To simplify it a little (leaving out some historical baggage):
public interface IEnumerable<T>
{
IEnumerator<T> GetEnumerator();
}
So you can get an enumerator from it. That interface (again, simplifying slightly to remove distracting noise):
public interface IEnumerator<T>
{
bool MoveNext();
T Current { get; }
}
So to loop through a list, you'd do this:
var e = list.GetEnumerator();
while (e.MoveNext())
{
var item = e.Current;
// blah
}
This pattern is captured neatly by the foreach keyword:
foreach (var item in list)
// blah
But what about creating a new kind of list? Yes, we can just use List<T> and fill it up with items. But what if we want to discover the items "on the fly" as they are requested? There is an advantage to this, which is that the client can abandon the iteration after the first three items, and they don't have to "pay the cost" of generating the whole list.
To implement this kind of lazy list by hand would be troublesome. We would have to write two classes, one to represent the list by implementing IEnumerable<T>, and the other to represent an active enumeration operation by implementing IEnumerator<T>.
Iterator methods do all the hard work for us. We just write:
IEnumerable<int> GetNumbers(int stop)
{
for (int n = 0; n < stop; n++)
yield return n;
}
And the compiler converts this into two classes for us. Calling the method is equivalent to constructing an object of the class that represents the list.

Iterators are an abstraction that decouples the concept of position in a collection from the collection itself. The iterator is a separate object storing the necessary state to locate an item in the collection and move to the next item in the collection. I have seen collections that kept that state inside the collection (i.e. a current position), but it is often better to move that state to an external object. Among other things it enables you to have multiple iterators iterating the same collection.

Simple example : a function that generates a sequence of integers :
static IEnumerable<int> GetSequence(int fromValue, int toValue)
{
if (toValue >= fromValue)
{
for (int i = fromValue; i <= toValue; i++)
{
yield return i;
}
}
else
{
for (int i = fromValue; i >= toValue; i--)
{
yield return i;
}
}
}
To do it without an iterator, you would need to create an array then enumerate it...

Iterate through the students in a class
The Iterator design pattern provides
us with a common method of enumerating
a list of items or array, while hiding
the details of the list's
implementation. This provides a
cleaner use of the array object and
hides unneccessary information from
the client, ultimately leading to
better code-reuse, enhanced
maintainability, and fewer bugs. The
iterator pattern can enumerate the
list of items regardless of their
actual storage type.

Iterate through a set of homework questions.
But seriously, Iterators can provide a unified way to traverse the items in a collection regardless of the underlying data structure.
Read the first two paragraphs here for a little more info.

A couple of things they're great for:
a) For 'perceived performance' while maintaining code tidiness - the iteration of something separated from other processing logic.
b) When the number of items you're going to iterate through is not known.
Although both can be done through other means, with iterators the code can be made nicer and tidier as someone calling the iterator don't need to worry about how it finds the stuff to iterate through...
Real life example: enumerating directories and files, and finding the first [n] that fulfill some criteria, e.g. a file containing a certain string or sequence etc...

Beside everything else, to iterate through lazy-type sequences - IEnumerators. Each next element of such sequence may be evaluated/initialized upon iteration step which makes it possible to iterate through infinite sequences using finite amount of resources...

The canonical and simplest example is that it makes infinite sequences possible without the complexity of having to write the class to do that yourself:
// generate every prime number
public IEnumerator<int> GetPrimeEnumerator()
{
yield return 2;
var primes = new List<int>();
primesSoFar.Add(2);
Func<int, bool> IsPrime = n => primes.TakeWhile(
p => p <= (int)Math.Sqrt(n)).FirstOrDefault(p => n % p == 0) == 0;
for (int i = 3; true; i += 2)
{
if (IsPrime(i))
{
yield return i;
primes.Add(i);
}
}
}
Obviously this would not be truly infinite unless you used a BigInt instead of int but it gives you the idea.
Writing this code (or similar) for each generated sequence would be tedious and error prone. the iterators do that for you. If the above example seems too complex for you consider:
// generate every power of a number from start^0 to start^n
public IEnumerator<int> GetPowersEnumerator(int start)
{
yield return 1; // anything ^0 is 1
var x = start;
while(true)
{
yield return x;
x *= start;
}
}
They come at a cost though. Their lazy behaviour means you cannot spot common errors (null parameters and the like) until the generator is first consumed rather than created without writing wrapping functions to check first. The current implementation is also incredibly bad(1) if used recursively.
Wiriting enumerations over complex structures like trees and object graphs is much easier to write as the state maintenance is largely done for you, you must simply write code to visit each item and not worry about getting back to it.
I don't use this word lightly - a O(n) iteration can become O(N^2)

An iterator is an easy way of implementing the IEnumerator interface. Instead of making a class that has the methods and properties required for the interface, you just make a method that returns the values one by one and the compiler creates a class with the methods and properties needed to implement the interface.
If you for example have a large list of numbers, and you want to return a collection where each number is multiplied by two, you can make an iterator that returns the numbers instead of creating a copy of the list in memory:
public IEnumerable<int> GetDouble() {
foreach (int n in originalList) yield return n * 2;
}
In C# 3 you can do something quite similar using extension methods and lambda expressions:
originalList.Select(n => n * 2)
Or using LINQ:
from n in originalList select n * 2

IEnumerator<Question> myIterator = listOfStackOverFlowQuestions.GetEnumerator();
while (myIterator.MoveNext())
{
Question q;
q = myIterator.Current;
if (q.Pertinent == true)
PublishQuestion(q);
else
SendMessage(q.Author.EmailAddress, "Your question has been rejected");
}
foreach (Question q in listOfStackOverFlowQuestions)
{
if (q.Pertinent == true)
PublishQuestion(q);
else
SendMessage(q.Author.EmailAddress, "Your question has been rejected");
}