Adding videos to chapters (algorithm-archivists#554)

* adding videos to chapters.

* fixing typo from youtube comment.

* Update contents/euclidean_algorithm/euclidean_algorithm.md

Co-Authored-By: leios <[email protected]>

* Apply suggestions from code review

Co-Authored-By: leios <[email protected]>

Author: leios

contents/bitlogic/bitlogic.md

@@ -133,6 +133,13 @@ There are a few other gates, but this is enough for most things. We'll add more
 
 That's about it for bitlogic. I realize it was a bit long, but this is absolutely essential to understanding how computers think and how to use programming as an effective tool!
 
+## Video Explanation
+Here is a video describing the contents of this chapter:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/zMuEk44Ufkw" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 <script>
 MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
 </script>

contents/euclidean_algorithm/euclidean_algorithm.md

@@ -142,6 +142,14 @@ Here, we set `b` to be the remainder of `a%b` and `a` to be whatever `b` was las
 
 The Euclidean Algorithm is truly fundamental to many other algorithms throughout the history of computer science and will definitely be used again later. At least to me, it's amazing how such an ancient algorithm can still have modern use and appeal. That said, there are still other algorithms out there that can find the greatest common divisor of two numbers that are arguably better in certain cases than the Euclidean algorithm, but the fact that we are discussing Euclid two millennia after his death shows how timeless and universal mathematics truly is. I think that's pretty cool.
 
+## Video Explanation
+
+Here's a video on the Euclidean algorithm:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/h86RzlyHfUE" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 
 {% method %}

contents/forward_euler_method/forward_euler_method.md

@@ -91,6 +91,14 @@ Verlet integration has a distinct advantage over the forward Euler method in bot
 That said, in practice, due to the instability of the forward Euler method and the error with larger timesteps, this method is rarely used in practice.
 That said, variations of this method *are* certainly used (for example Crank-Nicolson and [Runge-Kutta](../runge_kutta_methods/runge_kutta_methods.md), so the time spent reading this chapter is not a total waste!
 
+## Video Explanation
+
+Here is a video describing the forward Euler method:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/wG7h8g6VLBo" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 
 Like in the case of [Verlet Integration](../verlet_integration/verlet_integration.md), the easiest way to test to see if this method works is to test it against a simple test-case.

contents/gaussian_elimination/gaussian_elimination.md

@@ -82,7 +82,7 @@ $$
 This matrix form has a particular name: _Row Echelon Form_.
 Basically, any matrix can be considered in row echelon form if the leading coefficient or _pivot_ (the first non-zero element in every row when reading from left to right) is right of the pivot of the row above it.
 
-This creates a matrix that sometiems resembles an upper-triangular matrix; however, that doesn't mean that all row-echelon matrices are upper-triangular.
+This creates a matrix that sometimes resembles an upper-triangular matrix; however, that doesn't mean that all row-echelon matrices are upper-triangular.
 For example, all of the following matrices are in row echelon form:
 
 $$
@@ -529,6 +529,14 @@ How? Well, we can use an algorithm known as the _Tri-Diagonal Matrix Algorithm_
 
 There are also plenty of other solvers that do similar things that we will get to in due time.
 
+## Video Explanation
+
+Here's a video describing Gaussian elimination:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/2tlwSqblrvU" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 
 {% method %}

contents/huffman_encoding/huffman_encoding.md

@@ -47,6 +47,14 @@ and `bibbity_bobbity` becomes `01000010010111011110111000100101110`.
 As mentioned this uses the minimum number of bits possible for encoding.
 The fact that this algorithm is both conceptually simple and provably useful is rather extraordinary to me and is why Huffman encoding will always hold a special place in my heart.
 
+## Video Explanation
+
+Here is a quick video explanation for Huffman encoding:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/wHyUxTc2Ohk" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 In code, this can be a little tricky. It requires a method to continually sort the nodes as you add more and more nodes to the system.
 The most straightforward way to do this in some languages is with a priority queue, but depending on the language, this might be more or less appropriate.

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -108,6 +108,14 @@ As long as you can write some function to tell whether the provided point is ins
 This is obviously an incredibly powerful tool and has been used time and time again for many different areas of physics and engineering.
 I can guarantee that we will see similar methods crop up all over the place in the future!
 
+## Video Explanation
+
+Here is a video describing Monte Carlo integration:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/AyBNnkYrSWY" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 Monte Carlo methods are famous for their simplicity.
 It doesn't take too many lines to get something simple going.
@@ -179,8 +187,6 @@ Feel free to submit your version via pull request, and thanks for reading!
 [import, lang:"bash"](code/bash/monte_carlo.bash)
 {% endmethod %}
 
-
-
 <script>
 MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
 </script>

contents/split-operator_method/split-operator_method.md

@@ -161,6 +161,14 @@ As you can see from the code, this involves summing the density, multiplying tha
 
 The Split-Operator method is one of the most commonly used quantum simulation algorithms because of how straightforward it is to code and how quickly you can start really digging into the physics of the simulation results!
 
+## Video Explanation
+
+Here is a video describing the split-operator method:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/BBt8EugN03Q" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 This example code is a simulation of a gaussian distribution of atoms slightly offset in a harmonic trap in imaginary time.
 So long as the code is written appropriately, this means that the atoms should move towards the center of the trap and the energy should decay to $$\frac{1}{2}\hbar\omega$$, which will be simply $$\frac{1}{2}$$ in this simulation.

contents/stable_marriage_problem/stable_marriage_problem.md

@@ -18,6 +18,14 @@ To be clear, even though this algorithm seems conceptually simple, it is rather
 I do not at all claim that the code provided here is efficient and we will definitely be coming back to this problem in the future when we have more tools under our belt.
 I am incredibly interested to see what you guys do and how you implement the algorithm.
 
+## Video Explanation
+
+Here is a video describing the stable marriage problem:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/A7xRZQAQU8s" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 
 {% method %}

contents/tree_traversal/tree_traversal.md

@@ -269,6 +269,14 @@ And this is exactly what Breadth-First Search (BFS) does! On top of that, it can
 [import:81-96, lang:"emojicode"](code/emojicode/tree_traversal.emojic)
 {% endmethod %}
 
+## Video Explanation
+
+Here is a video describing tree traversal:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/cZPXfl_tUkA" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 {% method %}
 {% sample lang="jl" %}

contents/verlet_integration/verlet_integration.md

@@ -193,6 +193,14 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 
 Even though this method is more widely used than the simple Verlet method mentioned above, it unforunately has an error term of $$\mathcal{O}(\Delta t^2)$$, which is two orders of magnitude worse. That said, if you want to have a simulaton with many objects that depend on one another --- like a gravity simulation --- the Velocity Verlet algorithm is a handy choice; however, you may have to play further tricks to allow everything to scale appropriately. These types of simulatons are sometimes called *n-body* simulations and one such trick is the Barnes-Hut algorithm, which cuts the complexity of n-body simulations from $$\sim \mathcal{O}(n^2)$$ to $$\sim \mathcal{O}(n\log(n))$$.
 
+## Video Explanation
+
+Here is a video describing Verlet integration:
+
+<div style="text-align:center">
+<iframe width="560" height="315" src="https://www.youtube.com/embed/g55QvpAev0I" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
+</div>
+
 ## Example Code
 
 Both of these methods work simply by iterating timestep-by-timestep and can be written straightforwardly in any language. For reference, here are snippets of code that use both the classic and velocity Verlet methods to find the time it takes for a ball to hit the ground after being dropped from a given height.