#euclidean algorithm

The numbers were characters. I asked that same professor for a letter of recommendation and he said yes. Do you think he remembered the two page short story about 93 and 159 trying to find their gcd.

Euclidi-what? Math is painful.

So, I’m starting to learn Python with Truston Ailende and the Learn to Code Monthly group. The third video in his tutorial playlist is called Introduction to Algorithms and he introduced us to the concept of Euclidean Algorithms which Wikipedia describes as “efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both…

The recipe is very recursive. For example, confetti appears in the top left, but also as a step under gold (middle) and also as a step under silver (right). Silver is itself a substep of gold, so that causes another confetti to appear. That means the whole left branch would have been entirely repeated 4 times in the diagram.

Surely there’s a more efficient way to see how much of each thing to craft?

I present the new and improved expansion! It is based on the reverse of the Euclidean Algorithm for finding common factors. I expand the “most complicated” ingredient at each step, then combine like terms. For example, I collected all the confetti together, then expanded it once.

This is convenient for a few reasons:

Each ingredient is expanded once. The time it takes to expand is linear for the number of distinct ingredients. Before, having gold in the recipe approximately doubled the size of the tree. Here, it added one single line to the expansion.

The last line tells you what primitive ingredients you need (those that aren’t crafted from other things).

You can read off the expanded ingredient at each step to see how many to make. For example, suppose I’m crafting ribbon. I look for the step where I expanded ribbon, and it says 40 ribbon. So I know that’s exactly how many I need.

This only works if you expand the “most complicated” thing first (*see footnote). For example, I expanded gold first because it uses silver and confetti. If I started by expanding confetti, it would have showed up again later, and I would have to expand it again.

” MIND BEHIND GEOMETRY”

#Euclid was born on Mid-4th Century BC (not have a exact date of his birth)

# He was Greek mathematician.

# He was / is considered as the “Father of Geometry”.

# He worked on Conic Sections, Number Theory, Spherical Geometry and a small sets of “axioms” latter called “Euclidean Geometry”.

# He was also known for his work on “Euclidean Algorithms” where he showed how to find the “greatest common…

” MIND BEHIND GEOMETRY”

#Euclid was born on Mid-4th Century BC (not have a exact date of his birth)

# He was Greek mathematician.

# He was / is considered as the “Father of Geometry”.

# He worked on Conic Sections, Number Theory, Spherical Geometry and a small sets of “axioms” latter called “Euclidean Geometry”.

# He was also known for his work on “Euclidean Algorithms” where he showed how to find the “greatest common…