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exercises/practice/affine-cipher/.docs/instructions.md

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@@ -4,7 +4,7 @@ Create an implementation of the affine cipher, an ancient encryption system crea
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The affine cipher is a type of monoalphabetic substitution cipher.
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Each character is mapped to its numeric equivalent, encrypted with a mathematical function and then converted to the letter relating to its new numeric value.
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Although all monoalphabetic ciphers are weak, the affine cipher is much stronger than the atbash cipher, because it has many more keys.
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Although all monoalphabetic ciphers are weak, the affine cipher is much stronger than the Atbash cipher, because it has many more keys.
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[//]: # " monoalphabetic as spelled by Merriam-Webster, compare to polyalphabetic "
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# Instructions
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Your task is to, given a target word and a set of candidate words, to find the subset of the candidates that are anagrams of the target.
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Given a target word and one or more candidate words, your task is to find the candidates that are anagrams of the target.
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An anagram is a rearrangement of letters to form a new word: for example `"owns"` is an anagram of `"snow"`.
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A word is _not_ its own anagram: for example, `"stop"` is not an anagram of `"stop"`.
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The target and candidates are words of one or more ASCII alphabetic characters (`A`-`Z` and `a`-`z`).
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Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `StoP` is not an anagram of `sTOp`.
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The anagram set is the subset of the candidate set that are anagrams of the target (in any order).
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Words in the anagram set should have the same letter case as in the candidate set.
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The target word and candidate words are made up of one or more ASCII alphabetic characters (`A`-`Z` and `a`-`z`).
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Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `"StoP"` is not an anagram of `"sTOp"`.
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The words you need to find should be taken from the candidate words, using the same letter case.
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Given the target `"stone"` and candidates `"stone"`, `"tones"`, `"banana"`, `"tons"`, `"notes"`, `"Seton"`, the anagram set is `"tones"`, `"notes"`, `"Seton"`.
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Given the target `"stone"` and the candidate words `"stone"`, `"tones"`, `"banana"`, `"tons"`, `"notes"`, and `"Seton"`, the anagram words you need to find are `"tones"`, `"notes"`, and `"Seton"`.

exercises/practice/atbash-cipher/.docs/instructions.md

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# Instructions
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Create an implementation of the atbash cipher, an ancient encryption system created in the Middle East.
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Create an implementation of the Atbash cipher, an ancient encryption system created in the Middle East.
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The Atbash cipher is a simple substitution cipher that relies on transposing all the letters in the alphabet such that the resulting alphabet is backwards.
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The first letter is replaced with the last letter, the second with the second-last, and so on.

exercises/practice/atbash-cipher/.meta/config.json

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".meta/example.v"
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]
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},
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"blurb": "Create an implementation of the atbash cipher, an ancient encryption system created in the Middle East.",
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"blurb": "Create an implementation of the Atbash cipher, an ancient encryption system created in the Middle East.",
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"source": "Wikipedia",
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"source_url": "https://en.wikipedia.org/wiki/Atbash"
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}

exercises/practice/bob/.meta/tests.toml

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[66953780-165b-4e7e-8ce3-4bcb80b6385a]
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description = "multiple line question"
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include = false
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[5371ef75-d9ea-4103-bcfa-2da973ddec1b]
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description = "starting with whitespace"
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[12983553-8601-46a8-92fa-fcaa3bc4a2a0]
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description = "non-question ending with whitespace"
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[2c7278ac-f955-4eb4-bf8f-e33eb4116a15]
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description = "multiple line question"
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reimplements = "66953780-165b-4e7e-8ce3-4bcb80b6385a"

exercises/practice/bob/run_test.v

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assert response('\t\t\t\t\t\t\t\t\t\t') == 'Fine. Be that way!'
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}
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fn test_multiple_line_question() {
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assert response('\nDoes this cryogenic chamber make me look fat?\nNo.') == 'Whatever.'
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}
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fn test_starting_with_whitespace() {
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assert response(' hmmmmmmm...') == 'Whatever.'
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}
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fn test_non_question_ending_with_whitespace() {
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assert response('This is a statement ending with whitespace ') == 'Whatever.'
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}
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fn test_multiple_line_question() {
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assert response('\nDoes this cryogenic chamber make\n me look fat?') == 'Sure.'
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}
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# Instructions
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Correctly determine the fewest number of coins to be given to a customer such that the sum of the coins' value would equal the correct amount of change.
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Determine the fewest number of coins to give a customer so that the sum of their values equals the correct amount of change.
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## For example
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## Examples
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- An input of 15 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) or [5, 10]
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- An input of 40 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) and one quarter (25) or [5, 10, 25]
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## Edge cases
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- Does your algorithm work for any given set of coins?
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- Can you ask for negative change?
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- Can you ask for a change value smaller than the smallest coin value?
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- An amount of 15 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5 and one coin of value 10, or [5, 10].
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- An amount of 40 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5, one coin of value 10, and one coin of value 25, or [5, 10, 25].
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# Introduction
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In the mystical village of Coinholt, you stand behind the counter of your bakery, arranging a fresh batch of pastries.
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The door creaks open, and in walks Denara, a skilled merchant with a keen eye for quality goods.
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After a quick meal, she slides a shimmering coin across the counter, representing a value of 100 units.
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You smile, taking the coin, and glance at the total cost of the meal: 88 units.
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That means you need to return 12 units in change.
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Denara holds out her hand expectantly.
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"Just give me the fewest coins," she says with a smile.
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"My pouch is already full, and I don't want to risk losing them on the road."
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You know you have a few options.
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"We have Lumis (worth 10 units), Viras (worth 5 units), and Zenth (worth 2 units) available for change."
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You quickly calculate the possibilities in your head:
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- one Lumis (1 × 10 units) + one Zenth (1 × 2 units) = 2 coins total
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- two Viras (2 × 5 units) + one Zenth (1 × 2 units) = 3 coins total
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- six Zenth (6 × 2 units) = 6 coins total
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"The best choice is two coins: one Lumis and one Zenth," you say, handing her the change.
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Denara smiles, clearly impressed.
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"As always, you've got it right."
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# Instructions
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The Collatz Conjecture or 3x+1 problem can be summarized as follows:
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Take any positive integer n.
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If n is even, divide n by 2 to get n / 2.
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If n is odd, multiply n by 3 and add 1 to get 3n + 1.
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Repeat the process indefinitely.
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The conjecture states that no matter which number you start with, you will always reach 1 eventually.
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Given a number n, return the number of steps required to reach 1.
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## Examples
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Starting with n = 12, the steps would be as follows:
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0. 12
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1. 6
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2. 3
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3. 10
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4. 5
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5. 16
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6. 8
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7. 4
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8. 2
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9. 1
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Resulting in 9 steps.
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So for input n = 12, the return value would be 9.
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Given a positive integer, return the number of steps it takes to reach 1 according to the rules of the Collatz Conjecture.
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# Introduction
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One evening, you stumbled upon an old notebook filled with cryptic scribbles, as though someone had been obsessively chasing an idea.
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On one page, a single question stood out: **Can every number find its way to 1?**
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It was tied to something called the **Collatz Conjecture**, a puzzle that has baffled thinkers for decades.
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The rules were deceptively simple.
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Pick any positive integer.
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- If it's even, divide it by 2.
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- If it's odd, multiply it by 3 and add 1.
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Then, repeat these steps with the result, continuing indefinitely.
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Curious, you picked number 12 to test and began the journey:
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12 ➜ 6 ➜ 3 ➜ 10 ➜ 5 ➜ 16 ➜ 8 ➜ 4 ➜ 2 ➜ 1
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Counting from the second number (6), it took 9 steps to reach 1, and each time the rules repeated, the number kept changing.
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At first, the sequence seemed unpredictable — jumping up, down, and all over.
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Yet, the conjecture claims that no matter the starting number, we'll always end at 1.
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It was fascinating, but also puzzling.
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Why does this always seem to work?
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Could there be a number where the process breaks down, looping forever or escaping into infinity?
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The notebook suggested solving this could reveal something profound — and with it, fame, [fortune][collatz-prize], and a place in history awaits whoever could unlock its secrets.
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[collatz-prize]: https://mathprize.net/posts/collatz-conjecture/

exercises/practice/collatz-conjecture/.meta/config.json

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]
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},
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"blurb": "Calculate the number of steps to reach 1 using the Collatz conjecture.",
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"source": "An unsolved problem in mathematics named after mathematician Lothar Collatz",
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"source_url": "https://en.wikipedia.org/wiki/3x_%2B_1_problem"
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"source": "Wikipedia",
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"source_url": "https://en.wikipedia.org/wiki/Collatz_conjecture"
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}
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# Instructions
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A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
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A **complex number** is expressed in the form `z = a + b * i`, where:
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`a` is called the real part and `b` is called the imaginary part of `z`.
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The conjugate of the number `a + b * i` is the number `a - b * i`.
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The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate.
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- `a` is the **real part** (a real number),
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The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
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`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
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`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
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- `b` is the **imaginary part** (also a real number), and
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Multiplication result is by definition
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`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
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- `i` is the **imaginary unit** satisfying `i^2 = -1`.
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The reciprocal of a non-zero complex number is
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`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
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## Operations on Complex Numbers
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Dividing a complex number `a + i * b` by another `c + i * d` gives:
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`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
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### Conjugate
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Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`.
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The conjugate of the complex number `z = a + b * i` is given by:
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Implement the following operations:
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```text
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zc = a - b * i
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```
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- addition, subtraction, multiplication and division of two complex numbers,
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- conjugate, absolute value, exponent of a given complex number.
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### Absolute Value
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Assume the programming language you are using does not have an implementation of complex numbers.
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The absolute value (or modulus) of `z` is defined as:
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```text
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|z| = sqrt(a^2 + b^2)
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```
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The square of the absolute value is computed as the product of `z` and its conjugate `zc`:
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```text
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|z|^2 = z * zc = a^2 + b^2
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```
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### Addition
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The sum of two complex numbers `z1 = a + b * i` and `z2 = c + d * i` is computed by adding their real and imaginary parts separately:
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```text
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z1 + z2 = (a + b * i) + (c + d * i)
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= (a + c) + (b + d) * i
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```
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### Subtraction
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The difference of two complex numbers is obtained by subtracting their respective parts:
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```text
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z1 - z2 = (a + b * i) - (c + d * i)
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= (a - c) + (b - d) * i
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```
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### Multiplication
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The product of two complex numbers is defined as:
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```text
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z1 * z2 = (a + b * i) * (c + d * i)
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= (a * c - b * d) + (b * c + a * d) * i
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```
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### Reciprocal
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The reciprocal of a non-zero complex number is given by:
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```text
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1 / z = 1 / (a + b * i)
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= a / (a^2 + b^2) - b / (a^2 + b^2) * i
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```
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### Division
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The division of one complex number by another is given by:
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```text
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z1 / z2 = z1 * (1 / z2)
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= (a + b * i) / (c + d * i)
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= (a * c + b * d) / (c^2 + d^2) + (b * c - a * d) / (c^2 + d^2) * i
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```
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### Exponentiation
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Raising _e_ (the base of the natural logarithm) to a complex exponent can be expressed using Euler's formula:
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```text
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e^(a + b * i) = e^a * e^(b * i)
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= e^a * (cos(b) + i * sin(b))
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```
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## Implementation Requirements
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Given that you should not use built-in support for complex numbers, implement the following operations:
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- **addition** of two complex numbers
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- **subtraction** of two complex numbers
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- **multiplication** of two complex numbers
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- **division** of two complex numbers
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- **conjugate** of a complex number
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- **absolute value** of a complex number
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- **exponentiation** of _e_ (the base of the natural logarithm) to a complex number

exercises/practice/dominoes/.docs/instructions.md

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Make a chain of dominoes.
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Compute a way to order a given set of dominoes in such a way that they form a correct domino chain (the dots on one half of a stone match the dots on the neighboring half of an adjacent stone) and that dots on the halves of the stones which don't have a neighbor (the first and last stone) match each other.
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Compute a way to order a given set of domino stones so that they form a correct domino chain.
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In the chain, the dots on one half of a stone must match the dots on the neighboring half of an adjacent stone.
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Additionally, the dots on the halves of the stones without neighbors (the first and last stone) must match each other.
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For example given the stones `[2|1]`, `[2|3]` and `[1|3]` you should compute something
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like `[1|2] [2|3] [3|1]` or `[3|2] [2|1] [1|3]` or `[1|3] [3|2] [2|1]` etc, where the first and last numbers are the same.
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# Introduction
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In Toyland, the trains are always busy delivering treasures across the city, from shiny marbles to rare building blocks.
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The tracks they run on are made of colorful domino-shaped pieces, each marked with two numbers.
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For the trains to move, the dominoes must form a perfect chain where the numbers match.
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Today, an urgent delivery of rare toys is on hold.
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You've been handed a set of track pieces to inspect.
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If they can form a continuous chain, the train will be on its way, bringing smiles across Toyland.
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If not, the set will be discarded, and another will be tried.
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The toys are counting on you to solve this puzzle.
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Will the dominoes connect the tracks and send the train rolling, or will the set be left behind?

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