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exercises/practice/complex-numbers/.docs/instructions.md

@@ -1,29 +1,100 @@
 # Instructions
 
-A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+A **complex number** is expressed in the form `z = a + b * i`, where:
 
-`a` is called the real part and `b` is called the imaginary part of `z`.
-The conjugate of the number `a + b * i` is the number `a - b * i`.
-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.
+- `a` is the **real part** (a real number),
 
-The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
-`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
-`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
+- `b` is the **imaginary part** (also a real number), and
 
-Multiplication result is by definition
-`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
+- `i` is the **imaginary unit** satisfying `i^2 = -1`.
 
-The reciprocal of a non-zero complex number is
-`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
+## Operations on Complex Numbers
 
-Dividing a complex number `a + i * b` by another `c + i * d` gives:
-`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
+### Conjugate
 
-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)`.
+The conjugate of the complex number `z = a + b * i` is given by:
 
-Implement the following operations:
+```text
+zc = a - b * i
+```
 
-- addition, subtraction, multiplication and division of two complex numbers,
-- conjugate, absolute value, exponent of a given complex number.
+### Absolute Value
 
-Assume the programming language you are using does not have an implementation of complex numbers.
+The absolute value (or modulus) of `z` is defined as:
+
+```text
+|z| = sqrt(a^2 + b^2)
+```
+
+The square of the absolute value is computed as the product of `z` and its conjugate `zc`:
+
+```text
+|z|^2 = z * zc = a^2 + b^2
+```
+
+### Addition
+
+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:
+
+```text
+z1 + z2 = (a + b * i) + (c + d * i)
+        = (a + c) + (b + d) * i
+```
+
+### Subtraction
+
+The difference of two complex numbers is obtained by subtracting their respective parts:
+
+```text
+z1 - z2 = (a + b * i) - (c + d * i)
+        = (a - c) + (b - d) * i
+```
+
+### Multiplication
+
+The product of two complex numbers is defined as:
+
+```text
+z1 * z2 = (a + b * i) * (c + d * i)
+        = (a * c - b * d) + (b * c + a * d) * i
+```
+
+### Reciprocal
+
+The reciprocal of a non-zero complex number is given by:
+
+```text
+1 / z = 1 / (a + b * i)
+      = a / (a^2 + b^2) - b / (a^2 + b^2) * i
+```
+
+### Division
+
+The division of one complex number by another is given by:
+
+```text
+z1 / z2 = z1 * (1 / z2)
+        = (a + b * i) / (c + d * i)
+        = (a * c + b * d) / (c^2 + d^2) + (b * c - a * d) / (c^2 + d^2) * i
+```
+
+### Exponentiation
+
+Raising _e_ (the base of the natural logarithm) to a complex exponent can be expressed using Euler's formula:
+
+```text
+e^(a + b * i) = e^a * e^(b * i)
+              = e^a * (cos(b) + i * sin(b))
+```
+
+## Implementation Requirements
+
+Given that you should not use built-in support for complex numbers, implement the following operations:
+
+- **addition** of two complex numbers
+- **subtraction** of two complex numbers
+- **multiplication** of two complex numbers
+- **division** of two complex numbers
+- **conjugate** of a complex number
+- **absolute value** of a complex number
+- **exponentiation** of _e_ (the base of the natural logarithm) to a complex number

exercises/practice/dot-dsl/.meta/config.json

@@ -16,6 +16,9 @@
     "editor": [
       "src/main/java/Node.java",
       "src/main/java/Edge.java"
+    ],
+    "invalidator": [
+      "build.gradle"
     ]
   },
   "blurb": "Write a Domain Specific Language similar to the Graphviz dot language.",

exercises/practice/hamming/.docs/instructions.md

@@ -1,6 +1,6 @@
 # Instructions
 
-Calculate the Hamming Distance between two DNA strands.
+Calculate the Hamming distance between two DNA strands.
 
 Your body is made up of cells that contain DNA.
 Those cells regularly wear out and need replacing, which they achieve by dividing into daughter cells.
@@ -9,18 +9,18 @@ In fact, the average human body experiences about 10 quadrillion cell divisions
 When cells divide, their DNA replicates too.
 Sometimes during this process mistakes happen and single pieces of DNA get encoded with the incorrect information.
 If we compare two strands of DNA and count the differences between them we can see how many mistakes occurred.
-This is known as the "Hamming Distance".
+This is known as the "Hamming distance".
 
-We read DNA using the letters C,A,G and T.
+We read DNA using the letters C, A, G and T.
 Two strands might look like this:
 
     GAGCCTACTAACGGGAT
     CATCGTAATGACGGCCT
     ^ ^ ^  ^ ^    ^^
 
-They have 7 differences, and therefore the Hamming Distance is 7.
+They have 7 differences, and therefore the Hamming distance is 7.
 
-The Hamming Distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
+The Hamming distance is useful for lots of things in science, not just biology, so it's a nice phrase to be familiar with :)
 
 ## Implementation notes
 

exercises/practice/hamming/.meta/config.json

@@ -43,7 +43,7 @@
       "build.gradle"
     ]
   },
-  "blurb": "Calculate the Hamming difference between two DNA strands.",
+  "blurb": "Calculate the Hamming distance between two DNA strands.",
   "source": "The Calculating Point Mutations problem at Rosalind",
   "source_url": "https://rosalind.info/problems/hamm/"
 }

exercises/practice/luhn/.docs/instructions.md

@@ -22,7 +22,8 @@ The first step of the Luhn algorithm is to double every second digit, starting f
 We will be doubling
 
 ```text
-4_3_ 3_9_ 0_4_ 6_6_
+4539 3195 0343 6467
+↑ ↑  ↑ ↑  ↑ ↑  ↑ ↑  (double these)
 ```
 
 If doubling the number results in a number greater than 9 then subtract 9 from the product.

exercises/practice/pov/.meta/config.json

@@ -18,5 +18,5 @@
   },
   "blurb": "Reparent a graph on a selected node.",
   "source": "Adaptation of exercise from 4clojure",
-  "source_url": "https://www.4clojure.com/"
+  "source_url": "https://github.com/oxalorg/4ever-clojure"
 }

exercises/practice/protein-translation/.docs/instructions.md

@@ -2,12 +2,12 @@
 
 Translate RNA sequences into proteins.
 
-RNA can be broken into three nucleotide sequences called codons, and then translated to a polypeptide like so:
+RNA can be broken into three-nucleotide sequences called codons, and then translated to a protein like so:
 
 RNA: `"AUGUUUUCU"` => translates to
 
 Codons: `"AUG", "UUU", "UCU"`
-=> which become a polypeptide with the following sequence =>
+=> which become a protein with the following sequence =>
 
 Protein: `"Methionine", "Phenylalanine", "Serine"`
 
@@ -27,9 +27,9 @@ Protein: `"Methionine", "Phenylalanine", "Serine"`
 
 Note the stop codon `"UAA"` terminates the translation and the final methionine is not translated into the protein sequence.
 
-Below are the codons and resulting Amino Acids needed for the exercise.
+Below are the codons and resulting amino acids needed for the exercise.
 
-| Codon              | Protein       |
+| Codon              | Amino Acid    |
 | :----------------- | :------------ |
 | AUG                | Methionine    |
 | UUU, UUC           | Phenylalanine |

exercises/practice/pythagorean-triplet/.meta/config.json

@@ -36,7 +36,7 @@
       "build.gradle"
     ]
   },
-  "blurb": "There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the triplet.",
-  "source": "Problem 9 at Project Euler",
+  "blurb": "Given an integer N, find all Pythagorean triplets for which a + b + c = N.",
+  "source": "A variation of Problem 9 from Project Euler",
   "source_url": "https://projecteuler.net/problem=9"
 }

exercises/practice/rna-transcription/.docs/instructions.md

@@ -1,12 +1,12 @@
 # Instructions
 
-Your task is determine the RNA complement of a given DNA sequence.
+Your task is to determine the RNA complement of a given DNA sequence.
 
 Both DNA and RNA strands are a sequence of nucleotides.
 
-The four nucleotides found in DNA are adenine (**A**), cytosine (**C**), guanine (**G**) and thymine (**T**).
+The four nucleotides found in DNA are adenine (**A**), cytosine (**C**), guanine (**G**), and thymine (**T**).
 
-The four nucleotides found in RNA are adenine (**A**), cytosine (**C**), guanine (**G**) and uracil (**U**).
+The four nucleotides found in RNA are adenine (**A**), cytosine (**C**), guanine (**G**), and uracil (**U**).
 
 Given a DNA strand, its transcribed RNA strand is formed by replacing each nucleotide with its complement:
 

exercises/practice/square-root/.docs/instructions.md

@@ -1,13 +1,18 @@
 # Instructions
 
-Given a natural radicand, return its square root.
+Your task is to calculate the square root of a given number.
 
-Note that the term "radicand" refers to the number for which the root is to be determined.
-That is, it is the number under the root symbol.
+- Try to avoid using the pre-existing math libraries of your language.
+- As input you'll be given a positive whole number, i.e. 1, 2, 3, 4…
+- You are only required to handle cases where the result is a positive whole number.
 
-Check out the Wikipedia pages on [square root][square-root] and [methods of computing square roots][computing-square-roots].
+Some potential approaches:
 
-Recall also that natural numbers are positive real whole numbers (i.e. 1, 2, 3 and up).
+- Linear or binary search for a number that gives the input number when squared.
+- Successive approximation using Newton's or Heron's method.
+- Calculating one digit at a time or one bit at a time.
 
-[square-root]: https://en.wikipedia.org/wiki/Square_root
+You can check out the Wikipedia pages on [integer square root][integer-square-root] and [methods of computing square roots][computing-square-roots] to help with choosing a method of calculation.
+
+[integer-square-root]: https://en.wikipedia.org/wiki/Integer_square_root
 [computing-square-roots]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

exercises/practice/square-root/.docs/introduction.md

@@ -0,0 +1,10 @@
+# Introduction
+
+We are launching a deep space exploration rocket and we need a way to make sure the navigation system stays on target.
+
+As the first step in our calculation, we take a target number and find its square root (that is, the number that when multiplied by itself equals the target number).
+
+The journey will be very long.
+To make the batteries last as long as possible, we had to make our rocket's onboard computer very power efficient.
+Unfortunately that means that we can't rely on fancy math libraries and functions, as they use more power.
+Instead we want to implement our own square root calculation.

exercises/practice/state-of-tic-tac-toe/.docs/instructions.md

@@ -3,7 +3,7 @@
 In this exercise, you're going to implement a program that determines the state of a [tic-tac-toe][] game.
 (_You may also know the game as "noughts and crosses" or "Xs and Os"._)
 
-The games is played on a 3×3 grid.
+The game is played on a 3×3 grid.
 Players take turns to place `X`s and `O`s on the grid.
 The game ends when one player has won by placing three of marks in a row, column, or along a diagonal of the grid, or when the entire grid is filled up.
 

exercises/practice/sublist/.docs/instructions.md

@@ -8,8 +8,8 @@ Given any two lists `A` and `B`, determine if:
 - None of the above is true, thus lists `A` and `B` are unequal
 
 Specifically, list `A` is equal to list `B` if both lists have the same values in the same order.
-List `A` is a superlist of `B` if `A` contains a sub-sequence of values equal to `B`.
-List `A` is a sublist of `B` if `B` contains a sub-sequence of values equal to `A`.
+List `A` is a superlist of `B` if `A` contains a contiguous sub-sequence of values equal to `B`.
+List `A` is a sublist of `B` if `B` contains a contiguous sub-sequence of values equal to `A`.
 
 Examples: