From 634ef0c5e9fb54f6cc08bc8512a047a9ff65d1d4 Mon Sep 17 00:00:00 2001 From: keiravillekode Date: Tue, 3 Dec 2024 23:56:56 +1100 Subject: [PATCH] Sync exercise instructions (#225) [no important files changed] --- .../complex-numbers/.docs/instructions.md | 107 +++++++++++++++--- .../practice/hamming/.docs/instructions.md | 11 -- .../practice/hamming/.docs/introduction.md | 12 ++ exercises/practice/hamming/.meta/config.json | 2 +- .../protein-translation/.docs/instructions.md | 8 +- .../pythagorean-triplet/.docs/instructions.md | 2 +- .../pythagorean-triplet/.docs/introduction.md | 19 ++++ .../pythagorean-triplet/.meta/config.json | 4 +- .../rna-transcription/.docs/instructions.md | 6 +- .../square-root/.docs/instructions.md | 17 ++- .../square-root/.docs/introduction.md | 10 ++ 11 files changed, 152 insertions(+), 46 deletions(-) create mode 100644 exercises/practice/hamming/.docs/introduction.md create mode 100644 exercises/practice/pythagorean-triplet/.docs/introduction.md create mode 100644 exercises/practice/square-root/.docs/introduction.md diff --git a/exercises/practice/complex-numbers/.docs/instructions.md b/exercises/practice/complex-numbers/.docs/instructions.md index 50b19ae..2b8a7a4 100644 --- a/exercises/practice/complex-numbers/.docs/instructions.md +++ b/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 diff --git a/exercises/practice/hamming/.docs/instructions.md b/exercises/practice/hamming/.docs/instructions.md index b9ae6ef..8f47a17 100644 --- a/exercises/practice/hamming/.docs/instructions.md +++ b/exercises/practice/hamming/.docs/instructions.md @@ -2,15 +2,6 @@ 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. -In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime! - -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". - We read DNA using the letters C, A, G and T. Two strands might look like this: @@ -20,8 +11,6 @@ Two strands might look like this: 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 :) - ## Implementation notes The Hamming distance is only defined for sequences of equal length, so an attempt to calculate it between sequences of different lengths should not work. diff --git a/exercises/practice/hamming/.docs/introduction.md b/exercises/practice/hamming/.docs/introduction.md new file mode 100644 index 0000000..8419bf4 --- /dev/null +++ b/exercises/practice/hamming/.docs/introduction.md @@ -0,0 +1,12 @@ +# Introduction + +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. +In fact, the average human body experiences about 10 quadrillion cell divisions in a lifetime! + +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". + +The Hamming distance is useful in many areas of science, not just biology, so it's a nice phrase to be familiar with :) diff --git a/exercises/practice/hamming/.meta/config.json b/exercises/practice/hamming/.meta/config.json index e4c567b..86b2544 100644 --- a/exercises/practice/hamming/.meta/config.json +++ b/exercises/practice/hamming/.meta/config.json @@ -13,7 +13,7 @@ ".meta/proof.ci.wren" ] }, - "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/" } diff --git a/exercises/practice/protein-translation/.docs/instructions.md b/exercises/practice/protein-translation/.docs/instructions.md index 7dc34d2..4488080 100644 --- a/exercises/practice/protein-translation/.docs/instructions.md +++ b/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 | diff --git a/exercises/practice/pythagorean-triplet/.docs/instructions.md b/exercises/practice/pythagorean-triplet/.docs/instructions.md index 1c1a8ae..ced833d 100644 --- a/exercises/practice/pythagorean-triplet/.docs/instructions.md +++ b/exercises/practice/pythagorean-triplet/.docs/instructions.md @@ -1,4 +1,4 @@ -# Instructions +# Description A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which, diff --git a/exercises/practice/pythagorean-triplet/.docs/introduction.md b/exercises/practice/pythagorean-triplet/.docs/introduction.md new file mode 100644 index 0000000..3453c6e --- /dev/null +++ b/exercises/practice/pythagorean-triplet/.docs/introduction.md @@ -0,0 +1,19 @@ +# Introduction + +You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles. +One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project. +The letter reads: + +> Dear Mathematician, +> +> I need your help. +> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c². +> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N. +> Calculating these triplets by hand would take me years, but I hear you are more than up to the task. +> +> Time is of the essence. +> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem. + +Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition. +Your work could have far-reaching implications, unlocking new possibilities in science and engineering. +Can you rise to the challenge and make history? diff --git a/exercises/practice/pythagorean-triplet/.meta/config.json b/exercises/practice/pythagorean-triplet/.meta/config.json index 0993384..cefdd7a 100644 --- a/exercises/practice/pythagorean-triplet/.meta/config.json +++ b/exercises/practice/pythagorean-triplet/.meta/config.json @@ -13,7 +13,7 @@ ".meta/proof.ci.wren" ] }, - "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" } diff --git a/exercises/practice/rna-transcription/.docs/instructions.md b/exercises/practice/rna-transcription/.docs/instructions.md index 36da381..4dbfd3a 100644 --- a/exercises/practice/rna-transcription/.docs/instructions.md +++ b/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: diff --git a/exercises/practice/square-root/.docs/instructions.md b/exercises/practice/square-root/.docs/instructions.md index e9905e9..d258b86 100644 --- a/exercises/practice/square-root/.docs/instructions.md +++ b/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 diff --git a/exercises/practice/square-root/.docs/introduction.md b/exercises/practice/square-root/.docs/introduction.md new file mode 100644 index 0000000..1d69293 --- /dev/null +++ b/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.