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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. | ||
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"`. | ||
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`). | ||
Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `StoP` is not an anagram of `sTOp`. | ||
The anagram set is the subset of the candidate set that are anagrams of the target (in any order). | ||
Words in the anagram set should have the same letter case as in the candidate set. | ||
The target word and candidate words are made up of one or more ASCII alphabetic characters (`A`-`Z` and `a`-`z`). | ||
Lowercase and uppercase characters are equivalent: for example, `"PoTS"` is an anagram of `"sTOp"`, but `"StoP"` is not an anagram of `"sTOp"`. | ||
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"`. | ||
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"`. |
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# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[983a1528-4ceb-45e5-8257-8ce01aceb5ed] | ||
description = "Newly opened account has zero balance" | ||
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[e88d4ec3-c6bf-4752-8e59-5046c44e3ba7] | ||
description = "Single deposit" | ||
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[3d9147d4-63f4-4844-8d2b-1fee2e9a2a0d] | ||
description = "Multiple deposits" | ||
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[08f1af07-27ae-4b38-aa19-770bde558064] | ||
description = "Withdraw once" | ||
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[6f6d242f-8c31-4ac6-8995-a90d42cad59f] | ||
description = "Withdraw twice" | ||
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[45161c94-a094-4c77-9cec-998b70429bda] | ||
description = "Can do multiple operations sequentially" | ||
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[f9facfaa-d824-486e-8381-48832c4bbffd] | ||
description = "Cannot check balance of closed account" | ||
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[7a65ba52-e35c-4fd2-8159-bda2bde6e59c] | ||
description = "Cannot deposit into closed account" | ||
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[a0a1835d-faae-4ad4-a6f3-1fcc2121380b] | ||
description = "Cannot deposit into unopened account" | ||
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[570dfaa5-0532-4c1f-a7d3-0f65c3265608] | ||
description = "Cannot withdraw from closed account" | ||
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[c396d233-1c49-4272-98dc-7f502dbb9470] | ||
description = "Cannot close an account that was not opened" | ||
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[c06f534f-bdc2-4a02-a388-1063400684de] | ||
description = "Cannot open an already opened account" | ||
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[0722d404-6116-4f92-ba3b-da7f88f1669c] | ||
description = "Reopened account does not retain balance" | ||
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[ec42245f-9361-4341-8231-a22e8d19c52f] | ||
description = "Cannot withdraw more than deposited" | ||
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[4f381ef8-10ef-4507-8e1d-0631ecc8ee72] | ||
description = "Cannot withdraw negative" | ||
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[d45df9ea-1db0-47f3-b18c-d365db49d938] | ||
description = "Cannot deposit negative" | ||
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[ba0c1e0b-0f00-416f-8097-a7dfc97871ff] | ||
description = "Can handle concurrent transactions" |
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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. | ||
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 | ||
## 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] | ||
- 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? | ||
- Can you ask for negative change? | ||
- Can you ask for a change value smaller than the smallest coin value? | ||
- 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]. | ||
- 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. | ||
The door creaks open, and in walks Denara, a skilled merchant with a keen eye for quality goods. | ||
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. | ||
That means you need to return 12 units in change. | ||
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Denara holds out her hand expectantly. | ||
"Just give me the fewest coins," she says with a smile. | ||
"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. | ||
"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 | ||
- two Viras (2 × 5 units) + one Zenth (1 × 2 units) = 3 coins total | ||
- 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. | ||
"As always, you've got it right." |
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exercises/practice/collatz-conjecture/.docs/instructions.md
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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. | ||
If n is even, divide n by 2 to get n / 2. | ||
If n is odd, multiply n by 3 and add 1 to get 3n + 1. | ||
Repeat the process indefinitely. | ||
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 | ||
1. 6 | ||
2. 3 | ||
3. 10 | ||
4. 5 | ||
5. 16 | ||
6. 8 | ||
7. 4 | ||
8. 2 | ||
9. 1 | ||
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Resulting in 9 steps. | ||
So for input n = 12, the return value would be 9. | ||
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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exercises/practice/collatz-conjecture/.docs/introduction.md
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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. | ||
On one page, a single question stood out: **Can every number find its way to 1?** | ||
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. | ||
Pick any positive integer. | ||
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- If it's even, divide it by 2. | ||
- 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. | ||
At first, the sequence seemed unpredictable — jumping up, down, and all over. | ||
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. | ||
Why does this always seem to work? | ||
Could there be a number where the process breaks down, looping forever or escaping into infinity? | ||
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/ |
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exercises/practice/complex-numbers/.docs/instructions.md
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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`. | ||
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`. | ||
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), | ||
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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 | ||
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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`. | ||
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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 | ||
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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 | ||
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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)`. | ||
The conjugate of the complex number `z = a + b * i` is given by: | ||
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Implement the following operations: | ||
```text | ||
zc = a - b * i | ||
``` | ||
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- addition, subtraction, multiplication and division of two complex numbers, | ||
- conjugate, absolute value, exponent of a given complex number. | ||
### Absolute Value | ||
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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: | ||
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```text | ||
|z| = sqrt(a^2 + b^2) | ||
``` | ||
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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 | ||
|z|^2 = z * zc = a^2 + b^2 | ||
``` | ||
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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 | ||
z1 + z2 = (a + b * i) + (c + d * i) | ||
= (a + c) + (b + d) * i | ||
``` | ||
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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 | ||
z1 - z2 = (a + b * i) - (c + d * i) | ||
= (a - c) + (b - d) * i | ||
``` | ||
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### Multiplication | ||
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The product of two complex numbers is defined as: | ||
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```text | ||
z1 * z2 = (a + b * i) * (c + d * i) | ||
= (a * c - b * d) + (b * c + a * d) * i | ||
``` | ||
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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 | ||
1 / z = 1 / (a + b * i) | ||
= a / (a^2 + b^2) - b / (a^2 + b^2) * i | ||
``` | ||
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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 | ||
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 | ||
``` | ||
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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 | ||
e^(a + b * i) = e^a * e^(b * i) | ||
= e^a * (cos(b) + i * sin(b)) | ||
``` | ||
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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 | ||
- **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 |
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