meetforever/GRPO_CL huggingface dataset:
user: Normally, we decompose a number into binary digits by assigning it with powers of 2, with a coefficient of `0` or `1` for each term:

`25 = 1*16 + 1*8 + 0*4 + 0*2 + 1*1`

The choice of `0` and `1` is... not very binary. We shall perform the *true* binary expansion by expanding with powers of 2, but with a coefficient of `1` or `-1` instead:

`25 = 1*16 + 1*8 + 1*4 - 1*2 - 1*1`

Now *this* looks binary.

---

Given any positive number `n`, expand it using the true binary expansion, and return the result as an array, from the most significant digit to the least significant digit.

`true_binary(25) == [1,1,1,-1,-1]`

It should be trivial (the proofs are left as an exercise to the reader) to see that:

- Every odd number has infinitely many true binary expansions
- Every even number has no true binary expansions

Hence, `n` will always be an odd number, and you should return the *least* true binary expansion for any `n`.

Also, note that `n` can be very, very large, so your code should be very efficient.

Answer: {"fn_name": "true_binary", "inputs": [[25], [47], [1], [3], [1234567]], "outputs": [[[1, 1, 1, -1, -1]], [[1, 1, -1, 1, 1, 1]], [[1]], [[1, 1]], [[1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1]]]}
user: # Task
A newspaper is published in Walrusland. Its heading is `s1` , it consists of lowercase Latin letters. 

Fangy the little walrus wants to buy several such newspapers, cut out their headings, glue them one to another in order to get one big string. 

After that walrus erase several letters from this string in order to get a new word `s2`. 

It is considered that when Fangy erases some letter, there's no whitespace formed instead of the letter. That is, the string remains unbroken and it still only consists of lowercase Latin letters.

For example, the heading is `"abc"`. If we take two such headings and glue them one to the other one, we get `"abcabc"`. If we erase the 1st letter("a") and 5th letter("b"), we get a word `"bcac"`.

Given two string `s1` and `s2`, return the least number of newspaper headings `s1`, which Fangy will need to receive the word `s2`. If it is impossible to get the word `s2` in the above-described manner, return `-1`.

# Example

For `s1="abc", s2="bcac"`, the output should be `2`.

```
"abcabc" --> "bcac"
 x   x
```

For `s1="abc", s2="xyz"`, the output should be `-1`.

It's impossible to get the word `s2`.

Answer: {"fn_name": "buy_newspaper", "inputs": [["abc", "bcac"], ["abc", "xyz"], ["abc", "abcabc"], ["abc", "abccba"], ["abc", "aaaaaa"]], "outputs": [[2], [-1], [2], [4], [6]]}
user: # Task
Given an integer array `arr`. Your task is to remove one element, maximize the product of elements. 

The result is the element which should be removed. If more than one valid results exist, return the smallest one.


# Input/Output


`[input]` integer array `arr`

non-empty unsorted integer array. It contains positive integer, negative integer or zero.

`3 ≤ arr.length ≤ 15`

`-10 ≤ arr[i] ≤ 10`

`[output]` an integer

The element that should be removed.

# Example

For `arr = [1, 2, 3]`, the output should be `1`.

For `arr = [-1, 2, -3]`, the output should be `2`.

For `arr = [-1, -2, -3]`, the output should be `-1`.

For `arr = [-1, -2, -3, -4]`, the output should be `-4`.

Answer: {"fn_name": "maximum_product", "inputs": [[[1, 2, 3]], [[-1, 2, -3]], [[-1, -2, -3]], [[-1, -2, -3, -4]], [[0, 1, 2, 3]], [[0, -1, -2, -3]], [[0, -1, -2, -3, -4]], [[0, -1, 2, -3, 4]], [[0, -1, 2, 3]], [[0, -1, -2, -3, 4]], [[0, 0, 1]], [[0, 0, -1]], [[0, -1, 1]], [[0, 0, -1, 1]], [[0, 0, 0]], [[0, 0, 1, 2, 3]], [[-1, -2, -3, 0, 1, 2, 3]], [[-1, -2, 0, 1, 2]], [[-1, -2, 1, 2]], [[-1, -2, -3, 1, 2, 3]]], "outputs": [[1], [2], [-1], [-4], [0], [-3], [0], [0], [-1], [-3], [0], [-1], [-1], [-1], [0], [0], [-3], [0], [1], [-1]]}
user: It's been a tough week at work and you are stuggling to get out of bed in the morning.

While waiting at the bus stop you realise that if you could time your arrival to the nearest minute you could get valuable extra minutes in bed.

There is a bus that goes to your office every 15 minute, the first bus is at `06:00`, and the last bus is at `00:00`.

Given that it takes 5 minutes to walk from your front door to the bus stop, implement a function that when given the curent time will tell you much time is left, before you must leave to catch the next bus.

## Examples

```
"05:00"  =>  55
"10:00"  =>  10
"12:10"  =>  0
"12:11"  =>  14
```

### Notes

1. Return the number of minutes till the next bus
2. Input will be formatted as `HH:MM` (24-hour clock)
3. The input time might be after the buses have stopped running, i.e. after `00:00`

Answer: {"fn_name": "bus_timer", "inputs": [["10:00"], ["10:45"], ["15:05"], ["06:10"], ["05:10"], ["04:50"], ["05:55"], ["23:57"], ["00:00"], ["23:55"]], "outputs": [[10], [10], [5], [0], [45], [65], [0], [358], [355], [0]]}
user: You and your best friend Stripes have just landed your first high school jobs! You'll be delivering newspapers to your neighbourhood on weekends. For your services you'll be charging a set price depending on the quantity of the newspaper bundles.

The cost of deliveries is:

- $3.85 for 40 newspapers
- $1.93 for 20
- $0.97 for 10 
- $0.49 for 5 
- $0.10 for 1 

Stripes is taking care of the footwork doing door-to-door drops and your job is to take care of the finances. What you'll be doing is providing the cheapest possible quotes for your services.

Write a function that's passed an integer representing the amount of newspapers and returns the cheapest price. The returned number must be rounded to two decimal places.

![Paperboy](http://mametesters.org/file_download.php?file_id=1016&type=bug)

Answer: {"fn_name": "cheapest_quote", "inputs": [[1], [5], [10], [20], [40], [41], [80], [26], [0], [499]], "outputs": [[0.1], [0.49], [0.97], [1.93], [3.85], [3.95], [7.7], [2.52], [0.0], [48.06]]}
user: You know combinations: for example, 
if you take 5 cards from a 52 cards deck you have 2,598,960 different combinations.

In mathematics the number of x combinations you can take from a set of n elements
is called the binomial coefficient of n and x, or more often `n choose x`.
The formula to compute `m = n choose x` is: `m = n! / (x! * (n - x)!)`
where ! is the factorial operator.

You are a renowned poster designer and painter. You are asked to provide 6 posters 
all having the same design each in 2 colors. Posters must all have a different color combination and you have the choice of 4 colors: red, blue, yellow, green. 
How many colors can you choose for each poster?

The answer is two since `4 choose 2 = 6`. The combinations will be:
{red, blue}, {red, yellow}, {red, green}, {blue, yellow}, {blue, green}, {yellow, green}.

Now same question but you have 35 posters to provide and 7 colors available. How many colors for each poster?
If you take combinations `7 choose 2` you will get 21 with the above formula.
But 21 schemes aren't enough for 35 posters. If you take `7 choose 5` combinations you will get 21 too.
Fortunately if you take `7 choose 3` or `7 choose 4` combinations you get 35 and so each poster will have a different combination of
3 colors or 5 colors. You will take 3 colors because it's less expensive.

Hence the problem is: 

knowing `m` (number of posters to design), 
knowing `n` (total number of available colors), 
let us 
search `x` (number of colors for each poster so that each poster has a unique combination of colors and the number of combinations is exactly the same as the number of posters).

In other words we must find **x** such as `n choose x = m (1)` for a given m and a given n;
`m >= 0 and n > 0`. If many x are solutions give as result the smallest x.
It can happen that when m is given at random there are no x satisfying `equation (1)` then
return -1.

Examples:
```
checkchoose(6, 4) --> 2
checkchoose(4, 4) --> 1
checkchoose(4, 2) --> -1
checkchoose(35, 7) --> 3
checkchoose(36, 7) --> -1

a = 47129212243960
checkchoose(a, 50) --> 20
checkchoose(a + 1, 50) --> -1
```

Answer: {"fn_name": "checkchoose", "inputs": [[1, 6], [6, 4], [4, 4], [4, 2], [35, 7], [36, 7], [184756, 20], [184756, 10], [3268760, 25], [155117520, 30], [155117530, 30]], "outputs": [[0], [2], [1], [-1], [3], [-1], [10], [-1], [10], [15], [-1]]}
user: Goal
Given a list of elements [a1, a2, ..., an], with each ai being a string, write a function **majority** that returns the value that appears the most in the list. 

If there's no winner, the function should return None, NULL, nil, etc, based on the programming language.

Example
majority(["A", "B", "A"]) returns "A"
majority(["A", "B", "B", "A"]) returns None

Answer: {"fn_name": "majority", "inputs": [[["A", "B", "A"]], [["A", "B", "C"]], [["A", "B", "B", "A"]], [["A", "A", "A", "A"]], [["A"]], [["A", "A", "A", "BBBBBBBB"]], [["A", "B", "C", "C"]], [[]], [["B", "C", "", ""]]], "outputs": [["A"], [null], [null], ["A"], ["A"], ["A"], ["C"], [null], [""]]}
user: # Task
 Some people are standing in a row in a park. There are trees between them which cannot be moved. 
 
 Your task is to rearrange the people by their heights in a non-descending order without moving the trees.

# Example

 For `a = [-1, 150, 190, 170, -1, -1, 160, 180]`, the output should be

 `[-1, 150, 160, 170, -1, -1, 180, 190]`.

# Input/Output


 - `[input]` integer array `a`

    If a[i] = -1, then the ith position is occupied by a tree. Otherwise a[i] is the height of a person standing in the ith position.

    Constraints:

    `5 ≤ a.length ≤ 30,`

    `-1 ≤ a[i] ≤ 200.`


 - `[output]` an integer array

    `Sorted` array a with all the trees untouched.

Answer: {"fn_name": "sort_by_height", "inputs": [[[-1, 150, 190, 170, -1, -1, 160, 180]], [[-1, -1, -1, -1, -1]], [[4, 2, 9, 11, 2, 16]]], "outputs": [[[-1, 150, 160, 170, -1, -1, 180, 190]], [[-1, -1, -1, -1, -1]], [[2, 2, 4, 9, 11, 16]]]}
user: In music, if you double (or halve) the pitch of any note you will get to the same note again.

"Concert A" is fixed at 440 Hz, and every other note is defined based on that. 880 Hz is also an A, as is 1760 Hz, as is 220 Hz.

There are 12 notes in Western music: A, A#, B, C, C#, D, D#, E, F, F#, G, G#. You are given a preloaded dictionary with these 12 notes and one of the pitches that creates that note (starting at Concert A).

Now, given a pitch (in Hz), return the corresponding note. (All inputs will be valid notes).

For reference, the notes dictionary looks like this:

```python
notes_dictionary = {
    440: "A",
    466.16: "A#",
    493.88: "B",
    523.25: "C",
    554.37: "C#", 
    587.33: "D", 
    622.25: "D#", 
    659.25: "E", 
    698.46: "F", 
    739.99: "F#", 
    783.99: "G", 
    830.61: "G#"
}
```

Musicians: all pitches based on equal tempermanent, taken from [here](http://pages.mtu.edu/~suits/notefreqs.html).

Answer: {"fn_name": "get_note", "inputs": [[440], [220], [880], [523.25], [261.625], [1046.5]], "outputs": [["A"], ["A"], ["A"], ["C"], ["C"], ["C"]]}
user: #### Background: 
 

A linear regression line has an equation in the form `$Y = a + bX$`, where `$X$` is the explanatory variable and `$Y$` is the dependent variable. The parameter `$b$` represents the *slope* of the line, while `$a$` is called the *intercept* (the value of `$y$` when `$x = 0$`).

For more details visit the related [wikipedia page](http://en.wikipedia.org/wiki/Simple_linear_regression).

---
---
#### Task:
The function that you have to write accepts two list/array, `$x$` and `$y$`,  representing the coordinates of the points to regress (so that, for example, the first point has coordinates (`x[0], y[0]`)).

Your function should return a tuple (in Python) or an array (any other language) of two elements: `a` (intercept) and `b` (slope) in this order.

You must round your result to the first 4 decimal digits

#### Formula:

   

`$x_i$` and `$y_i$` is `$x$` and `$y$` co-ordinate of `$i$`-th point;  
`$n$` is length of input.  

`$a =  \dfrac{\sum x_i^2\cdot \sum y_i - \sum x_i \cdot\sum x_iy_i}{n\sum x_i^2 - (\sum x_i)^2}$`

`$b =  \dfrac{n\sum x_i y_i - \sum x_i \cdot \sum y_i}{n\sum x^2_i - (\sum x_i)^2}$`
#### Examples:

```python
regressionLine([25,30,35,40,45,50], [78,70,65,58,48,42]) == (114.381, -1.4457)

regressionLine([56,42,72,36,63,47,55,49,38,42,68,60], [147,125,160,118,149,128,150,145,115,140,152,155]) == (80.7777, 1.138)
```
----

Answer: {"fn_name": "regressionLine", "inputs": [[[25, 30, 35, 40, 45, 50], [78, 70, 65, 58, 48, 42]], [[56, 42, 72, 36, 63, 47, 55, 49, 38, 42, 68, 60], [147, 125, 160, 118, 149, 128, 150, 145, 115, 140, 152, 155]], [[0, 10, 20, 30, 40], [0.51, 0.55, 0.57, 0.59, 0.63]]], "outputs": [[[114.381, -1.4457]], [[80.7777, 1.138]], [[0.514, 0.0028]]]}
user: Bob is a theoretical coder - he doesn't write code, but comes up with theories, formulas and algorithm ideas. You are his secretary, and he has tasked you with writing the code for his newest project - a method for making the short form of a word. Write a function ```shortForm```(C# ```ShortForm```, Python ```short_form```) that takes a string and returns it converted into short form using the rule: Remove all vowels, except for those that are the first or last letter. Do not count 'y' as a vowel, and ignore case. Also note, the string given will not have any spaces; only one word, and only Roman letters. 

Example:
```
shortForm("assault");
short_form("assault")
ShortForm("assault");
// should return "asslt"
```

 
Also, FYI: I got all the words with no vowels from 
https://en.wikipedia.org/wiki/English_words_without_vowels

Answer: {"fn_name": "short_form", "inputs": [["typhoid"], ["fire"], ["destroy"], ["kata"], ["codewars"], ["assert"], ["insane"], ["nice"], ["amazing"], ["incorrigible"], ["HeEllO"], ["inCRediBLE"], ["IMpOsSiblE"], ["UnInTENtiONAl"], ["AWESOme"], ["rhythm"], ["hymn"], ["lynx"], ["nymph"], ["pygmy"]], "outputs": [["typhd"], ["fre"], ["dstry"], ["kta"], ["cdwrs"], ["assrt"], ["insne"], ["nce"], ["amzng"], ["incrrgble"], ["HllO"], ["inCRdBLE"], ["IMpsSblE"], ["UnnTNtNl"], ["AWSme"], ["rhythm"], ["hymn"], ["lynx"], ["nymph"], ["pygmy"]]}
user: Given a positive number n > 1 find the prime factor decomposition of n.
The result will be a string with the following form :
```
 "(p1**n1)(p2**n2)...(pk**nk)"
```
where ```a ** b``` means ```a``` to the power of ```b```

with the p(i) in increasing order and n(i) empty if
n(i) is 1.
```
Example: n = 86240 should return "(2**5)(5)(7**2)(11)"
```

Answer: {"fn_name": "primeFactors", "inputs": [[7775460], [7919], [18195729], [933555431], [342217392], [35791357], [782611830], [775878912]], "outputs": [["(2**2)(3**3)(5)(7)(11**2)(17)"], ["(7919)"], ["(3)(17**2)(31)(677)"], ["(7537)(123863)"], ["(2**4)(3)(11)(43)(15073)"], ["(7)(5113051)"], ["(2)(3**2)(5)(7**2)(11)(13)(17)(73)"], ["(2**8)(3**4)(17)(31)(71)"]]}
user: Complete the code which should return `true` if the given object is a single ASCII letter (lower or upper case), `false` otherwise.

Answer: {"fn_name": "is_letter", "inputs": [[""], ["a"], ["X"], ["7"], ["_"], ["ab"], ["a\n"]], "outputs": [[false], [true], [true], [false], [false], [false], [false]]}
user: As you may know, once some people pass their teens, they jokingly only celebrate their 20th or 21st birthday, forever. With some maths skills, that's totally possible - you only need to select the correct number base!

For example, if they turn 32, that's exactly 20 - in base 16... Already 39? That's just 21, in base 19!

Your task is to translate the given age to the much desired 20 (or 21) years, and indicate the number base, in the format specified below.

**Note:** input will be always > 21


### Examples:

```
32  -->  "32? That's just 20, in base 16!"
39  -->  "39? That's just 21, in base 19!"
```

*Hint: if you don't know (enough) about [numeral systems](https://en.wikipedia.org/wiki/Numeral_system) and [radix](https://en.wikipedia.org/wiki/Radix), just observe the pattern!*

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

---

### *Translations are welcome!*

Answer: {"fn_name": "womens_age", "inputs": [[32], [39], [22], [65], [83]], "outputs": [["32? That's just 20, in base 16!"], ["39? That's just 21, in base 19!"], ["22? That's just 20, in base 11!"], ["65? That's just 21, in base 32!"], ["83? That's just 21, in base 41!"]]}
user: ~~~if-not:ruby,python
Return `1` when *any* odd bit of `x` equals 1; `0` otherwise.
~~~
~~~if:ruby,python
Return `true` when *any* odd bit of `x` equals 1; `false` otherwise.
~~~

Assume that:
* `x` is an unsigned, 32-bit integer;
* the bits are zero-indexed (the least significant bit is position 0)


## Examples

```
  2  -->  1 (true) because at least one odd bit is 1 (2 = 0b10)
  5  -->  0 (false) because none of the odd bits are 1 (5 = 0b101)
170  -->  1 (true) because all of the odd bits are 1 (170 = 0b10101010)
```

Answer: {"fn_name": "any_odd", "inputs": [[2863311530], [128], [131], [2], [24082], [0], [85], [1024], [1], [1365]], "outputs": [[true], [true], [true], [true], [true], [false], [false], [false], [false], [false]]}
user: Given a string, remove any characters that are unique from the string.

Example: 

input: "abccdefee"

output: "cceee"

Answer: {"fn_name": "only_duplicates", "inputs": [["abccdefee"], ["hello"], ["colloquial"], ["foundersandcoders"], ["12314256aaeff"]], "outputs": [["cceee"], ["ll"], ["ollol"], ["ondersndoders"], ["1212aaff"]]}
user: Let's take an integer number, ``` start``` and let's do the iterative process described below:

- we take its digits and raise each of them to a certain power, ```n```, and add all those values up. (result = ```r1```)

- we repeat the same process with the value ```r1``` and so on, ```k``` times.

Let's do it with ```start = 420, n = 3, k = 5```

```
420 ---> 72 (= 4³ + 2³ + 0³) ---> 351 (= 7³ + 2³) ---> 153 ---> 153 ----> 153
```

We can observe that it took ```3``` steps to reach a cyclical pattern ```[153]```(```h = 3```). The length of this cyclical pattern is ```1```, ```patt_len```. The last term of our k operations is 153, ```last_term```

Now, ```start = 420, n = 4, k = 30```

```
420 ---> 272 ---> 2433 ---> 434 ---> 593 ---> 7267 --->
6114 ---> 1554 ---> 1507 ---> 3027 ---> 2498 ---> 10929 --->
13139 ---> 6725 ---> 4338 ---> 4514 ---> 1138 ---> 4179 ---> 9219 ---> 
13139 ---> 6725 ---> 4338 ---> 4514 ---> 1138 ---> 4179 ---> 9219 ---> 
13139 ---> 6725 ---> 4338 ---> 4514 ---> 1138 ---> 4179 ---> 9219......
```

In this example we can observe that the cyclical pattern (```cyc_patt_arr```) is ```[13139, 6725, 4338, 4514, 1138, 4179, 9219]``` with a length of ```7```, (```patt_len = 7```), and it took ```12``` steps (```h = 12```) to reach the cyclical pattern. The last term after doing ```30``` operations is ```1138```

Make the function ```sum_pow_dig_seq()```, that receives the arguments in the order shown below with the corresponding output:
```python
sum_pow_dig_seq(start, n, k) ---> [h, cyc_patt_arr, patt_len, last_term]
```

For our given examples, 
```python
sum_pow_dig_seq(420, 3, 5) == [3, [153], 1, 153]

sum_pow_dig_seq(420, 4, 30) == [12, [13139, 6725, 4338, 4514, 1138, 4179, 9219], 7, 1138]
```

Constraints for tests:
```
500 ≤ start ≤ 8000
2 ≤ n ≤ 9
100 * n ≤ k ≤ 200 * n
```
Do your best!

Answer: {"fn_name": "sum_pow_dig_seq", "inputs": [[420, 3, 5], [420, 4, 30], [420, 5, 100]], "outputs": [[[3, [153], 1, 153]], [[12, [13139, 6725, 4338, 4514, 1138, 4179, 9219], 7, 1138]], [[23, [9045, 63198, 99837, 167916, 91410, 60075, 27708, 66414, 17601, 24585, 40074, 18855, 71787, 83190, 92061, 66858, 84213, 34068, 41811, 33795, 79467, 101463], 22, 18855]]]}
user: **This Kata is intended as a small challenge for my students**

All Star Code Challenge #19

You work for an ad agency and your boss, Bob, loves a catchy slogan. He's always jumbling together "buzz" words until he gets one he likes. You're looking to impress Boss Bob with a function that can do his job for him.

Create a function called sloganMaker() that accepts an array of string "buzz" words. The function returns an array of all possible UNIQUE string permutations of the buzz words (concatonated and separated by spaces).

Your boss is not very bright, so anticipate him using the same "buzz" word more than once, by accident. The function should ignore these duplicate string inputs.

```
sloganMaker(["super", "hot", "guacamole"]);
//[ 'super hot guacamole',
//  'super guacamole hot',
//  'hot super guacamole',
//  'hot guacamole super',
//  'guacamole super hot',
//  'guacamole hot super' ]

sloganMaker(["cool", "pizza", "cool"]); // => [ 'cool pizza', 'pizza cool' ]
```

Note:  
There should be NO duplicate strings in the output array

The input array MAY contain duplicate strings, which should STILL result in an output array with all unique strings

An empty string is valid input

```if-not:python,crystal
The order of the permutations in the output array does not matter
```
```if:python,crystal
The order of the output array must match those rules:
1. Generate the permutations in lexicographic order of the original array.
2. keep only the first occurence of a permutation, when duplicates are found.
```

Answer: {"fn_name": "slogan_maker", "inputs": [[["super"]], [["super", "hot"]], [["super", "hot", "guacamole"]], [["super", "guacamole", "super", "super", "hot", "guacamole"]], [["testing", "testing", "testing"]]], "outputs": [[["super"]], [["super hot", "hot super"]], [["super hot guacamole", "super guacamole hot", "hot super guacamole", "hot guacamole super", "guacamole super hot", "guacamole hot super"]], [["super guacamole hot", "super hot guacamole", "guacamole super hot", "guacamole hot super", "hot super guacamole", "hot guacamole super"]], [["testing"]]]}