meetforever/GRPO_CL huggingface dataset:
user: # Connect Four

Take a look at wiki description of Connect Four game:

[Wiki Connect Four](https://en.wikipedia.org/wiki/Connect_Four)

The grid is 6 row by 7 columns, those being named from A to G.

You will receive a list of strings showing the order of the pieces which dropped in columns:

```python
  pieces_position_list = ["A_Red",
                          "B_Yellow",
                          "A_Red",
                          "B_Yellow",
                          "A_Red",
                          "B_Yellow",
                          "G_Red",
                          "B_Yellow"]
```

The list may contain up to 42 moves and shows the order the players are playing.

The first player who connects four items of the same color is the winner.

You should return "Yellow", "Red" or "Draw" accordingly.

Answer: {"fn_name": "who_is_winner", "inputs": [[["C_Yellow", "E_Red", "G_Yellow", "B_Red", "D_Yellow", "B_Red", "B_Yellow", "G_Red", "C_Yellow", "C_Red", "D_Yellow", "F_Red", "E_Yellow", "A_Red", "A_Yellow", "G_Red", "A_Yellow", "F_Red", "F_Yellow", "D_Red", "B_Yellow", "E_Red", "D_Yellow", "A_Red", "G_Yellow", "D_Red", "D_Yellow", "C_Red"]], [["C_Yellow", "B_Red", "B_Yellow", "E_Red", "D_Yellow", "G_Red", "B_Yellow", "G_Red", "E_Yellow", "A_Red", "G_Yellow", "C_Red", "A_Yellow", "A_Red", "D_Yellow", "B_Red", "G_Yellow", "A_Red", "F_Yellow", "B_Red", "D_Yellow", "A_Red", "F_Yellow", "F_Red", "B_Yellow", "F_Red", "F_Yellow", "G_Red", "A_Yellow", "F_Red", "C_Yellow", "C_Red", "G_Yellow", "C_Red", "D_Yellow", "D_Red", "E_Yellow", "D_Red", "E_Yellow", "C_Red", "E_Yellow", "E_Red"]], [["F_Yellow", "G_Red", "D_Yellow", "C_Red", "A_Yellow", "A_Red", "E_Yellow", "D_Red", "D_Yellow", "F_Red", "B_Yellow", "E_Red", "C_Yellow", "D_Red", "F_Yellow", "D_Red", "D_Yellow", "F_Red", "G_Yellow", "C_Red", "F_Yellow", "E_Red", "A_Yellow", "A_Red", "C_Yellow", "B_Red", "E_Yellow", "C_Red", "E_Yellow", "G_Red", "A_Yellow", "A_Red", "G_Yellow", "C_Red", "B_Yellow", "E_Red", "F_Yellow", "G_Red", "G_Yellow", "B_Red", "B_Yellow", "B_Red"]], [["A_Yellow", "B_Red", "B_Yellow", "C_Red", "G_Yellow", "C_Red", "C_Yellow", "D_Red", "G_Yellow", "D_Red", "G_Yellow", "D_Red", "F_Yellow", "E_Red", "D_Yellow"]], [["A_Red", "B_Yellow", "A_Red", "B_Yellow", "A_Red", "B_Yellow", "G_Red", "B_Yellow"]]], "outputs": [["Yellow"], ["Yellow"], ["Red"], ["Red"], ["Yellow"]]}
user: In this kata we want to convert a string into an integer. The strings simply represent the numbers in words.

Examples:

* "one" => 1
* "twenty" => 20
* "two hundred forty-six" => 246
* "seven hundred eighty-three thousand nine hundred and nineteen" => 783919

Additional Notes:

* The minimum number is "zero" (inclusively)
* The maximum number, which must be supported is 1 million (inclusively)
* The "and" in e.g. "one hundred and twenty-four" is optional, in some cases it's present and in others it's not
* All tested numbers are valid, you don't need to validate them

Answer: {"fn_name": "parse_int", "inputs": [["zero"], ["one"], ["two"], ["three"], ["four"], ["five"], ["six"], ["seven"], ["eight"], ["nine"], ["ten"], ["twenty"], ["twenty-one"], ["thirty-seven"], ["forty-six"], ["fifty-nine"], ["sixty-eight"], ["seventy-two"], ["eighty-three"], ["ninety-four"], ["one hundred"], ["one hundred one"], ["one hundred and one"], ["one hundred sixty-nine"], ["two hundred and ninety-nine"], ["seven hundred thirty-six"], ["two thousand"], ["one thousand three hundred and thirty-seven"], ["ten thousand"], ["twenty-six thousand three hundred and fifty-nine"], ["thirty-five thousand"], ["ninety-nine thousand nine hundred and ninety-nine"], ["six hundred sixty-six thousand six hundred sixty-six"], ["seven hundred thousand"], ["two hundred thousand three"], ["two hundred thousand and three"], ["two hundred three thousand"], ["five hundred thousand three hundred"], ["eight hundred eighty-eight thousand eight hundred and eighty-eight"], ["one million"]], "outputs": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [20], [21], [37], [46], [59], [68], [72], [83], [94], [100], [101], [101], [169], [299], [736], [2000], [1337], [10000], [26359], [35000], [99999], [666666], [700000], [200003], [200003], [203000], [500300], [888888], [1000000]]}
user: I started this as a joke among friends, telling that converting numbers to other integer bases is for n00bs, while an actual coder at least converts numbers to more complex bases like [pi (or π or however you wish to spell it in your language)](http://en.wikipedia.org/wiki/Pi), so they dared me proving I was better.

And I did it in few hours, discovering that what I started as a joke actually has [some math ground and application (particularly the conversion to base pi, it seems)](http://en.wikipedia.org/wiki/Non-integer_representation).

That said, now I am daring you to do the same, that is to build a function so that it takes a **number** (any number, you are warned!) and optionally the **number of decimals** (default: 0) and a **base** (default: pi), returning the proper conversion **as a string**:

#Note
In Java there is no easy way with optional parameters so all three parameters will be given; the same in C# because, as of now, the used version is not known. 

```python
converter(13) #returns '103'
converter(13,3) #returns '103.010'
converter(-13,0,2) #returns '-1101'
```

I know most of the world uses a comma as a [decimal mark](http://en.wikipedia.org/wiki/Decimal_mark), but as English language and culture are *de facto* the Esperanto of us coders, we will stick to our common glorious traditions and uses, adopting the trivial dot (".") as decimal separator; if the absolute value of the result is <1, you have of course to put one (and only one) leading 0 before the decimal separator.

Finally, you may assume that decimals if provided will always be >= 0 and that no test base will be smaller than 2 (because, you know, converting to base 1 is pretty lame) or greater than 36; as usual, for digits greater than 9 you can use uppercase alphabet letter, so your base of numeration is going to be: '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'.

That is my first 3-languages-kata, so I count on you all to give me extensive feedback, no matter how harsh it may sound, so to improve myself even further :)

Answer: {"fn_name": "converter", "inputs": [[13], [10], [13, 3], [13, 0, 8], [10, 0, 16], [10000, 4, 13], [7, 0, 19], [13.5, 4, 16], [10.81, 0, 16], [1, 2, 2], [-10, 0, 23], [0, 4, 26], [-15.5, 2, 23], [13, 0, 10], [5.5, 1, 10]], "outputs": [["103"], ["100"], ["103.010"], ["15"], ["A"], ["4723.0000"], ["7"], ["D.8000"], ["A"], ["1.00"], ["-A"], ["0.0000"], ["-F.BB"], ["13"], ["5.5"]]}
user: Create a function that differentiates a polynomial for a given value of `x`.

Your function will receive 2 arguments: a polynomial as a string, and a point to evaluate the equation as an integer.

## Assumptions:

* There will be a coefficient near each `x`, unless the coefficient equals `1` or `-1`.
* There will be an exponent near each `x`, unless the exponent equals `0` or `1`.
* All exponents will be greater or equal to zero

## Examples:

```python
differenatiate("12x+2", 3)      ==>   returns 12
differenatiate("x^2+3x+2", 3)   ==>   returns 9
```

Answer: {"fn_name": "differentiate", "inputs": [["12x+2", 3], ["x-66", 3], ["x^2-x", 3], ["-5x^2+10x+4", 3], ["x^2+3x+3", 3], ["1000x^2+300x+200", 531], ["21x^2+35x+3", 2071], ["66x^3+3x^2+3", 441], ["21x^4+3x^3", 414], ["-21x^5+3x^3", 12398], ["-x^2+3x-3", 1234567908], ["-7x^5+22x^4-55x^3-94x^2+87x-56", -3], ["-123x^5+3x", 8559], ["x^2", 59884848483559]], "outputs": [[12], [1], [5], [-20], [9], [1062300], [87017], [38509884], [5962009860], [-2480823269890144044], [-2469135813], [-6045], [-3300404885229567012], [119769696967118]]}
user: My little sister came back home from school with the following task:
given a squared sheet of paper she has to cut it in pieces
which, when assembled, give squares the sides of which form
an increasing sequence of numbers.
At the beginning it was lot of fun but little by little we were tired of seeing the pile of torn paper.
So we decided to write a program that could help us and protects trees.

## Task

Given a positive integral number n, return a **strictly increasing** sequence (list/array/string depending on the language) of numbers, so that the sum of the squares is equal to n².

If there are multiple solutions (and there will be), return as far as possible the result with the largest possible values:

## Examples

`decompose(11)` must return `[1,2,4,10]`. Note that there are actually two ways to decompose 11²,
11² = 121 = 1 + 4 + 16 + 100 = 1² + 2² + 4² + 10² but don't return `[2,6,9]`, since 9 is smaller than 10.

For `decompose(50)` don't return `[1, 1, 4, 9, 49]` but `[1, 3, 5, 8, 49]` since `[1, 1, 4, 9, 49]`
doesn't form a strictly increasing sequence.

## Note
Neither `[n]` nor `[1,1,1,…,1]` are valid solutions. If no valid solution exists, return `nil`, `null`, `Nothing`, `None` (depending on the language) or `"[]"` (C) ,`{}` (C++), `[]` (Swift, Go).

The function "decompose" will take a positive integer n 
and return the decomposition of N = n² as:

- [x1 ... xk]
or
- "x1 ... xk"
or
- Just [x1 ... xk]
or
- Some [x1 ... xk]
or
- {x1 ... xk}
or
- "[x1,x2, ... ,xk]"

depending on the language (see "Sample tests")

# Note for Bash
```
decompose 50 returns "1,3,5,8,49"
decompose 4  returns "Nothing"
```
# Hint

Very often `xk` will be `n-1`.

Answer: {"fn_name": "decompose", "inputs": [[12], [6], [50], [44], [625], [5], [7100], [123456], [1234567], [7654321], [4], [7654322]], "outputs": [[[1, 2, 3, 7, 9]], [null], [[1, 3, 5, 8, 49]], [[2, 3, 5, 7, 43]], [[2, 5, 8, 34, 624]], [[3, 4]], [[2, 3, 5, 119, 7099]], [[1, 2, 7, 29, 496, 123455]], [[2, 8, 32, 1571, 1234566]], [[6, 10, 69, 3912, 7654320]], [null], [[1, 4, 11, 69, 3912, 7654321]]]}
user: Write a function that counts how many different ways you can make change for an amount of money, given an array of coin denominations. For example, there are 3 ways to give change for 4 if you have coins with denomination 1 and 2: 
```
1+1+1+1, 1+1+2, 2+2.
```
The order of coins does not matter:
```
1+1+2 == 2+1+1
```
Also, assume that you have an infinite amount of coins.

Your function should take an amount to change and an array of unique denominations for the coins:

```python
  count_change(4, [1,2]) # => 3
  count_change(10, [5,2,3]) # => 4
  count_change(11, [5,7]) # => 0
```

Answer: {"fn_name": "count_change", "inputs": [[4, [1, 2]], [10, [5, 2, 3]], [11, [5, 7]], [98, [3, 14, 8]], [199, [3, 5, 9, 15]], [300, [5, 10, 20, 50, 100, 200, 500]], [301, [5, 10, 20, 50, 100, 200, 500]], [419, [2, 5, 10, 20, 50]]], "outputs": [[3], [4], [0], [19], [760], [1022], [0], [18515]]}
user: ## Story

Before we dive into the exercise, I would like to show you why these numbers are so important in computer programming today.

It all goes back to the time of 19th century. Where computers we know today were non-existing. The first ever **computer program** was for the Analytical Engine to compute **Bernoulli numbers**. A woman named Ada Lovelace wrote the very first program. The sad part is the engine was never fully build so her code was never tested. She also predicted the start of **AI** (artificial intelligence).

Computers will be able to compose music by themselves, solve problems (not only numbers) ... So in her honor reproduce what was done back in 1842. The Bernoulli numbers are a sequence of rational numbers with deep connections to number theory. The Swiss mathematician Jakob Bernoulli and the Japanese mathematician Seki Kowa discovered the numbers around the same time at the start of the 18th Century. If you want to read more about her or Bernoulli numbers follow these links:

https://en.wikipedia.org/wiki/Ada_Lovelace

https://en.wikipedia.org/wiki/Bernoulli_number

http://mathworld.wolfram.com/BernoulliNumber.html

## Exercise

Your job is to write a function `bernoulli_number(n)` which outputs the n-th Bernoulli number. The input will always be a non-negative integer so you do not need to worry about exceptions. How you will solve the problem is none of my business but here are some guidelines.  
You can make pascal triangle and then with the basic formula generate all Bernoulli numbers. Look example below.

For the sake of floating numbers, just use `Fractions` so there will be no problems with rounding.


0 = 1 + 2b1 ............................................................... 
  b1 = - 1/2

0 = 1 + 3b1 + 3b2 ...................................................    b2        = 1/6

0 = 1 + 4b1 + 6b2 + 4b3 .......................................  b3 = 0

0 = 1 + 5b1 + 10b2 + 10b3 + 5b4 ...................... b4 = - 1/30

... and so on.

```
bernoulli_number(0) # return 1
bernoulli_number(1) # return Fraction(-1,2) or Rational(-1,2) or "1/2"
bernoulli_number(6) # return Fraction(1,42) or ...
bernoulli_number(42) # return Fraction(1520097643918070802691,1806) or ...
bernoulli_number(22) # return Fraction(854513,138) or ... "854513/138"
```

## Note

See "Sample Tests" to see the return type for each language.

Good luck and happy coding! 

PS: be careful some numbers might exceed `1000`.
If this kata is too hard for you try to solve pascal triangle and something similar to this and then come back :).

Answer: {"fn_name": "bernoulli_number", "inputs": [[0], [3], [1337]], "outputs": [[1], [0], [0]]}
user: The number ```89``` is the first positive integer that has a particular, curious property:

The square of ```89``` is ```7921```; ```89² = 7921```

The reverse of ```7921``` is ```1297```, and ```1297``` is a prime number.

The cube of ```89``` is ```704969```; ```89³ = 704969```

The reverse of ```704969``` is ```969407```, and ```969407``` is a prime number.

The first four terms of this sequence having this special property are:
```
n-th term      term value
    1               89 
    2              271
    3              325
    4              328
```

Create a function ```sq_cub_rev_prime()```, that receives the ordinal number of the sequence and outputs its correspoding value.

Use the above table to show how the function should work:
```python 
sq_cub_rev_prime(1) == 89 
sq_cub_rev_prime(2) == 271
sq_cub_rev_prime(3) == 325
sq_cub_rev_prime(4) == 328
```
Your code will be tested up to the 250th term

This is not a registered sequence of OESIS, so if you are one of the first ten people that solve this kata, you may have the privilege to register the sequence at https://oeis.org, with your name. If you do so, please, mention in your biography that you are a Codewarrior.

Memoize your results to pass the tests.

Enjoy it!

Answer: {"fn_name": "sq_cub_rev_prime", "inputs": [[1], [2], [3], [4]], "outputs": [[89], [271], [325], [328]]}
user: Consider the following array:

```
[1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891011...]
```

If we join these blocks of numbers, we come up with an infinite sequence which starts with `112123123412345123456...`. The list is infinite.

You will be given an number (`n`) and your task will be to return the element at that index in the sequence, where `1 ≤ n ≤ 10^18`. Assume the indexes start with `1`, not `0`.  For example:

```
solve(1) = 1, because the first character in the sequence is 1. There is no index 0. 
solve(2) = 1, because the second character is also 1.
solve(3) = 2, because the third character is 2.
```

More examples in the test cases. Good luck!

Answer: {"fn_name": "solve", "inputs": [[1], [2], [3], [100], [2100], [31000], [55], [123456], [123456789], [999999999999999999], [1000000000000000000], [999999999999999993]], "outputs": [[1], [1], [2], [1], [2], [2], [1], [6], [3], [4], [1], [7]]}
user: If n is the numerator and d the denominator of a fraction, that fraction is defined a (reduced) proper fraction if and only if GCD(n,d)==1.

For example `5/16` is a proper fraction, while `6/16` is not, as both 6 and 16 are divisible by 2, thus the fraction can be reduced to `3/8`.

Now, if you consider a given number d, how many proper fractions can be built using d as a denominator?

For example, let's assume that d is 15: you can build a total of 8 different proper fractions between 0 and 1 with it: 1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15 and 14/15.

You are to build a function that computes how many proper fractions you can build with a given denominator:
```python
proper_fractions(1)==0
proper_fractions(2)==1
proper_fractions(5)==4
proper_fractions(15)==8
proper_fractions(25)==20
```

Be ready to handle big numbers.

Edit: to be extra precise, the term should be "reduced" fractions, thanks to [girianshiido](http://www.codewars.com/users/girianshiido) for pointing this out and sorry for the use of an improper word :)

Answer: {"fn_name": "proper_fractions", "inputs": [[1], [2], [5], [15], [25], [9999999], [500000003], [1532420], [123456789], [9999999999]], "outputs": [[0], [1], [4], [8], [20], [6637344], [500000002], [608256], [82260072], [5890320000]]}
user: # Task
 Sorting is one of the most basic computational devices used in Computer Science. 
 
 Given a sequence (length ≤ 1000) of 3 different key values (7, 8, 9), your task is to find the minimum number of exchange operations necessary to make the sequence sorted. 

 One operation is the switching of 2 key values in the sequence.

# Example

 For `sequence = [7, 7, 8, 8, 9, 9]`, the result should be `0`.
 
 It's already a sorted sequence.

 For `sequence = [9, 7, 8, 8, 9, 7]`, the result should be `1`.
 
 We can switching `sequence[0]` and `sequence[5]`.
 
 For `sequence = [8, 8, 7, 9, 9, 9, 8, 9, 7]`, the result should be `4`.
 
 We can:
```
 [8, 8, 7, 9, 9, 9, 8, 9, 7] 
 switching sequence[0] and sequence[3]
 --> [9, 8, 7, 8, 9, 9, 8, 9, 7]
 switching sequence[0] and sequence[8]
 --> [7, 8, 7, 8, 9, 9, 8, 9, 9]
 switching sequence[1] and sequence[2]
 --> [7, 7, 8, 8, 9, 9, 8, 9, 9]
 switching sequence[5] and sequence[7]
 --> [7, 7, 8, 8, 8, 9, 9, 9, 9] 
```
So `4` is the minimum number of operations for the sequence to become sorted.

# Input/Output


 - `[input]` integer array `sequence`

  The Sequence.


 - `[output]` an integer

  the minimum number of operations.

Answer: {"fn_name": "exchange_sort", "inputs": [[[7, 7, 8, 8, 9, 9]], [[9, 7, 8, 8, 9, 7]], [[8, 8, 7, 9, 9, 9, 8, 9, 7]], [[9, 9, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7]], [[9, 9, 9, 7, 7, 8, 9, 7, 8, 9, 7, 9]], [[9, 9, 7, 7, 8, 8]], [[9, 7, 9]], [[8, 7, 8]], [[7, 8, 7, 8]], [[8, 8, 7, 8]], [[8, 8, 7, 7, 8]]], "outputs": [[0], [1], [4], [6], [4], [4], [1], [1], [1], [1], [2]]}
user: Story:
In the realm of numbers, the apocalypse has arrived. Hordes of zombie numbers have infiltrated and are ready to turn everything into undead. The properties of zombies are truly apocalyptic: they reproduce themselves unlimitedly and freely interact with each other. Anyone who equals them is doomed. Out of an infinite number of natural numbers, only a few remain. This world needs a hero who leads remaining numbers in hope for survival: The highest number to lead those who still remain.

Briefing:
There is a list of positive natural numbers. Find the largest number that cannot be represented as the sum of this numbers, given that each number can be added unlimited times. Return this number, either 0 if there are no such numbers, or -1 if there are an infinite number of them.

Example:
```
Let's say [3,4] are given numbers. Lets check each number one by one:
1 - (no solution) - good
2 - (no solution) - good
3 = 3 won't go
4 = 4 won't go
5 - (no solution) - good
6 = 3+3 won't go
7 = 3+4 won't go
8 = 4+4 won't go
9 = 3+3+3 won't go
10 = 3+3+4 won't go
11 = 3+4+4 won't go
13 = 3+3+3+4 won't go
```
...and so on. So 5 is the biggest 'good'. return 5

Test specs:
Random cases will input up to 10 numbers with up to 1000 value

Special thanks:
Thanks to Voile-sama, mathsisfun-sama, and Avanta-sama for heavy assistance. And to everyone who tried and beaten the kata ^_^

Answer: {"fn_name": "survivor", "inputs": [[[7, 11]], [[1, 7, 15]], [[2, 10]], [[687, 829, 998]], [[]], [[1]]], "outputs": [[59], [0], [-1], [45664], [-1], [0]]}
user: ## Snail Sort

Given an `n x n` array, return the array elements arranged from outermost elements to the middle element, traveling clockwise.

```
array = [[1,2,3],
         [4,5,6],
         [7,8,9]]
snail(array) #=> [1,2,3,6,9,8,7,4,5]
```

For better understanding, please follow the numbers of the next array consecutively:

```
array = [[1,2,3],
         [8,9,4],
         [7,6,5]]
snail(array) #=> [1,2,3,4,5,6,7,8,9]
```

This image will illustrate things more clearly:



NOTE: The idea is not sort the elements from the lowest value to the highest; the idea is to traverse the 2-d array in a clockwise snailshell pattern.

NOTE 2: The 0x0 (empty matrix) is represented as en empty array inside an array `[[]]`.

Answer: {"fn_name": "snail", "inputs": [[[[]]], [[[1]]], [[[1, 2, 3], [4, 5, 6], [7, 8, 9]]], [[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]], [[[1, 2, 3, 4, 5, 6], [20, 21, 22, 23, 24, 7], [19, 32, 33, 34, 25, 8], [18, 31, 36, 35, 26, 9], [17, 30, 29, 28, 27, 10], [16, 15, 14, 13, 12, 11]]]], "outputs": [[[]], [[1]], [[1, 2, 3, 6, 9, 8, 7, 4, 5]], [[1, 2, 3, 4, 5, 10, 15, 20, 25, 24, 23, 22, 21, 16, 11, 6, 7, 8, 9, 14, 19, 18, 17, 12, 13]], [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]]]}
user: Given two numbers: 'left' and 'right' (1 <= 'left' <= 'right' <= 200000000000000)
return sum of all '1' occurencies in binary representations of numbers between 'left' and 'right' (including both)

``` 
Example:
countOnes 4 7 should return 8, because:
4(dec) = 100(bin), which adds 1 to the result.
5(dec) = 101(bin), which adds 2 to the result.
6(dec) = 110(bin), which adds 2 to the result.
7(dec) = 111(bin), which adds 3 to the result.
So finally result equals 8.
```
WARNING: Segment may contain billion elements, to pass this kata, your solution cannot iterate through all numbers in the segment!

Answer: {"fn_name": "countOnes", "inputs": [[1, 1000000000]], "outputs": [[14846928141]]}