Kata

Different colour pattern lists produce different numerical sequences in colours.

For example the sequence ['red', 'yellow'', 'blue''], produces the following coloured sequence:

1 2 3 4 5 6 7 8 9 10 11 12 13.....

The sequence ['red', 'yellow', 'blue', 'orange', 'green'] produce the sequence:

1 2 3 4 5 6 7 8 9 10 11 12 13.....

We have the following recursive sequence:

• a₁ = 1
• a_n = a_n-1 + n + k

having that k may be positive or negative.

Task

Create a function count_col_hits(), (javascript countColHits()that receives the following arguments:

• the value of k

• a certain pattern colour list, pat_col,or array of colours (that has an specific order as it was shown above)

• a range of values, range_, an array of two elements, having a lower and upper bound, [a, b], such that a < b

The function should output an array with two elements:

• the maximum number of hits that each colour has in the range [a, b], such that every value, val, that hits the sequence of coloured numbers are such that, a ≤ val ≤ b

• the corresponding name of the colour that produces this maximum amount of hits (or it may be also colours that produce the maximum amount of hits).

Examples

k = -4
pat_col = ['red', 'yellow', 'blue', 'orange', 'green']
range_ = [20, 40]

ith term    value     colour     hit or not
1             1         red         yes         
2            -1         ---          no   (negative values do not hit)
3            -2         ---          no
4            -2         ---          no
5            -1         ---          no
6             1         red         yes
7             4        orange       yes
8             8         blue        yes
9            13         blue        yes
10           19        orange       yes
11           26         red         yes <---- hit in the range, 20 ≤ 26 ≤ 40
12           34        orange       yes <---- hit in the range, 20 ≤ 34 ≤ 40

count_col_hits(k, pat_col, range_) == [1, ['orange', 'red']]  # If there is more than one colour the array should be sorted alphabetically

Having another case changing the input:

k = -7
pat_col = ['red', 'yellow', 'blue', 'orange', 'green', 'pink']
range_ = [20, 150]

count_col_hits(k, pat_col, range_) == [4, 'orange'] #If there is only one colour with maximum amount of hits there is no need to use an array of colours in the result.

# The other colours had the result: 'red': 3, 'green': 2, 'yellow': 1, 'blue': 0, 'pink': 0

Your code should handle carefully the cases where there are no hits at all. For that case the output should be an empty array.

k = 50
pat_col = ['red', 'yellow', 'blue', 'orange', 'green', 'pink']
range_ = [20, 50]
count_col_hits(k, pat_col, range_) == []

You will be always receiving valid inputs for the arguments of the function.

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Features of the random tests:

• Numpber of tests: 200
• -100 ≤ k ≤ 100
• length of pattern colour array: 5 ≤ l ≤ 20
• 100 ≤ a ≤ 100000, 1000 ≤ b ≤ 10**8 and always a < b