Kata

We want to generate all the numbers of three digits where:

• the sum of their digits is equal to 10
• their digits are in increasing order (the numbers may have two or more equal contiguous digits)

The numbers that fulfill these constraints are: [118, 127, 136, 145, 226, 235, 244, 334]. There are 8 numbers in total with 118 being the lowest and 334 being the greatest.

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Task

Implement a function which receives two arguments:

1. the sum of digits (sum)
2. the number of digits (count)

This function should return three values:

1. the total number of values which have count digits that add up to sum and are in increasing order
2. the lowest such value
3. the greatest such value

Note: if there are no values which satisfy these constaints, you should return an empty value (refer to the examples to see what exactly is expected).

Examples

find_all(10, 3)  =>  [8, 118, 334]
find_all(27, 3)  =>  [1, 999, 999]
find_all(84, 4)  =>  []

find_all(10, 3)  =>  [8, 118, 334]
find_all(27, 3)  =>  [1, 999, 999]
find_all(84, 4)  =>  []

find_all(10, 3)  =>  [8, 118, 334]
find_all(27, 3)  =>  [1, 999, 999]
find_all(84, 4)  =>  []

findAll(10, 3)  =>  [8, "118", "334"]
findAll(27, 3)  =>  [1, "999", "999"]
findAll(84, 4)  =>  []

findAll 10 3  =>  ( 8, Just 118, Just 334 )
findAll 27 3  =>  ( 1, Just 999, Just 999 )
findAll 84 4  =>  ( 0, Nothing, Nothing )

// The output type is List<Long>
HowManyNumbers.findAll(10, 3)  =>  [8, 118, 334]
HowManyNumbers.findAll(27, 3)  =>  [1, 999, 999]
HowManyNumbers.findAll(84, 4)  =>  []

// The output type is List<long>
HowManyNumbers.FindAll(10, 3)  =>  [8, 118, 334]
HowManyNumbers.FindAll(27, 3)  =>  [1, 999, 999]
HowManyNumbers.FindAll(84, 4)  =>  []

// The output type is optional<tuple<uint32_t, uint64_t, uint64_t>>
find_all(10, 3)  =>  (8, 118, 334)
find_all(27, 3)  =>  (1, 999, 999)
find_all(84, 4)  =>  nullopt

// (Long, Long) => Option[(Long, Long, Long)]
findAll(10, 3)  =>  Some(8L, 118L, 334L)
findAll(27, 3)  =>  Some(1L, 999L, 999L)
findAll(84, 4)  =>  None

find_all 10 3  =>  Some (8, 188, 334)
find_all 27 3  =>  Some (1, 999, 999)
find_all 84 4  =>  None

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Features of the random tests:

• Number of tests: 112
• Sum of digits value between 20 and 65
• Amount of digits between 2 and 17