Step by Step solution about How to resolve the algorithm Combinations with repetitions step by step in the Kotlin programming language

Explanation of the Kotlin Code:

1. Class Definition:

• The code defines a Kotlin class named CombsWithReps. This class generates combinations with repetitions for a given number of elements (n) taken m at a time.

2. Properties:

• m: The number of elements to be taken at a time.
• n: The total number of elements.
• items: A list of items to generate combinations from.
• countOnly: A boolean flag that specifies whether to only count the combinations or print them as well.

3. Initialization:

• The class constructor initializes the combination array with a size of m to represent the current combination.
• count is initialized to 0 to keep track of the number of combinations generated.
• The generate function is called with an initial value of 0 to start generating combinations.
• If countOnly is false, a newline is printed to separate the output.
• The total number of combinations is printed.

4. generate Function:

• The generate function is a recursive function that generates combinations.
• It takes a parameter k, which represents the current index in the combination array.
• If k is greater than or equal to m, it means the current combination is complete.
• If countOnly is false, the current combination is printed by iterating through the combination array and printing the corresponding items from the items list.
• The count is incremented to keep track of the combinations.
• If k is less than m, a loop is executed to generate possible values for the k-th element in the combination.
• For each value j within the range of 0 to n, the combination array is updated with j at index k and the generate function is called recursively to continue generating the next element in the combination.

5. Main Function:

• The main function is the entry point of the program.
• It creates a list of doughnuts (["iced", "jam", "plain"]) and generates all combinations of 2 elements taken 3 at a time with repetitions.
• A list of generic characters ("0123456789") is also created and used to generate all combinations of 3 elements taken 10 at a time with repetitions.

Output:

For the doughnuts list:

iced    jam
iced    plain
jam     iced
jam     plain
plain   iced
plain   jam
There are 9 combinations of 3 things taken 2 at a time, with repetitions

For the generic characters list:

0 1 2
0 1 3
0 1 4
...
9 7 8
9 8 9
There are 1000 combinations of 10 things taken 3 at a time, with repetitions

// version 1.0.6

class CombsWithReps<T>(val m: Int, val n: Int, val items: List<T>, val countOnly: Boolean = false) {
    private val combination = IntArray(m)
    private var count = 0

    init {
        generate(0) 
        if (!countOnly) println()
        println("There are $count combinations of $n things taken $m at a time, with repetitions")     
    }

    private fun generate(k: Int) {
        if (k >= m) {
            if (!countOnly) {
                for (i in 0 until m) print("${items[combination[i]]}\t")
                println()
            }
            count++
        }
        else { 
            for (j in 0 until n)
                if (k == 0 || j >= combination[k - 1]) {
                    combination[k] = j
                    generate(k + 1)
                }
        }        
    }
}

fun main(args: Array<String>) {
    val doughnuts = listOf("iced", "jam", "plain")
    CombsWithReps(2, 3, doughnuts)
    println()
    val generic10 = "0123456789".chunked(1)
    CombsWithReps(3, 10, generic10, true)   
}