Step by Step solution about How to resolve the algorithm Paraffins step by step in the Kotlin programming language

The code you provided is written in Kotlin and is a program that counts the number of unrooted and rooted trees with a given number of nodes.

The program uses a recursive function called tree to calculate the number of trees with a given number of nodes and a given number of branches. The function takes the following arguments:

• br: The number of branches in the current tree.
• n: The number of nodes in the current tree.
• l: The length of the current tree.
• s: The sum of the lengths of all the branches in the current tree.
• cnt: The number of trees with the given number of nodes and branches that have already been counted.

The function tree first calculates the sum of the lengths of all the branches in the current tree. Then, it iterates over all possible values of b, which is the number of branches in the next tree. For each value of b, the function calculates the number of trees with the given number of nodes and branches that have already been counted, and it adds this number to the sum of the lengths of all the branches in the current tree.

If the sum of the lengths of all the branches in the current tree is greater than the maximum length of a tree, or if the length of the current tree is greater than twice the sum of the lengths of all the branches in the current tree, then the function returns. Otherwise, the function calculates the number of rooted and unrooted trees with the given number of nodes and branches, and it adds these numbers to the sum of the lengths of all the branches in the current tree.

The function bicenter calculates the number of bicentered trees with a given number of nodes. A bicentered tree is a tree with two centers, which are nodes that have the same number of descendants. The function bicenter takes the following argument:

• s: The number of nodes in the tree.

The function bicenter first checks if the number of nodes in the tree is even. If it is, then the function calculates the number of rooted trees with half the number of nodes as the given tree. Then, the function adds this number to the sum of the lengths of all the branches in the given tree.

The function main calls the functions tree and bicenter to calculate the number of rooted and unrooted trees with a given number of nodes. The function main takes the following argument:

• args: An array of strings that contains the command-line arguments.

The function main first iterates over all possible values of n, which is the number of nodes in the tree. For each value of n, the function calls the function tree to calculate the number of rooted and unrooted trees with n nodes. Then, the function calls the function bicenter to calculate the number of bicentered trees with n nodes. The function main prints the number of rooted and unrooted trees with n nodes to the console.

// version 1.1.4-3

import java.math.BigInteger

const val MAX_N = 250
const val BRANCHES = 4

val rooted   = Array(MAX_N + 1) { if (it < 2) BigInteger.ONE else BigInteger.ZERO }
val unrooted = Array(MAX_N + 1) { if (it < 2) BigInteger.ONE else BigInteger.ZERO }
val c = Array(BRANCHES) { BigInteger.ZERO }

fun tree(br: Int, n: Int, l: Int, s: Int, cnt: BigInteger) {
    var sum = s
    for (b in (br + 1)..BRANCHES) {
        sum += n
        if (sum > MAX_N || (l * 2 >= sum && b >= BRANCHES)) return

        var tmp = rooted[n]
        if (b == br + 1) {
            c[br] = tmp * cnt
        }
        else {
            val diff = (b - br).toLong()
            c[br] *= tmp + BigInteger.valueOf(diff - 1L)
            c[br] /= BigInteger.valueOf(diff)
        }
 
        if (l * 2 < sum) unrooted[sum] += c[br]
        if (b < BRANCHES) rooted[sum] += c[br]
        for (m in n - 1 downTo 1) tree(b, m, l, sum, c[br])
    }
}

fun bicenter(s: Int) {
    if ((s and 1) == 0) {
        var tmp = rooted[s / 2]
        tmp *= tmp + BigInteger.ONE
        unrooted[s] += tmp.shiftRight(1)
    }
}

fun main(args: Array<String>) {
    for (n in 1..MAX_N) {
        tree(0, n, n, 1, BigInteger.ONE)
        bicenter(n)
        println("$n: ${unrooted[n]}")
    }
}