Kotlin coding test course, finding the binomial coefficient 1

Hello! Today we will learn how to calculate binomial coefficients using Kotlin. The binomial coefficient is an important concept in combinations, representing the number of ways to choose k objects from a given n objects. This topic frequently appears in coding tests, so it is essential to understand it.

Problem Description

Given two integers n and k, write a program to calculate nCk (n choose k). The binomial coefficient is defined by the following formula:

C(n, k) = n! / (k! * (n - k)!)

Here, n! signifies the factorial of n. A factorial is the product of all natural numbers from 1 to n.

Input Format

The first line contains integers n (0 ≤ n ≤ 30) and k (0 ≤ k ≤ n).

Output Format

Print the value of nCk.

Example Input

5 2

Example Output

10

Problem Solving Methods

To solve this problem, you can use two methods:

1. Recursive factorial calculation
2. Dynamic programming for binomial coefficient calculation

1. Recursive Factorial Calculation

The most basic method is to calculate the factorial recursively. This method is easy to understand but can become inefficient as n grows larger. Here is a Kotlin example of calculating factorial recursively:

fun factorial(n: Int): Long {
    return if (n == 0 || n == 1) 1 else n * factorial(n - 1)
}

2. Dynamic Programming for Binomial Coefficient Calculation

To efficiently calculate the binomial coefficient, dynamic programming can be utilized. The binomial coefficient can be computed using the properties of Pascal’s triangle, defined by the following recurrence relation:

C(n, k) = C(n - 1, k - 1) + C(n - 1, k)

The base cases are as follows:

• C(n, 0) = 1 (n >= 0)
• C(n, n) = 1 (n >= 0)

Let’s calculate the binomial coefficient using a dynamic programming array based on Pascal’s triangle:

fun binomialCoefficient(n: Int, k: Int): Long {
    val dp = Array(n + 1) { LongArray(k + 1) }
    for (i in 0..n) {
        for (j in 0..minOf(i, k)) {
            if (j == 0 || j == i) {
                dp[i][j] = 1
            } else {
                dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]
            }
        }
    }
    return dp[n][k]
}

Code Integration Example

Based on the above methods, let’s write the final code:

fun main() {
    val input = readLine()!!.split(" ").map { it.toInt() }
    val n = input[0]
    val k = input[1]
    
    println(binomialCoefficient(n, k))
}

fun binomialCoefficient(n: Int, k: Int): Long {
    val dp = Array(n + 1) { LongArray(k + 1) }
    for (i in 0..n) {
        for (j in 0..minOf(i, k)) {
            if (j == 0 || j == i) {
                dp[i][j] = 1
            } else {
                dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]
            }
        }
    }
    return dp[n][k]
}

Conclusion

We have learned how to calculate binomial coefficients. We can solve this problem using recursion and dynamic programming, and it is important to understand the advantages and disadvantages of each method. The binomial coefficient can be applied in many fields beyond combinatorics, so it is beneficial to have a solid understanding of this concept.

We hope you continue to explore various algorithm problem-solving processes using Kotlin. Thank you!