Kotlin coding test course, calculating the binomial coefficient

Introduction

Kotlin is a modern programming language widely used for coding tests and algorithm problem-solving. In this tutorial, we will explore how to calculate the binomial coefficient. The binomial coefficient is a very important concept used to compute combinations. This post will cover two methods for calculating the binomial coefficient: a recursive method and a dynamic programming method.

Problem Description

Let’s solve the problem of calculating nCk (n choose k) for given natural numbers n and k. The binomial coefficient is defined as n! / (k! * (n-k)!). The values of n and k must satisfy the following conditions:

• 0 ≤ k ≤ n
• n is provided as a natural number.

For example, if n is 5 and k is 2, then 5C2 is 10. This is because 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 × 4) / (2 × 1) = 10.

Solution Method

1. Recursive Method

The binomial coefficient can be calculated recursively. The key point to note is the underlying formula. The binomial coefficient has the following property and can be implemented recursively:

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

Based on the above formula, let’s implement the binomial coefficient recursively.

fun binomialCoefficient(n: Int, k: Int): Int {
    // Base case
    if (k == 0 || k == n) return 1
    // Recursive case
    return binomialCoefficient(n - 1, k - 1) + binomialCoefficient(n - 1, k)
}
            

2. Dynamic Programming Method

The recursive method can be inefficient in terms of execution time and memory. To improve this, we can use dynamic programming. This method saves previous computation results to avoid unnecessary calculations. Let’s create a DP table to compute the binomial coefficient.

fun binomialCoefficientDP(n: Int, k: Int): Int {
    // Create a 2D array to store results
    val dp = Array(n + 1) { IntArray(k + 1) }
    
    // Fill the table according to base cases
    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]
            }
        }
    }
    
    // Result is stored at dp[n][k]
    return dp[n][k]
}
            

Code Execution Example

We can calculate the binomial coefficient using the two methods above. Here’s how to execute it in Kotlin.

fun main() {
    val n = 5 // value of n
    val k = 2 // value of k

    // Using the recursive method
    val resultRecursive = binomialCoefficient(n, k)
    println("Recursive method: $n C $k = $resultRecursive")

    // Using the dynamic programming method
    val resultDP = binomialCoefficientDP(n, k)
    println("Dynamic programming method: $n C $k = $resultDP")
}
            

Executing the above code will yield the following results:

Recursive method: 5 C 2 = 10
Dynamic programming method: 5 C 2 = 10
            

Conclusion

In this post, we explored two methods for calculating the binomial coefficient using Kotlin. The recursive method is intuitive for understanding, but it can be inefficient with larger input values. On the other hand, dynamic programming uses more memory but significantly reduces time complexity. We hope this helps you understand ways to efficiently solve algorithm problems.

We hope this tutorial is helpful in your preparation for coding tests. Thank you!