Kotlin Coding Test, I Will Become the President of the Residents' Association

Coding tests are an important tool that many companies use to evaluate candidates.
In particular, algorithm problems are effective in measuring coding skills and problem-solving abilities.
In this course, we will address the algorithm problem titled “I will become the head of the residents’ association.”
Through this problem, you will be able to develop your understanding of Kotlin’s basic syntax and algorithmic thinking.
I will explain in detail the essence of the problem, the approach, the code implementation, and optimization methods.

Problem Description

One day, a person who wants to become the head of the residents’ association lives in an apartment.
The structure of this apartment is as follows:

Ground Floor: There is 1 person living in each unit from 1 to n.
1st Floor: The number of people in unit 1 is obtained by adding the number of people on the ground floor, and …
k-th Floor: The number of residents in unit n is the sum of the number of people from the ground up to the k-th floor.

The problem is to calculate the number of residents in a given unit based on the floor and unit number.

Input Format

First line: The number of test cases T (1 ≤ T ≤ 10)
For each test case, two integers K (0 ≤ K ≤ 14) and N (1 ≤ N ≤ 14) are given.

Output Format

For each test case, print the number of residents in the corresponding unit.

Problem Approach

This problem can be solved using Dynamic Programming.
You can approach it in the following way:

Understand the characteristics of the apartment structure and remember that each unit on the ground floor has 1 resident.
Then, the number of people on the 1st floor is determined by repeatedly adding the number of people on the ground floor.
The number of residents in unit N on the K-th floor is the sum of the residents in unit 1 + unit 2 + … + unit N on the (K-1)-th floor.
This has a recursive nature, so it can be solved through recursive calls.
When implementing, create a 2D array to store the number of residents for specific floors and units to facilitate memoization.

Code Implementation

Below is the code implementing the above algorithm in Kotlin.


        fun main() {
            val t = readLine()!!.toInt()
            val results = IntArray(t)

            for (i in 0 until t) {
                val (k, n) = readLine()!!.split(' ').map { it.toInt() }
                results[i] = calculateResidents(k, n)
            }

            for (result in results) {
                println(result)
            }
        }

        fun calculateResidents(k: Int, n: Int): Int {
            // Initialize structure for 14 floors and 14 units
            val dp = Array(15) { IntArray(15) }

            // 1 resident for each unit on the ground floor
            for (j in 1..14) {
                dp[0][j] = 1
            }

            // Iterate over each floor and each unit
            for (i in 1..k) {
                for (j in 1..n) {
                    // Add the number of people in unit j on the (i-1)th floor
                    for (m in 1..j) {
                        dp[i][j] += dp[i - 1][m]
                    }
                }
            }

            return dp[k][n] // Return the number of residents in unit n on the k-th floor
        }

Code Explanation

In the above code, the `calculateResidents` function calculates the number of residents in the given K-th floor N-th unit.
This function proceeds through the following steps:

Create a 2D array `dp` and initialize a 15×15 structure.
Set that there is 1 resident in each unit on the ground floor.
For the K-th floor and N-th unit, accumulate the number of people from the (K-1)th floor for all units.
Finally, return the number of residents in unit N on the K-th floor from the DP table.

Time Complexity Analysis

The time complexity of this problem is O(K * N^2). Since K is at most 14,
the overall time complexity can be treated as a constant. Therefore, we can solve the problem quickly and efficiently.
It is important to optimize the code and save memory while implementing it.

Conclusion

The “I will become the head of the residents’ association” problem is a typical algorithm problem that can be solved through dynamic programming.
By utilizing Kotlin’s syntax and solving the problem through DP, you can develop your algorithmic thinking.
Solving such problems can enhance your competitiveness in coding tests.
I hope the content learned through this course will be helpful in your actual coding test preparation!

Kotlin Coding Test, I Will Become the President of the Residents’ Association