Java Coding Test Course, Understanding Combinations

1. Introduction

Programming algorithms and data structures play a very important role in modern software development.
One of the major parts of coding tests is combination problems.
Understanding this provides the foundation needed to algorithmically solve problems.
In this article, we will explain the concept of combinations, how to solve this problem using Java, and detail the process of solving example problems.

2. What are Combinations?

A combination refers to the number of ways to choose R objects from N objects.
Generally, a combination represents a set of selected objects without regard to the order.
For example, when there are three objects {A, B, C}, the combinations of selecting two out of them are as follows:

  • {A, B}
  • {A, C}
  • {B, C}

The number of combinations is calculated using the following mathematical formula:

C(N, R) = N! / (R! * (N – R)!)

In this formula, N is the total number of objects, R is the number of objects to be selected, and “!” denotes factorial.

3. Problem Definition

The problem we will solve in this article is as follows:

Given N integers, output all combinations that can be made by selecting K of them.
The order of input does not matter.

4. Problem-Solving Approach

This problem can be solved using recursion.
It is a method of generating combinations by dividing into cases of selection and non-selection.
Here is the basic mechanism of the algorithm to solve this problem:

  1. Declare an array for generating combinations.
  2. Define a recursive function to create combinations.
  3. Set base conditions to terminate the recursive calls.
  4. Once a combination is complete, print the result.

This approach will repeatedly perform selections and non-selections for each number to generate all combinations.

5. Java Code Implementation


import java.util.ArrayList;
import java.util.List;

public class Combination {
    public static void main(String[] args) {
        int[] numbers = {1, 2, 3, 4, 5}; // Array of numbers to generate combinations
        int K = 3; // Number to select
        List> result = new ArrayList<>(); // List to store results
        generateCombinations(numbers, K, 0, new ArrayList(), result);
        
        // Print results
        for (List combination : result) {
            System.out.println(combination);
        }
    }

    // Recursive function to generate combinations
    private static void generateCombinations(int[] numbers, int K, int start, List combination, List> result) {
        // Base condition: when the number of selected items reaches K, add to results
        if (combination.size() == K) {
            result.add(new ArrayList<>(combination));
            return;
        }

        // Generate combinations
        for (int i = start; i < numbers.length; i++) {
            combination.add(numbers[i]); // Select
            generateCombinations(numbers, K, i + 1, combination, result); // Recursive call
            combination.remove(combination.size() - 1); // Deselect
        }
    }
}

The above code demonstrates the method of creating combinations and printing the results through recursion.
The `generateCombinations` function generates combinations starting from the index of the current number.
At this time, the selected number is added to the `combination` list, and once K numbers are selected, it is added to the results.

6. Time Complexity Analysis

The time complexity of the combination problem is O(C(N, K)).
Here, C(N, K) represents the number of combinations of selecting K from N objects.
The depth of the recursive calls is K, which is related to the number of calls made to select K items.
Therefore, as N increases, the number of combinations increases sharply.
Practically, the time taken to calculate combinations can become very large, especially when K is close to half of N.

7. Conclusion

Combination problems are frequently posed in algorithm questions and have various variations.
In this column, we learned about the concept of combinations and how to implement it using Java.
By understanding the structure of combinations algorithmically, it becomes easier to solve more complex problems.
I wish you good results in coding tests through practice with combination problems!