Swift Coding Test Course, 'Finding Good Numbers'

In the Subrimari coding test, problems frequently involve finding a “good number.” In this session, we will solve a problem that involves finding specific numbers that satisfy the conditions referred to as “good numbers.” This process will illustrate how to approach and solve problems when using the Swift language.

Problem Description

The problem is as follows:

For a given natural number N, a friend has defined a good number. Specifically, among the numbers from 1 to N, if the sum of any two numbers x and y equals N, then x and y are considered good numbers. You need to find and output the pairs of good numbers for the given N. Note that x must be less than or equal to y, and x + y must equal N.

Input Format

The first line contains the natural number N (1 ≤ N ≤ 1000).

Output Format

Output all pairs of good numbers (x, y) one pair per line.

Approach to the Problem

To find good numbers, we can use the following approach:

Use two loops to generate all possible pairs from 1 to N.
Check if the sum of each pair is N.
Output the pairs whose sum equals N.

Algorithm Implementation

In Swift, we can solve the problem using the following structure:

import Foundation

func findGoodNumbers(N: Int) {
    var goodPairs: [(Int, Int)] = []
    
    for x in 1...N {
        for y in x...N {
            if x + y == N {
                goodPairs.append((x, y))
            }
        }
    }
    
    // Output result
    for pair in goodPairs {
        print("Good number pair: \(pair.0), \(pair.1)")
    }
}

let N = 10 // Example input
findGoodNumbers(N: N)

Code Explanation

In the Swift code above, we can see the following important details:

The function findGoodNumbers takes a natural number N as a parameter and finds the pairs of good numbers for it.
A nested for loop is used to generate all pairs of x and y.
If the sum equals N, that pair is added to the goodPairs array.
Finally, the pairs of good numbers stored in the array are printed.

Execution Result

If the input N is 10, the program produces the following output:

Good number pair: 1, 9
Good number pair: 2, 8
Good number pair: 3, 7
Good number pair: 4, 6
Good number pair: 5, 5

Complexity Analysis

The time complexity of this algorithm is O(N^2). Since we use a nested loop for N, the execution time may increase for larger values of N. However, since the maximum value of N is limited to 1000, this level of time complexity is practically feasible.

Conclusion

In this article, we explored the approach to solve the “good number” problem and implemented the solution in Swift code. We learned how to resolve the problem through a simple yet effective nested loop. I hope this helps improve algorithmic thinking through similar problems in the future.

Additional Considerations

Various methods can be explored to solve this problem. For example:

Using a hashmap to find good numbers with O(N) time complexity
When N is even, restricting the range of x to up to N/2
Solutions through recursive methods

Through these various approaches, a deeper understanding of algorithms can be achieved. In the next session, we will address additional problems related to this topic. Thank you!

Swift Coding Test Course, ‘Finding Good Numbers’