Swift Coding Test Course, Creating an Ascending Sequence with Stack

Problem Description

Implement an algorithm to create an ascending sequence from the given sequence seq. The sequence consists of integers, and you should demonstrate how to use a stack to obtain a sorted ascending sequence. At this time, you can only manipulate the elements of the sequence by pushing and popping them onto the stack.

For example, if the input sequence is [3, 2, 4, 1, 5], how should we use the stack to sort it in ascending order? Create a sequence that outputs the necessary order through the stack.

Input Format

  • The first line contains the length of the sequence n. (1 ≤ n ≤ 1000)
  • The second line contains each element of the sequence a1, a2, ..., an. (1 ≤ ai ≤ 1000)

Output Format

Output the sorted ascending sequence. The elements of the sequence should be listed in the order they are popped from the stack, with each element printed on a new line.

Approach

To solve the problem, I will describe the process of sorting numbers in ascending order using a stack. The stack functions as a LIFO (Last In, First Out) structure, where the most recently added data is the first to be removed. By utilizing this characteristic, we can manipulate numbers from the given sequence.

  1. Read the input sequence.
  2. Initialize the stack.
  3. Traverse the given sequence. Push or pop each element to create the required ascending sequence.
  4. Finally, pop from the stack to output the result.

Implementation

The following Swift code solves this problem:

import Foundation

func makeAscendingSequence(seq: [Int]) {
    var stack = [Int]()
    var output = [Int]()
    var current = 1
    let n = seq.count

    for number in seq {
        while current <= n {
            stack.append(current)
            current += 1
        }

        if stack.isEmpty || stack.last! != number {
            print("Impossible") // Impossible case
            return
        }

        output.append(stack.removeLast())
    }

    // Output the result
    for num in output {
        print(num)
    }
}

// Test case
let seq = [3, 2, 4, 1, 5]
makeAscendingSequence(seq: seq)

Code Explanation

The above Swift code is implemented in the following manner:

1. Variable Initialization

  • stack: An array that will serve as the stack.
  • output: An array that will store the final ascending sequence.
  • current: Represents the number to be added to the stack.

2. Sequence Traversal

As you traverse the input sequence, for each element number, perform the following actions:

  1. While the current is less than or equal to n, push current onto the stack and increment current by 1.
  2. If the top element of the stack is not equal to the current number, print “Impossible” and terminate.
  3. Add the top element of the stack to the output array.

3. Output Result

Finally, output all the numbers stored in the output array.

Exception Handling

A crucial point in the above algorithm is that there needs to be handling for when the stack is empty or the top element of the stack differs from the current number being explored. In such cases, output “Impossible” since sorting is not feasible.

Conclusion

The problem of creating an ascending sequence using a stack is very useful for understanding the fundamentals of stack structures. Through this algorithm, you can learn how to utilize the LIFO structure of stacks and techniques for manipulating numbers. To prepare for various types of problems that may appear in coding tests, practice with a variety of examples utilizing stacks.

Additional Practice Problems

  • Write a program that outputs the elements of the given sequence in reverse order.
  • Implement a stack algorithm with a set maximum size.
  • Use a stack to convert infix notation to postfix notation.