Javascript Coding Test Course, Creating an Ascending Sequence with Stack

Problem Description

This problem involves taking an array of given natural numbers and using a stack to create a sequence sorted in ascending order.
The array of natural numbers consists of integers between 1 and 1000, and each natural number is unique.
Additionally, the sequence must be constructed using only a stack while satisfying the following conditions:

  • Each natural number can be used only once.
  • The given natural numbers must be pushed onto the stack, and the numbers must be sorted in ascending order by popping from the stack.
  • During the sequence creation, the state of the stack must be output at intermediate steps.

Input Example

5
    3
    2
    4
    1

Output Example

1
    2
    3
    4
    5

Solution Process

To solve this problem, we need to utilize the LIFO (Last-In-First-Out) characteristic of the stack.
By using the fundamental operations of the stack, push and pop, we should be able to create a sequence sorted in ascending order from the given numbers.

Step 1: Problem Analysis

To solve the problem, we must first push the given natural numbers onto the stack and appropriately pop them to output the required sequence.
Specifically, we need to consider how to manipulate the stack to sequentially output the smallest number first.
In other words, while pushing numbers onto the stack, we should compare the top number of the stack with the number we need to output later and pop appropriately.

Step 2: Algorithm Design

The following algorithm describes the step-by-step process to output the given sequence in ascending order using a stack.

  1. Read the natural numbers sequentially.
  2. Add the read number to the stack.
  3. Check the current minimum value, and if the top number of the stack equals this minimum value, perform a pop operation and output it.
  4. Repeat the above process until all input numbers are processed.

Step 3: JavaScript Code Implementation

function createSortedSequence(arr) {
        // Initialize Stack
        const stack = [];
        const result = [];
        
        // Initialize the next number to be output
        let next = 1;
        
        // Iterate through the given array
        for (let i = 0; i < arr.length; i++) {
            // Push the current number onto the stack
            stack.push(arr[i]);

            // If the top number of the stack equals next, pop it
            while (stack.length > 0 && stack[stack.length - 1] === next) {
                result.push(stack.pop());
                next++;
            }
        }
        
        // Return the result
        return result;
    }
    
    const inputArray = [3, 2, 4, 1, 5];
    console.log(createSortedSequence(inputArray));

Step 4: Code Explanation

In the above code, the createSortedSequence function takes an array containing natural numbers as input.
It initializes a stack and uses a next variable to determine which number should be output.
Then, it pushes the given array of numbers onto the stack and compares the top number of the stack with next.
If they match, it pops the number and adds it to the result array. This process continues to obtain an array sorted in ascending order.

Step 5: Test Results

When the code is executed, the following result is produced. 


    [1, 2, 3, 4, 5]

Step 6: Conclusion

Through this problem, we gained a basic understanding of how to use stacks and learned how to utilize the properties of stacks to sort the given numbers.
Moreover, we were able to systematically carry out the entire process from problem interpretation to algorithm design, code implementation, and testing.
Solving such problems is not only useful for preparing for algorithm interviews but also in real applications.

Additional Learning Resources

To gain a deeper understanding of stack structures, we recommend referring to the following materials:

Frequently Asked Questions

Q: Is it possible to solve this problem without using a stack?
A: Since the problem requires the use of the properties of stacks, it cannot be solved without using a stack.

Q: Could there be performance issues if the input is a very large array?
A: This algorithm operates with O(n) time complexity, so it works efficiently. However, memory usage may increase depending on the size of the array.