Python Coding Test Course, Creating an Ascending Sequence with a Stack

Problem Description

Given an integer N, create a sequence of numbers sorted in ascending order from 1 to N using a stack. You are allowed to perform the following operations:

• Push the numbers from 1 to N onto the stack in order.
• Pop the value on the top of the stack and print it.

You will receive two numbers as input:

• Integer N (1 <= N <= 100,000)
• Integer K (1 <= K <= N)

The output should be K numbers printed in ascending order. You can use the stack, and you must appropriately push and pop the given input numbers from the stack. Your goal is to generate a sequence in ascending order using the stack operations.

Problem Approach

This problem utilizes the Last-In-First-Out (LIFO) characteristic of stacks to output the given numbers in ascending order. First, you should push the numbers from 1 to N onto the stack, then pop the required numbers in order to output them. There are several important points to consider in this process:

• The numbers that can be pushed to the stack are from 1 to N.
• When popping from the stack, you must always pop from the topmost number.
• The final output numbers must be sorted in ascending order.

Algorithm Implementation

Now, let’s implement the algorithm based on the problem approach. The basic logic of the algorithm is as follows:

1. Push the numbers up to N onto the stack in order.
2. Pop the top number from the stack and output the desired K numbers.

Below is the code implemented in Python:

def create_sorted_sequence(N, K):
    stack = []
    result = []
    num = 1
    
    for i in range(N):
        while num <= N:
            stack.append(num)
            num += 1
        
        if stack:  # If the stack is not empty
            result.append(stack.pop())
        
        if len(result) == K:  # Stop when K numbers have been output
            break
            
    return result

# Example input
N = 5
K = 3
output = create_sorted_sequence(N, K)
print("Ascending sequence:", output)

            

The function create_sorted_sequence(N, K) takes N and K as inputs and generates a sequence of K numbers in ascending order. It stores the numbers using the stack and pops them to add to the result array as needed.

Code Explanation

Let’s explain each part of the code in detail:

1. Initializing the stack and result array:

   stack = [] and result = [] are used to initialize an empty stack and result array.

2. Number Push Logic:

   The condition while num <= N: is used to push numbers from 1 to N onto the stack. The num variable determines the next number to be pushed.

3. Number Pop Logic:

   The if stack: is used to pop the top number from the stack and add it to the result array if the stack is not empty.

4. K Output Condition:

   The condition if len(result) == K: checks if the number of output amounts has reached K, and if so, the loop is exited.

Time Complexity

The time complexity of this algorithm is as follows:

• Process of pushing numbers onto the stack: O(N)
• Process of popping K numbers from the stack: O(K)

Thus, the overall time complexity is O(N + K). This is an efficient approach and performs quickly enough.

Conclusion

The problem of sorting numbers in ascending order using a stack requires a creative and systematic approach. Through this lecture, you learned the basic principles of stacks and how to solve problems using them. I hope you continue to improve your skills by tackling various algorithm problems.