Check if a queue can be sorted into another queue using a stack

Sorting a Queue using a Stack: Queue Transformation

Queues and stacks are essential data structures in computer science, each with its own set of functions and application scenarios. We frequently meet situations where we must change one data structure into another depending on particular criteria or needs. One such fascinating challenge includes utilizing a stack to sort the components of a queue into another queue.

Understanding the Methodology

Using a temporary stack, the idea is to sort elements from the input to the output queue. The goal is to rearrange the items so that the output queue is sorted in ascending order, using the stack as an intermediary step.

Example

Consider the input queue: [4, 2, 5, 1, 3].

We'll employ a stack to rearrange these elements into a sorted output queue.

Steps:

1. Input Queue: [4, 2, 5, 1, 3]

Stack: Initially empty
Output Queue: Initially empty

2. Algorithm Execution:

Processing Steps:
Iterating through the input queue:
Stack: 4 (Initially, as the stack is empty)
Comparing 2 with the top element of the stack (4). 2 is smaller, so it remains in the stack.
Stack: 4, 2
Comparing 5 with the top element of the stack (2). 5 is larger, so 2 moves to the output queue.
Stack: 4, Output Queue: 2
Similarly, 1 will move to the output queue.
Stack: 4, Output Queue: 2, 1
3 will also move to the output queue.
Stack: 4, Output Queue: 2, 1, 3

Finalization:

Stack: 4

Move the remaining element in the stack to the output queue.

Output Queue: 2, 1, 3, 4

Validation:

Check if the Output Queue ([2, 1, 3, 4]) is sorted.
Since [2, 1, 3, 4] is sorted in ascending order, the original queue [4, 2, 5, 1, 3] can be sorted into another queue using a stack.

Algorithm

Create two data structures:
- Input Queue
- Output Queue (initially empty)
- Stack (initially empty)
Iterate through the Input Queue:
- While the Input Queue is not empty:
- If the Stack is empty or the front element of the Input Queue is smaller than the top element of the Stack:
- Enqueue the front element of the Input Queue into the Output Queue.
- If the front element of the Input Queue is larger than the top element of the Stack:
- Push the top element of the Stack into the Output Queue and pop it from the Stack.
- Continue this until the Input Queue is empty.
Empty the Stack:
- While the Stack is not empty:
- Push the top element of the Stack into the Output Queue and pop it from the Stack.
Check if the Output Queue is sorted:
- Compare the Output Queue with a sorted version of itself.
- If the Output Queue matches the sorted version, return True (indicating it's possible to sort the Input Queue into the Output Queue using a stack). Otherwise, return False.

Pseudocode

FUNCTION check_sorted_queue(input_queue):
    output_queue = empty queue
    stack = empty stack
    WHILE input_queue is not empty, DO
        IF stack is empty OR front element of input_queue < top element of stack THEN
            Enqueue front element of input_queue into output_queue
        ELSE
            Push top element of stack into output_queue and pop it from stack
        END IF
    END WHILE
    WHILE stack is not empty DO
        Push top element of stack into output_queue and pop it from stack
    END WHILE
    RETURN is_sorted(output_queue)
FUNCTION is_sorted(queue):
    sorted_queue = sorted(queue)
    RETURN queue == sorted_queue

Implementation

def check_sorted_queue(queue):
    output_queue = []
    stack = []
    while queue:
        if not stack:
            stack.append(queue.pop(0))
        else:
            if queue[0] < stack[-1]:
                output_queue.append(queue.pop(0))
            else:
                output_queue.append(stack.pop())
    while stack:
        output_queue.append(stack.pop())
    return output_queue == sorted(output_queue)
input_queue = [4, 2, 5, 1, 3]
result = check_sorted_queue(input_queue)
if result:
    print("The queue can be sorted into another queue using a stack.")
else:
    print("The queue cannot be sorted into another queue using a stack.")

Output:

Check if a queue can be sorted into another queue using a stack

Explanation

Task: Check if a row of numbers can be arranged in ascending order using a stack.
Approach:
- Start with an empty row for the sorted numbers (output_queue) and an empty container (stack).
- Compare numbers in the row with those in the stack.
- Put smaller numbers in the output row; if a number in the row is larger or equal to the top number in the stack, put the top number in the output row.
- Empty the remaining numbers in the stack into the output row.
Check:
- Verify if the arranged row is in ascending order.
- If it is, the original row can be arranged using this method; otherwise, it can't be arranged this way.
Example:
- If given the row [4, 2, 5, 1, 3], this method can sort it into ascending order using a stack.