How to Implement Quicksort Iteratively Without Recursion or Stack

How can I implement the quicksort algorithm without using recursion or a stack?

def iterative_quicksort(arr):
    size = len(arr)
    # Create an auxiliary stack to hold indices
    stack = [0] * size
    top = -1

    # Push the initial values onto the stack
    stack[top + 1] = 0
    stack[top + 2] = size - 1
    top += 2

    # Main loop
    while top >= 0:
        # Pop the top values
        end = stack[top]
        top -= 1
        start = stack[top]
        top -= 1

        # Perform partitioning
        pivot = arr[end]
        p_index = partition(arr, start, end, pivot)
        if p_index - 1 > start:
            stack[top + 1] = start
            stack[top + 2] = p_index - 1
            top += 2
        if p_index + 1 < end:
            stack[top + 1] = p_index + 1
            stack[top + 2] = end
            top += 2

    return arr

Implementing the quicksort algorithm without recursion or a stack can seem challenging, but it can be effectively done through an iterative approach using a fixed-size auxiliary array for managing sub-array indices. This method eliminates the need for function call overhead associated with recursion and achieves efficient sorting of an array.

def partition(arr, low, high, pivot):
    i = low - 1
    for j in range(low, high):
        if arr[j] <= pivot:
            i += 1
            arr[i], arr[j] = arr[j], arr[i]
    arr[i + 1], arr[high] = arr[high], arr[i + 1]
    return i + 1

# Example usage
arr = [10, 7, 8, 9, 1, 5]
iterative_quicksort(arr)
print(arr)

Causes

• Standard quicksort implementations utilize recursion to manage sub-array sorting and pivot placement.
• Recursive methods can lead to stack overflow for large arrays due to deep recursion levels.

Solutions

• Having an auxiliary stack in the form of a fixed-size array to store the starting and ending indexes of the sub-arrays that need sorting.
• Using a loop structure to process the stack, which allows the algorithm to manage the necessary sorting without requiring additional function calls.

Mistake: Forgetting to define a base case for the while loop, which could potentially lead to an infinite loop.

Solution: Ensure that your while loop has a proper termination condition based on the state of the stack.

Mistake: Not managing the stack correctly which can lead to missing elements for sorting.

Solution: Always keep track of the top of the stack accurately after every push/pop operation.