Over Thinking Push Swap - kevshouse/The-Under_C_World GitHub Wiki

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Hi BB, I thinking about a puzzle in which one needs to sort an array of numbers using two stacks, A, and B. I can push, pop or rotate both arrays and swap the top of each between them. I am wondering if I used a circular array as part of my sorting a sorting machine.

BLACKBOXAI

Okay, I need to help the user understand how to sort an array using two stacks (A and B) with operations like push, pop, rotate, and swap. They also mentioned using a circular array as part of a sorting machine. Let me look through the search results to find relevant information.

The search results are all from the same Medium article about the Push_Swap algorithm. It describes using two stacks and a third helper stack (C) to determine the sorted positions. The key steps involve duplicating stack A into an array, sorting it with quicksort to get target indices, then using those indices to efficiently move elements between stacks A and B. The algorithm focuses on minimizing moves by calculating the least number of operations needed for each element.

The user is interested in using a circular array. The article mentions a circular doubly linked list for stack implementation. Maybe the circular array refers to this structure, allowing rotations (ra/rra) which are efficient in circular buffers. The core idea is to determine each element's target position using a sorted array (stack C), then move elements from B back to A optimally by considering rotation costs.

I should outline the steps: duplicate stack A into an array, sort it, assign indices, push elements to B, then calculate moves based on rotations needed to position each element correctly in A. Also, mention optimizations like combining rotations (rr/rrr) and handling the minimum element's position. The circular nature allows efficient rotations, which is crucial for minimizing move counts.

1. Core Concept: Target Positions via a Sorted Array

   Duplicate Stack A: Create a copy of the original stack A into an array (referred to as "stack C" in the search results). This array is
   sorted using an algorithm like quicksort to determine the target positions of each element. Assign Indices: Each element in stack A is assigned an index representing its position in the sorted array. This allows tracking where each element should end up in the final sorted stack.

2. Sorting Strategy

   Push to Stack B: Move all elements from stack A to stack B except for a pre-identified longest sorted subsequence (to minimize later adjustments). Calculate Optimal Moves: For each element in stack B, compute the number of rotations (ra, rb, rra, rrb) required to place it in the correct position in stack A. Prioritize elements that require the fewest total moves. Combine Rotations: Use rr (rotate both stacks) or rrr (reverse rotate both stacks) when possible to reduce the total number of operations.

3. Circular Array/Rotations

   Efficient Rotations: The circular nature of the stacks (implemented via circular doubly linked lists) allows efficient rotations. For example: ra (rotate A) moves the first element to the end. rra (reverse rotate A) moves the last element to the front. Handling Edge Cases: After sorting, ensure the smallest element is at the top of stack A by rotating (ra or rra) based on its position.

4. Key Optimizations Pre-Sorted Subsequence: Identify the longest subsequence of already sorted elements in stack A and retain them to minimize unnecessary moves. Move Calculation: For each element in stack B, compute: sa/sb: Swap costs. ra/rb vs. rra/rrb: Choose the rotation direction (forward or backward) with fewer steps. Tester Validation: Use a tester script to verify the algorithm’s efficiency (e.g., ensuring ≤12 moves for 5 elements and ≤700 moves for 100 elements).

Duplicating Stack A (to create the sorted reference array):

int *stack_dup(t_node *stack) {
    int *array = malloc(sizeof(int) * stack_size(stack));
    t_node *node = stack;
    int i = 0;
    while (node->next != stack) {
        array[i++] = node->nb;
        node = node->next;
    }
    array[i] = node->nb;
    return array;
}

void quicksort(int *array, int start, int end) {
    if (start < end) {
        int pivot_index = partition(array, start, end);
        quicksort(array, start, pivot_index - 1);
        quicksort(array, pivot_index + 1, end);
    }
}

Final Steps

• Push Back to Stack A: Select elements from stack B that require the least moves, considering combined rotations.
• Adjust Stack A: Rotate stack A to position the smallest element at the top if necessary. This method ensures minimal operations by leveraging pre-sorting, circular rotations, and strategic move combinations.