System: You are a helpful and precise assistant in checking the quality of the answer.
User: We would like to request your feedback on the performance of the response of the assistant to the user instruction displayed below. In the feedback, I want you to rate the quality of the response in these 3 categories according to each scoring rubric:

Logical Efficiency: Is the response logically efficient? The logic behind the response should have no redundant step, remaining simple and efficient. For tasks involving coding, the proposed solution should also consider time complexity.
Score 1: The logic behind the response is significantly inefficient and redundant, necessitating a complete reorganization of logic for clarity and efficiency.
Score 2: The logic of the response lacks efficiency and conciseness, requiring a substantial reorganization for better optimization.
Score 3: The logic of the response is not efficient enough, necessitating major edits for improved optimization.
Score 4: The logic of the response is largely efficient, but it still has some redundant steps. It could be handled from minor edits for better optimization.
Score 5: The logic of the response is optimally efficient, requiring no further optimization.
Logical Robustness: Does the model ensure general applicability and avoid logical contradictions in its reasoning steps for an instruction that requires step-by-step logical process? This includes the consideration of edge cases for coding and mathematical problems, and the absence of any counterexamples.
Score 1: The logic of the model's response is completely incoherent.
Score 2: The model's response contains major logical inconsistencies or errors.
Score 3: The model's response contains some logical inconsistencies or errors, but they are not significant.
Score 4: The model's response is logically sound, but it does not consider some edge cases.
Score 5: The model's response is logically flawless and it takes into account all potential edge cases.
Comprehension: Does the response fulfill the requirements of the instruction by providing relevant information especially when the instruction is complex and includes multiple requirements? This includes responding in accordance with the explicit and implicit purpose of given instruction.
Score 1: The response is completely unrelated to the instruction, or the model entirely misunderstands the instruction.
Score 2: Most of the key points in the response are irrelevant to the instruction, and the response misses major requirements of the instruction.
Score 3: Some major points in the response contain irrelevant information or miss some requirements of the instruction.
Score 4: The response is relevant to the instruction but misses minor requirements of the instruction.
Score 5: The response is perfectly relevant to the instruction, and the model fulfills all of the requirements of the instruction.
[Instruction]
Given an array of integers nums, sort the array in ascending order and return it.

You must solve the problem without using any built-in functions in O(nlog(n)) time complexity and with the smallest space complexity possible.

 

Example 1:

Input: nums = [5,2,3,1]
Output: [1,2,3,5]
Explanation: After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).

[Ground truth Answer]
To achieve this task, you can implement a merge sort algorithm, which has an O(nlog(n)) time complexity.

Here's an example of Merge Sort in Python:

```python
def merge_sort(arr):
    if len(arr) > 1:
        mid = len(arr) // 2
        left = arr[:mid]
        right = arr[mid:]

        merge_sort(left)
        merge_sort(right)

        i = j = k = 0

        while i < len(left) and j < len(right):
            if left[i] < right[j]:
                arr[k] = left[i]
                i += 1
            else:
                arr[k] = right[j]
                j += 1
            k += 1

        while i < len(left):
            arr[k] = left[i]
            i += 1
            k += 1

        while j < len(right):
            arr[k] = right[j]
            j += 1
            k += 1

    return arr

# Example usage:
nums = [5, 2, 3, 1]
sorted_nums = merge_sort(nums)
print(sorted_nums)
```

Output:
```[1, 2, 3, 5]```

[Assistant's Response]
¡Hola! Para resolver el problema de ordenar un array de enteros sin usar funciones integradas y cumpliendo con la complejidad de tiempo O(n log n), una buena opción es implementar el algoritmo de **Quicksort**. Este algoritmo es eficiente y tiene un buen rendimiento en la mayoría de los casos.

Aquí te dejo una implementación básica de Quicksort en Python:

```python
def quicksort(nums):
    if len(nums) <= 1:
        return nums
    pivot = nums[len(nums) // 2]
    left = [x for x in nums if x < pivot]
    middle = [x for x in nums if x == pivot]
    right = [x for x in nums if x > pivot]
    return quicksort(left) + middle + quicksort(right)

# Ejemplo de uso
nums = [5, 2, 3, 1]
sorted_nums = quicksort(nums)
print(sorted_nums)  # Salida: [1, 2, 3, 5]
```

### Explicación:
1. **Elección del pivote**: Se elige un elemento del array como pivote (en este caso, el del medio).
2. **División**: Se crean tres listas: una para los elementos menores que el pivote, otra para los que son iguales y otra para los mayores.
3. **Recursión**: Se aplica el mismo proceso a las listas de elementos menores y mayores.
4. **Combinación**: Finalmente, se combinan las listas para obtener el array ordenado.

### Complejidad:
- **Tiempo**: O(n log n) en promedio.
- **Espacio**: Aunque esta implementación utiliza espacio adicional para las listas, se puede optimizar para usar menos espacio modificando el array en su lugar.

Si necesitas una versión que modifique el array original y use menos espacio, podemos implementar una variante de Quicksort que lo haga in-place. ¡Déjame saber si te gustaría eso!

[The End of Assistant's Response]

Please give feedback on the assistant's responses. Also, provide the assistant with a score on a scale of 1 to 5 for each category, where a higher score indicates better overall performance. Make sure to give feedback or comments for each category first and then write the score for each category. Only write the feedback corresponding to the scoring rubric for each category. The scores of each category should be orthogonal, indicating that 'Efficiency of User Alignment' should not be considered for 'Readability of User Alignment' category, for example. 

Lastly, return a Python dictionary object that has skillset names as keys and the corresponding scores as values.

[System]



Assistant: