问题

You are an expert Python programmer, and here is your task: Write a function to find the similar elements from the given two tuple lists. Your code should pass these tests:

assert similar_elements((3, 4, 5, 6),(5, 7, 4, 10)) == (4, 5)
assert similar_elements((1, 2, 3, 4),(5, 4, 3, 7)) == (3, 4)
assert similar_elements((11, 12, 14, 13),(17, 15, 14, 13)) == (13, 14)

[BEGIN]
'def similar_elements(test_tup1, test_tup2):
res = tuple(set(test_tup1) & set(test_tup2))
return (res)'
[DONE]


You are an expert Python programmer, and here is your task: Write a python function to identify non-prime numbers. Your code should pass these tests:

assert is_not_prime(2) == False
assert is_not_prime(10) == True
assert is_not_prime(35) == True

[BEGIN]
'import math
def is_not_prime(n):
result = False
for i in range(2,int(math.sqrt(n)) + 1):
if n % i == 0:
result = True
return result'
[DONE]


You are an expert Python programmer, and here is your task: Write a function to find the largest integers from a given list of numbers using heap queue algorithm. Your code should pass these tests:

assert heap_queue_largest( [25, 35, 22, 85, 14, 65, 75, 22, 58],3)==[85, 75, 65]
assert heap_queue_largest( [25, 35, 22, 85, 14, 65, 75, 22, 58],2)==[85, 75]
assert heap_queue_largest( [25, 35, 22, 85, 14, 65, 75, 22, 58],5)==[85, 75, 65, 58, 35]

[BEGIN]
'import heapq as hq
def heap_queue_largest(nums,n):
largest_nums = hq.nlargest(n, nums)
return largest_nums'
[DONE]


You are an expert Python programmer, and here is your task: Write a python function to find the sum of squares of first n even natural numbers. Your code should pass these tests:

assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120

[BEGIN]

答案

模型 模型答案 测试结果
金声玉亮2.0 ```python
def square_Sum(n):
return sum(i**2 for i in range(2, 2*n+1, 2))
```
[DONE]		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
deepseekr1

To solve this problem, we need to calculate the sum of the squares of the first n even natural numbers. An even natural number can be represented as 2k where k is a natural number starting from 1. The task involves squaring each of these numbers and summing them up efficiently.

### Approach
The approach to solve this problem leverages a mathematical formula to compute the result directly, which is both efficient and concise. The key steps are as follows:

1. **Identify the sequence**: The first n even natural numbers are 2, 4, 6, ..., 2n.
2. **Square each term**: Each term in the sequence is squared, resulting in (2k)² for k from 1 to n.
3. **Sum the squares**: The sum of these squared terms can be derived using a mathematical formula. The sum of the squares of the first n even natural numbers is given by the formula: \( \text{Sum} = \frac{2n(n + 1)(2n + 1)}{3} \).

This formula is derived from the sum of squares formula for the first n natural numbers, adjusted for the even terms. Using this formula allows us to compute the result in constant time, O(1), which is highly efficient.

### Solution Code

```python
def square_Sum(n):
return (2 * n * (n + 1) * (2 * n + 1)) // 3
```

### Explanation
- **Mathematical Derivation**: The sum of the squares of the first n even natural numbers can be expressed as \( \sum_{k=1}^{n} (2k)^2 \). This simplifies to \( 4 \sum_{k=1}^{n} k^2 \). Using the known formula for the sum of squares of the first n natural numbers, \( \sum_{k=1}^{n} k^2 = \frac{n(n + 1)(2n + 1)}{6} \), we substitute and multiply by 4 to get the final formula.
- **Efficiency**: By using the derived formula, the solution computes the result in constant time, making it extremely efficient even for very large values of n.

This approach ensures that we avoid the need for iterative loops, thus optimizing both time and space complexity.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
gpto1 ```python
def square_Sum(n):
return (2 * n * (n + 1) * (2 * n + 1)) // 3
```		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
GPT-4o Sure, here is the implementation of the function to find the sum of squares of the first `n` even natural numbers:

```python
def square_Sum(n):
sum_of_squares = sum((2 * i) ** 2 for i in range(1, n + 1))
return sum_of_squares

# Testing the function
assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
```

Explanation:
- The even natural numbers are in the form `2 * i` where `i` is an integer starting from 1.
- We square each even number `(2 * i) ** 2` and sum them up using a generator expression within the `sum()` function.
- Finally, the function returns the sum of these squares.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
llama3.1-70B-Instruct

def square_Sum(n):
return sum([i**2 for i in range(2, 2*n+1, 2)])		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
llama3.1-405B-Instruct

def square_Sum(n):
return sum([i**2 for i in range(2, 2*n+1, 2)])		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
DeepSeek-Coder-V2 ```python
def square_Sum(n):
return sum(i**2 for i in range(2, 2*n+1, 2))
```
[DONE]		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
Qwen2-72B-Instruct 'def square_Sum(n):
sum = 0
for i in range(1, n+1):
even = 2 * i
sum += even**2
return sum'
[DONE]		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
baichuan4 Here's the Python function to find the sum of squares of the first n even natural numbers:

```python
def square_Sum(n):
return sum([i**2 for i in range(2, 2*n + 1, 2)])
```

This function works by generating a list of the first n even natural numbers using a list comprehension with a range() function that starts at 2 (the first even natural number), increments by 2 (to ensure only even numbers are generated), and goes up to but not including 2*n + 1 (to get n even numbers). Each number in this list is then squared using the `**` operator, and finally, the sum() function is used to add up all the squared values.

Let's run the tests you provided:

```python
assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
```

All tests should pass successfully with this implementation.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
doubao 'def square_Sum(n):
sum = 0
for i in range(2, 2*n+1, 2):
sum += i**2
return sum'
[DONE]		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
minimax ```python
def square_Sum(n):
return sum((2*i)**2 for i in range(1, n+1))

# Test cases
assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
```

This function calculates the sum of squares of the first `n` even natural numbers by using a generator expression within the `sum()` function. The generator expression `(2*i)**2 for i in range(1, n+1)` generates the squares of the first `n` even numbers (2, 4, 6, ...), and `sum()` adds them up.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
kimi Here's the code for each task:

1. Function to find similar elements in two tuple lists:

```python
def similar_elements(test_tup1, test_tup2):
res = tuple(sorted(set(test_tup1) & set(test_tup2)))
return res
```

2. Function to identify non-prime numbers:

```python
import math

def is_not_prime(n):
if n <= 1:
return True
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return True
return False
```

3. Function to find the largest integers from a given list of numbers using heap queue algorithm:

```python
import heapq

def heap_queue_largest(nums, n):
largest_nums = heapq.nlargest(n, nums)
return largest_nums
```

4. Function to find the sum of squares of first n even natural numbers:

```python
def square_Sum(n):
return sum([i**2 for i in range(2, 2*n+1, 2)])
```

Each function is designed to pass the provided test cases.		 failed
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
wenxinyiyan 'def square_Sum(n):
sum_of_squares = 0
for i in range(1, n+1):
even_num = 2 * i
sum_of_squares += even_num ** 2
return sum_of_squares'
[DONE]

Explanation:
The function `square_Sum` takes an integer `n` as input and calculates the sum of squares of the first `n` even natural numbers. It initializes a variable `sum_of_squares` to 0, which will store the running sum of squares. Then, it iterates from 1 to `n` (inclusive) using a `for` loop. In each iteration, it calculates the current even number by multiplying `i` by 2 (`even_num = 2 * i`). It then squares this even number (`even_num ** 2`) and adds it to the `sum_of_squares`. Finally, it returns the `sum_of_squares` as the result.

Note: The indentation in the provided code snippet is incorrect. I have fixed the indentation in my explanation above.

Now, let's test the function with the given assertions:


```python
assert square_Sum(2) == 20 # 2^2 + 4^2 = 4 + 16 = 20
assert square_Sum(3) == 56 # 2^2 + 4^2 + 6^2 = 4 + 16 + 36 = 56
assert square_Sum(4) == 120 # 2^2 + 4^2 + 6^2 + 8^2 = 4 + 16 + 36 + 64 = 120
```
All assertions should pass, indicating that the function works correctly.		 failed
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
zhipu To solve this task, we need to understand that the first \( n \) even natural numbers are \( 2, 4, 6, \ldots, 2n \). The square of the \( i \)-th even number is \( (2i)^2 = 4i^2 \). Therefore, the sum of squares of the first \( n \) even natural numbers can be calculated as:

\[ \text{Sum} = 4(1^2 + 2^2 + 3^2 + \ldots + n^2) \]

The sum of squares of the first \( n \) natural numbers is given by the formula:

\[ \text{Sum of squares} = \frac{n(n + 1)(2n + 1)}{6} \]

Using this formula, we can derive the sum of squares of the first \( n \) even natural numbers:

\[ \text{Sum of squares of even numbers} = 4 \times \frac{n(n + 1)(2n + 1)}{6} \]

Let's implement this in a function:

```python
def square_Sum(n):
return 4 * (n * (n + 1) * (2 * n + 1)) // 6

# Test cases
assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120

print("All tests passed!")
```

This function calculates the sum of squares of the first \( n \) even natural numbers using the derived formula and checks against the provided test cases. If all tests pass, it prints "All tests passed!".

You can run this code to verify that it meets the requirements.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
gpto1 ```python
def square_Sum(n):
return (2 * n * (n + 1) * (2 * n + 1)) // 3
```		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
deepseekv3 To solve the problem of finding the sum of squares of the first `n` even natural numbers, we can follow these steps:

1. **Identify the first `n` even natural numbers**: These are 2, 4, 6, ..., 2n.
2. **Square each of these numbers**: This gives us 4, 16, 36, ..., (2n)^2.
3. **Sum the squared numbers**: Calculate the sum of these squared numbers.

Here's the Python function to achieve this:

```python
def square_Sum(n):
return sum((2 * i) ** 2 for i in range(1, n + 1))

# Test cases
assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120
```

### Explanation:
- **Range**: `range(1, n + 1)` generates numbers from 1 to `n`.
- **Even Numbers**: `2 * i` generates the `i`-th even number.
- **Squaring**: `(2 * i) ** 2` squares the `i`-th even number.
- **Summing**: `sum(...)` adds up all the squared numbers.

### Example Walkthrough:
- For `n = 2`:
- Even numbers: 2, 4
- Squares: 4, 16
- Sum: 4 + 16 = 20
- For `n = 3`:
- Even numbers: 2, 4, 6
- Squares: 4, 16, 36
- Sum: 4 + 16 + 36 = 56
- For `n = 4`:
- Even numbers: 2, 4, 6, 8
- Squares: 4, 16, 36, 64
- Sum: 4 + 16 + 36 + 64 = 120

This function correctly calculates the sum of squares of the first `n` even natural numbers.		 pass
测试用例：assert square_Sum(2) == 20
assert square_Sum(3) == 56
assert square_Sum(4) == 120