| 模型 | 模型答案 | 测试结果 |
|---|---|---|
| 金声玉亮2.0 | ```python def binomial_Coeff(n, k): # Base Cases if k > n: return 0 if k == 0 or k == n: return 1 # Recursive calculation return binomial_Coeff(n-1, k-1) + binomial_Coeff(n-1, k) ``` [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| deepseekr1 | [BEGIN] def binomial_Coeff(n, k): if k < 0 or k > n: return 0 if k == 0 or k == n: return 1 result = 1 for i in range(k): result = result * (n - i) // (i + 1) return result [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| gpto1 | [BEGIN] 'def binomial_Coeff(n, k): if k < 0 or k > n: return 0 c = 1 for i in range(1, k+1): c = c * (n - i + 1) // i return c' [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| GPT-4o | Sure, to find the binomial coefficient, we can use the formula: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] Where \( C(n, k) \) is the binomial coefficient, \( n! \) is the factorial of \( n \), and \( k! \) is the factorial of \( k \). Here is the Python function to compute the binomial coefficient: ```python import math def binomial_Coeff(n, k): return math.comb(n, k) # Tests assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 ``` The `math.comb` function, available from Python 3.8 onward, calculates the binomial coefficient directly and efficiently. If you're using a version of Python prior to 3.8, you can implement it manually as shown below: ```python def binomial_Coeff(n, k): return math.factorial(n) // (math.factorial(k) * math.factorial(n - k)) # Tests assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 ``` Both approaches will yield the correct results for the given test cases. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| llama3.1-70B-Instruct | import math def binomial_Coeff(n, r): return math.comb(n, r) |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| llama3.1-405B-Instruct | import math def binomial_Coeff(n, k): return math.comb(n, k) |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| DeepSeek-Coder-V2 | ```python def binomial_Coeff(n, k): # Base Cases if k > n: return 0 if k == 0 or k == n: return 1 # Recursive calculation return binomial_Coeff(n-1, k-1) + binomial_Coeff(n-1, k) ``` [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| Qwen2-72B-Instruct | 'def binomial_Coeff(n, k): if k > n - k: k = n - k res = 1 for i in range(k): res *= (n - i) res //= (i + 1) return res' [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| baichuan4 | To find the binomial coefficient, you can use the formula C(n, k) = n! / (k! * (n - k)!), where "!" denotes the factorial operation. Here's the Python function that implements this formula: ```python def binomial_Coeff(n, k): if k > n - k: # Take advantage of symmetry: C(n, k) == C(n, n-k) k = n - k result = 1 for i in range(k): result *= (n - i) result //= (i + 1) # Use integer division to keep the result as an integer return result ``` This function first checks if `k` is greater than `n - k` to potentially reduce the computation by calculating the coefficient for the smaller value of `k`. Then, it iteratively computes the binomial coefficient using the formula. Let's test the function with the provided assertions: ```python assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` If the function is correct, these assertions should pass without any errors. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| doubao | 'from math import factorial def binomial_Coeff(n, k): return factorial(n) // (factorial(k) * factorial(n - k))' [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| minimax | ```python def binomial_Coeff(n, k): if k > n: return 0 if k == 0 or k == n: return 1 k = min(k, n - k) # Take advantage of symmetry result = 1 for i in range(k): result = result * (n - i) result = result // (i + 1) return result # Test cases assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` This function calculates the binomial coefficient using a simple iterative approach, which is efficient for small values of `n` and `k`. The test cases should pass with this implementation. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| kimi | Certainly! Let's start with the first task: ```python def similar_elements(test_tup1, test_tup2): # Using set intersection to find common elements res = tuple(sorted(set(test_tup1) & set(test_tup2))) return res # Test cases 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) ``` Next, for the function to identify non-prime numbers: ```python import math def is_not_prime(n): if n <= 1: return True # 0 and 1 are not prime numbers for i in range(2, int(math.sqrt(n)) + 1): if n % i == 0: return True return False # Test cases assert is_not_prime(2) == False assert is_not_prime(10) == True assert is_not_prime(35) == True ``` Now, for the function to find the largest integers using the heap queue algorithm: ```python import heapq def heap_queue_largest(nums, n): # Using nlargest from heapq to find the n largest numbers largest_nums = heapq.nlargest(n, nums) return largest_nums # Test cases 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] ``` Lastly, for the function to find the binomial coefficient: ```python def binomial_Coeff(n, k): if k > n: return 0 if k == 0 or k == n: return 1 if k > n - k: k = n - k coeff = 1 for i in range(k): coeff *= n - i coeff //= i + 1 return coeff # Test cases assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` These functions should pass the tests provided. |
failed 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| wenxinyiyan | 'def binomial_Coeff(n, k): from math import factorial ```bash if k > n: return 0 elif k > n - k: k = n - k numer = factorial(n) denom = factorial(k) * factorial(n - k) return numer // denom' ``` [DONE] Note: The provided code snippet for calculating the binomial coefficient has been indented and modified slightly to fit within the function definition. However, it's important to note that using factorial to compute the binomial coefficient can lead to numerical overflow for large values of `n` and `k`. In practice, more efficient and numerically stable algorithms, such as Pascal's Triangle or dynamic programming approaches, are often used. For the tests provided, the factorial-based approach should suffice. But keep in mind its limitations for larger inputs. Here's the corrected and formatted version of the `binomial_Coeff` function: ```python def binomial_Coeff(n, k): from math import factorial if k > n: return 0 elif k > n - k: k = n - k numer = factorial(n) denom = factorial(k) * factorial(n - k) return numer // denom ``` And here are the tests to verify the function: ```python assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` These tests should pass with the provided function implementation. However, remember to consider more efficient algorithms for larger inputs to avoid numerical issues. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| zhipu | To find the binomial coefficient, we can use the formula for combinations, which is: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] where \( n! \) denotes the factorial of \( n \). Here's a Python function to compute the binomial coefficient: ```python def factorial(n): if n == 0 or n == 1: return 1 return n * factorial(n - 1) def binomial_Coeff(n, k): return factorial(n) // (factorial(k) * factorial(n - k)) # Test cases assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` This function defines a helper function `factorial` to compute the factorial of a number, and then uses it to compute the binomial coefficient according to the formula. Let's put it all together in a single code block: ```python def factorial(n): if n == 0 or n == 1: return 1 return n * factorial(n - 1) def binomial_Coeff(n, k): return factorial(n) // (factorial(k) * factorial(n - k)) # Test cases assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` This code should pass the given tests. The use of the `//` operator ensures that the result is an integer. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| gpto1 | [BEGIN] 'def binomial_Coeff(n, k): if k < 0 or k > n: return 0 c = 1 for i in range(1, k+1): c = c * (n - i + 1) // i return c' [DONE] |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |
| deepseekv3 | To find the binomial coefficient, often denoted as \( C(n, k) \) or \( \binom{n}{k} \), we can use the formula: \[ C(n, k) = \frac{n!}{k! \cdot (n - k)!} \] Here, \( n! \) denotes the factorial of \( n \), which is the product of all positive integers up to \( n \). We can implement this in Python using the `math` module, which provides a `factorial` function. Here's the function to compute the binomial coefficient: ```python import math def binomial_Coeff(n, k): return math.factorial(n) // (math.factorial(k) * math.factorial(n - k)) # Test cases assert binomial_Coeff(5, 2) == 10 assert binomial_Coeff(4, 3) == 4 assert binomial_Coeff(3, 2) == 3 ``` ### Explanation: 1. **Factorial Calculation**: The `math.factorial(n)` function calculates the factorial of `n`. 2. **Binomial Coefficient Calculation**: The binomial coefficient is computed using the formula \( \frac{n!}{k! \cdot (n - k)!} \). 3. **Integer Division**: The `//` operator is used to ensure the result is an integer. This function will correctly compute the binomial coefficient and pass the provided test cases. |
pass 测试用例：assert binomial_Coeff(5,2) == 10 assert binomial_Coeff(4,3) == 4 assert binomial_Coeff(3,2) == 3 |