Orig Description
How many ways?
Write a program that calculates the number of combinations of three different integers that satisfy the following conditions:
You must choose three different integers from 1 to n.
The sum of the three integers is x.
For example, if n = 5 and x = 9, there are two combinations:
1 + 3 + 5 = 9
2 + 3 + 4 = 9
Input
The input consists of multiple datasets. For each dataset, two integers n and x are given on one line.
The input is terminated by two zeros (n and x). Do not process the program for these end symbols.
Constraints
3 ≤ n ≤ 100
0 ≤ x ≤ 300
Output
For each dataset, output the number of combinations on one line.
Sample Input
5 9
0 0
Sample Output
2
Note
Commentary
Extracted Specification
An integer n (3 ≤ n ≤ 100), representing some quantity or size.
An integer x (0 ≤ x ≤ 300), representing some value.
### Example Input:
```
5 9
0 0
```
### Function Signature:
Write a function f(inputs) that takes in the input as a list of tuples.
def f(inputs: List[Tuple[int, int]]):
'''
inputs: a list of tuples, where each tuple contains two integers
'''
Test Case Generator
Certainly! Based on the problem statement for "How many ways?", I will create a test case generator that produces multiple datasets and terminates with the end symbols (0, 0). The function will ensure that each dataset adheres to the constraints provided.
Here's the test case generator:
```python
import random
def generate_test_cases(num_cases):
test_cases = []
for _ in range(num_cases):
n = random.randint(3, 100)
x = random.randint(0, 300)
# Ensure we are not generating the terminating case until the end
if (n, x) != (0, 0):
test_cases.append((n, x))
# Adding the terminating case (0, 0)
test_cases.append((0, 0))
return test_cases
# Example usage:
num_cases = 5 # Number of non-terminating test cases to generate
test_cases = generate_test_cases(num_cases)
for tc in test_cases:
print(f"{tc[0]} {tc[1]}")
```
This function `generate_test_cases` takes an argument `num_cases` to specify the number of non-terminating test cases to generate. It generates random values for `n` and `x` within the specified constraints, ensuring that the terminating case `(0, 0)` is only added once at the end. Each test case is printed in the format expected by the problem.
Sample output might look like this:
```
45 127
10 28
100 250
3 5
78 195
0 0
```
You can adjust the `num_cases` variable to generate more or fewer test cases as needed.
Extract Arguments
def extract_arguments(fh):
inputs = []
while True:
line = fh.readline().strip()
n, x = map(int, line.split())
if n == 0 and x == 0:
break
inputs.append((n, x))
return inputs