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 another quantity.
### Example Input:
```
5 9
0 0
```
### Function Signature:
Write a function `f(inputs)` that takes in the input.
```python
def f(inputs: List[Tuple[int, int]]):
'''
inputs: a list of tuples where each tuple contains two integers
'''
```
Test Case Generator
Sure, here is the test case generator for the given problem statement "How many ways?":
```python
import random
def tcgen():
# Generate n within the range [3, 100]
n = random.randint(3, 100)
# Generate x within the range [0, 300]
x = random.randint(0, 300)
return n, x
# Example usage:
# Generate a random test case
n, x = tcgen()
print(n, x)
```
This function generates random values for `n` and `x` within the specified constraints. You can use this function to create multiple test cases for your problem. Here's how it works:
- `n` is generated as a random integer between 3 and 100 (inclusive).
- `x` is generated as a random integer between 0 and 300 (inclusive).
This will give you varied test cases that you can use to ensure your solution handles different inputs correctly.
Additionally, here is a small script to generate multiple test cases and append the end symbols (0, 0):
```python
def generate_multiple_test_cases(num_cases):
test_cases = []
for _ in range(num_cases):
test_cases.append(tcgen())
test_cases.append((0, 0)) # Append the end symbols
return test_cases
# Example usage:
# Generate 5 random test cases
test_cases = generate_multiple_test_cases(5)
for n, x in test_cases:
print(n, x)
```
This function `generate_multiple_test_cases` creates a specified number of test cases and appends the terminating `0 0` at the end, ensuring you can test the program with multiple datasets consecutively.
Extract Arguments
def extract_arguments(fh):
inputs = []
while True:
n, x = map(int, fh.readline().strip().split())
if n == 0 and x == 0:
break
inputs.append((n, x))
return inputs
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# inputs = extract_arguments(fh)
# f(inputs)