Orig Description
Tax Rate Changed
VAT (value-added tax) is a tax imposed at a certain rate proportional to the sale price.
Our store uses the following rules to calculate the after-tax prices.
When the VAT rate is x%,
for an item with the before-tax price of p yen,
its after-tax price of the item is p (100+x) / 100 yen, fractions rounded off.
The total after-tax price of multiple items paid at once is
the sum of after-tax prices of the items.
The VAT rate is changed quite often.
Our accountant has become aware that
"different pairs of items that had the same total after-tax price
may have different total after-tax prices after VAT rate changes."
For example, when the VAT rate rises from 5% to 8%,
a pair of items that had the total after-tax prices of 105 yen before
can now have after-tax prices either of 107, 108, or 109 yen, as shown in the table below.
Before-tax prices of two itemsAfter-tax price with 5% VATAfter-tax price with 8% VAT
20, 8021 + 84 = 10521 + 86 = 107
2, 992 + 103 = 1052 + 106 = 108
13, 8813 + 92 = 10514 + 95 = 109
Our accountant is examining effects of VAT-rate changes on after-tax prices.
You are asked to write a program that calculates the possible maximum
total after-tax price of two items with the new VAT rate,
knowing their total after-tax price before the VAT rate change.
Input
The input consists of multiple datasets.
Each dataset is in one line,
which consists of three integers x, y, and s separated by a space.
x is the VAT rate in percent before the VAT-rate change,
y is the VAT rate in percent after the VAT-rate change,
and s is the sum of after-tax prices of two items before the VAT-rate change.
For these integers, 0 < x < 100, 0 < y < 100,
10 < s < 1000, and x ≠ y hold.
For before-tax prices of items, all possibilities of 1 yen through s-1 yen should be considered.
The end of the input is specified by three zeros separated by a space.
Output
For each dataset,
output in a line the possible maximum total after-tax price when the VAT rate is changed to y%.
Sample Input
5 8 105
8 5 105
1 2 24
99 98 24
12 13 26
1 22 23
1 13 201
13 16 112
2 24 50
1 82 61
1 84 125
1 99 999
99 1 999
98 99 999
1 99 11
99 1 12
0 0 0
Output for the Sample Input
109
103
24
24
26
27
225
116
62
111
230
1972
508
1004
20
7
Hints
In the following table,
an instance of a before-tax price pair that has the maximum after-tax price after the VAT-rate change
is given for each dataset of the sample input.
DatasetBefore-tax pricesAfter-tax price with y% VAT
5 8 105 13, 88 14 + 95 = 109
8 5 105 12, 87 12 + 91 = 103
1 2 24 1, 23 1 + 23 = 24
99 98 24 1, 12 1 + 23 = 24
12 13 26 1, 23 1 + 25 = 26
1 22 23 1, 22 1 + 26 = 27
1 13 201 1,199 1 +224 = 225
13 16 112 25, 75 29 + 87 = 116
2 24 50 25, 25 31 + 31 = 62
1 82 61 11, 50 20 + 91 = 111
1 84 125 50, 75 92 +138 = 230
1 99 999 92,899183+1789 =1972
99 1 999 1,502 1 +507 = 508
98 99 999 5,500 9 +995 =1004
1 99 11 1, 10 1 + 19 = 20
99 1 12 1, 6 1 + 6 = 7
Extracted Specification
An integer x (0 < x < 100), representing a percentage.
An integer y (0 < y < 100), representing a percentage and not equal to x.
An integer s (10 < s < 1000), representing a sum.
The end of the input is specified by three zeros separated by a space.
### Example Input:
```
5 8 105
0 0 0
```
### Function Signature:
Write a function f(inputs) that takes in the input as a list of tuples.
```python
def f(inputs: List[Tuple[int, int, int]]):
'''
inputs: a list of tuples, where each tuple contains three integers
'''
```
Test Case Generator
Sure, here is a test case generator for the "Tax Rate Changed" problem statement:
```python
import random
def generate_test_case():
# VAT rates: 0 < x < 100 and 0 < y < 100, and x ≠ y
x = random.randint(1, 99)
y = random.randint(1, 99)
while y == x:
y = random.randint(1, 99)
# Total after-tax price s: 10 < s < 1000
s = random.randint(11, 999)
return f"{x} {y} {s}"
def generate_multiple_test_cases(num_cases):
test_cases = [generate_test_case() for _ in range(num_cases)]
test_cases.append("0 0 0") # End of input
return test_cases
if __name__ == "__main__":
num_cases = 20
test_cases = generate_multiple_test_cases(num_cases)
for case in test_cases:
print(case)
```
The above code will generate a specified number of test cases for the "Tax Rate Changed" problem. Each test case consists of three integers: `x`, `y`, and `s` as per the problem's constraints. The end of the input is marked by the line "0 0 0".
You can adjust `num_cases` to generate a different number of test cases. Here are a few example test cases generated by the function:
```
45 67 123
10 55 234
32 98 567
99 1 999
...
0 0 0
```
Each test case is printed on a new line and follows the rules specified in the problem statement.
Extract Arguments
def extract_arguments(fh):
inputs = []
while True:
line = fh.readline().strip()
if line == "0 0 0":
break
x, y, s = map(int, line.split())
inputs.append((x, y, s))
return inputs
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# inputs = extract_arguments(fh)
# f(inputs)