Orig Description
Problem A: Grey Area
Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the
world everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is
a simple self-made histogram generator.
Figure 1 is an example of histogram automatically produced by his histogram.
A histogram is a visual display of frequencies of value occurrences as bars. In this example, values
in the interval 0-9 occur five times, those in the interval 10-19 occur three times, and 20-29
and 30-39 once each.
Dr. Grey’s histogram generator is a simple tool. First, the height of the histogram is fixed, that
is, the height of the highest bar is always the same and those of the others are automatically
adjusted proportionately. Second, the widths of bars are also fixed. It can only produce a
histogram of uniform intervals, that is, each interval of a histogram should have the same width
(10 in the above example). Finally, the bar for each interval is painted in a grey color, where
the colors of the leftmost and the rightmost intervals are black and white, respectively, and the
darkness of bars monotonically decreases at the same rate from left to right. For instance, in
Figure 1, the darkness levels of the four bars are 1, 2/3, 1/3, and 0, respectively.
In this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness.
Input
The input consists of multiple datasets, each of which contains integers and specifies a value
table and intervals for the histogram generator, in the following format.
n w
v1
v2
.
.
vn
n is the total number of value occurrences for the histogram, and each of the n lines following
the first line contains a single value. Note that the same value may possibly occur multiple
times.
w is the interval width. A value v is in the first (i.e. leftmost) interval if 0 ≤ v < w, the second
one if w ≤ v < 2w, and so on. Note that the interval from 0 (inclusive) to w (exclusive) should
be regarded as the leftmost even if no values occur in this interval. The last (i.e. rightmost)
interval is the one that includes the largest value in the dataset.
You may assume the following.
1 ≤ n ≤ 100
10 ≤ w ≤ 50
0 ≤ vi ≤ 100 for 1 ≤ i ≤ n
You can also assume that the maximum value is no less than w. This means that the histogram
has more than one interval.
The end of the input is indicated by a line containing two zeros.
Output
For each dataset, output a line containing the amount of ink consumed in printing the histogram.
One unit of ink is necessary to paint one highest bar black. Assume that 0.01 units of ink per
histogram is consumed for various purposes except for painting bars such as drawing lines and
characters (see Figure 1). For instance, the amount of ink consumed in printing the histogram
in Figure 1 is:
Each output value should be in a decimal fraction and may have an error less than 10-5 .
Sample Input
3 50
100
0
100
3 50
100
100
50
10 10
1
2
3
4
5
16
17
18
29
30
0 0
Output for the Sample Input
0.51
0.26
1.4766666666666667
Extracted Specification
### Canonicalized Input Description:
An integer \( n \) (1 ≤ \( n \) ≤ 100), representing some quantity or size.
An integer \( w \) (10 ≤ \( w \) ≤ 50), representing an interval width.
A list of \( n \) integers \( v \) (0 ≤ \( v[i] \) ≤ 100), representing values.
### Example Input:
```
3 50
100
0
100
```
### Function Signature:
Write a function `f(inputs)` that takes in the input.
```python
def f(inputs: List[Tuple[int, int, List[int]]]):
'''
inputs: a list of tuples, where each tuple contains:
- an integer
- an integer
- a list of integers
'''
```
Test Case Generator
Sure! Here is the test case generator for the "Grey Area" problem:
```python
import random
def tcgen():
test_cases = []
while True:
# Randomly decide whether to generate another test case or stop
if random.random() < 0.2: # 20% chance to stop
break
# Generate n and w
n = random.randint(1, 100)
w = random.randint(10, 50)
# Generate n values for the histogram
values = [random.randint(0, 100) for _ in range(n)]
# Add the generated test case to the list
test_cases.append((n, w, values))
# Add the end line indicating the end of input
test_cases.append((0, 0, []))
return test_cases
# Function to print the test cases in the required format
def print_test_cases(test_cases):
for n, w, values in test_cases:
print(f"{n} {w}")
for value in values:
print(value)
if n == 0 and w == 0:
break
# Generate and print the test cases
test_cases = tcgen()
print_test_cases(test_cases)
```
### Explanation:
1. **Stopping Condition**: The generator has a 20% chance to stop generating new test cases on each iteration to ensure we don't generate an indefinite number of test cases. When it stops, it adds the `(0, 0)` line to indicate the end of the input.
2. **Generating `n` and `w`**: `n` is chosen randomly between 1 and 100, and `w` is chosen randomly between 10 and 50.
3. **Generating Values**: For each test case, `n` values are generated randomly between 0 and 100.
4. **Output**: The function `print_test_cases` formats and prints the test cases in the required input format.
This generator creates multiple datasets, each containing a number of value occurrences and their respective intervals, and ends with a line containing two zeros.
Extract Arguments
def extract_arguments(fh):
inputs = []
while True:
n, w = map(int, fh.readline().strip().split())
if n == 0 and w == 0:
break
values = [int(fh.readline().strip()) for _ in range(n)]
inputs.append((n, w, values))
return inputs
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# inputs = extract_arguments(fh)
# f(inputs)