Orig Description
Problem B. Colorful Drink
In the Jambo Amusement Garden (JAG), you sell colorful drinks consisting of multiple color layers. This colorful drink can be made by pouring multiple colored liquids of different density from the bottom in order.
You have already prepared several colored liquids with various colors and densities. You will receive a drink request with specified color layers. The colorful drink that you will serve must satisfy the following conditions.
You cannot use a mixed colored liquid as a layer. Thus, for instance, you cannot create a new liquid with a new color by mixing two or more different colored liquids, nor create a liquid with a density between two or more liquids with the same color by mixing them.
Only a colored liquid with strictly less density can be an upper layer of a denser colored liquid in a drink. That is, you can put a layer of a colored liquid with density $x$ directly above the layer of a colored liquid with density $y$ if $x < y$ holds.
Your task is to create a program to determine whether a given request can be fulfilled with the prepared colored liquids under the above conditions or not.
Input
The input consists of a single test case in the format below.
$N$
$C_1$ $D_1$
$\vdots$
$C_N$ $D_N$
$M$
$O_1$
$\vdots$
$O_M$
The first line consists of an integer $N$ ($1 \leq N \leq 10^5$), which represents the number of the prepared colored liquids. The following $N$ lines consists of $C_i$ and $D_i$ ($1 \leq i \leq N$). $C_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th prepared colored liquid. The length of $C_i$ is between $1$ and $20$ inclusive. $D_i$ is an integer and represents the density of the $i$-th prepared colored liquid. The value of $D_i$ is between $1$ and $10^5$ inclusive. The ($N+2$)-nd line consists of an integer $M$ ($1 \leq M \leq 10^5$), which represents the number of color layers of a drink request. The following $M$ lines consists of $O_i$ ($1 \leq i \leq M$). $O_i$ is a string consisting of lowercase alphabets and denotes the color of the $i$-th layer from the top of the drink request. The length of $O_i$ is between $1$ and $20$ inclusive.
Output
If the requested colorful drink can be served by using some of the prepared colored liquids, print 'Yes'. Otherwise, print 'No'.
Examples
Sample Input 1
2
white 20
black 10
2
black
white
Output for Sample Input 1
Yes
Sample Input 2
2
white 10
black 10
2
black
white
Output for Sample Input 2
No
Sample Input 3
2
white 20
black 10
2
black
orange
Output for Sample Input 3
No
Sample Input 4
3
white 10
red 20
white 30
3
white
red
white
Output for Sample Input 4
Yes
Sample Input 5
4
red 3444
red 3018
red 3098
red 3319
4
red
red
red
red
Output for Sample Input 5
Yes
Extracted Specification
An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
A list of N tuples, each containing a string and an integer. The string is a sequence of lowercase alphabets of length between 1 and 20, and the integer is between 1 and 10^5.
An integer M (1 ≤ M ≤ 10^5).
A list of M strings, each string is a sequence of lowercase alphabets of length between 1 and 20.
### Example Input:
```
2
white 20
black 10
2
black
white
```
### Function Signature:
Write a function f(N, A, M, B) that takes in the input.
```python
def f(N: int, A: List[Tuple[str, int]], M: int, B: List[str]):
'''
N: an integer
A: a list of tuples, where each tuple contains a string and an integer
M: an integer
B: a list of strings
'''
```
Test Case Generator
Sure, I can help you write a test case generator for the "Colorful Drink" problem. Here's a Python script that generates random test cases based on the given problem constraints:
```python
import random
import string
def random_color():
length = random.randint(1, 20)
return ''.join(random.choices(string.ascii_lowercase, k=length))
def tcgen():
# Generate N (number of prepared colored liquids)
N = random.randint(1, 10**5)
# Generate N lines of (C_i, D_i)
prepared_liquids = []
for _ in range(N):
C_i = random_color()
D_i = random.randint(1, 10**5)
prepared_liquids.append((C_i, D_i))
# Generate M (number of color layers in the drink request)
M = random.randint(1, 10**5)
# Generate M lines of O_i (color for each requested layer)
requested_layers = [random_color() for _ in range(M)]
# Format the generated data into the required input format
input_data = f"{N}\n"
input_data += '\n'.join(f"{C} {D}" for C, D in prepared_liquids)
input_data += f"\n{M}\n"
input_data += '\n'.join(requested_layers)
return input_data
# Example usage
test_case = tcgen()
print(test_case)
```
### Explanation:
1. **random_color() Function:** Generates a random string of lowercase letters with a length between 1 and 20.
2. **tcgen() Function:**
- Randomly generates the number of prepared colored liquids \(N\).
- For each of the \(N\) colored liquids, it generates a color \(C_i\) using the `random_color` function and a density \(D_i\) using `random.randint`.
- Randomly generates the number of color layers \(M\) in the drink request.
- For each of the \(M\) requested layers, it generates a color \(O_i\) using the `random_color` function.
- Formats the generated data into the required input format.
### Note:
- This script ensures that the generated test cases adhere to the constraints provided in the problem statement.
- Due to the possible large size of \(N\) and \(M\) (up to \(10^5\)), the generated test cases can be very large. Make sure to handle them appropriately when running the test cases.
You can use the `tcgen` function to generate test cases for the "Colorful Drink" problem and test your solution with different inputs.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
prepared_liquids = []
for _ in range(N):
parts = fh.readline().strip().split()
color = parts[0]
density = int(parts[1])
prepared_liquids.append((color, density))
M = int(fh.readline().strip())
requested_layers = []
for _ in range(M):
color = fh.readline().strip()
requested_layers.append(color)
return N, prepared_liquids, M, requested_layers