Orig Description
Wall Painting
Here stands a wall made of a number of vertical panels. The panels are not painted yet.
You have a number of robots each of which can paint panels in a single color, either red, green, or blue. Each of the robots, when activated, paints panels between a certain position and another certain position in a certain color. The panels painted and the color to paint them are fixed for each of the robots, but which of them are to be activated and the order of their activation can be arbitrarily decided.
You’d like to have the wall painted to have a high aesthetic value. Here, the aesthetic value of the wall is defined simply as the sum of aesthetic values of the panels of the wall, and the aesthetic value of a panel is defined to be:
0, if the panel is left unpainted.
The bonus value specified, if it is painted only in a single color, no matter how many times it is painted.
The penalty value specified, if it is once painted in a color and then overpainted in one or more different colors.
Input
The input consists of a single test case of the following format.
$n$ $m$ $x$ $y$
$c_1$ $l_1$ $r_1$
.
.
.
$c_m$ $l_m$ $r_m$
Here, $n$ is the number of the panels ($1 \leq n \leq 10^9$) and $m$ is the number of robots ($1 \leq m \leq 2 \times 10^5$). $x$ and $y$ are integers between $1$ and $10^5$, inclusive. $x$ is the bonus value and $-y$ is the penalty value. The panels of the wall are consecutively numbered $1$ through $n$. The $i$-th robot, when activated, paints all the panels of numbers $l_i$ through $r_i$ ($1 \leq l_i \leq r_i \leq n$) in color with color number $c_i$ ($c_i \in \{1, 2, 3\}$). Color numbers 1, 2, and 3 correspond to red, green, and blue, respectively.
Output
Output a single integer in a line which is the maximum achievable aesthetic value of the wall.
Sample Input 1
8 5 10 5
1 1 7
3 1 2
1 5 6
3 1 4
3 6 8
Sample Output 1
70
Sample Input 2
26 3 9 7
1 11 13
3 1 11
3 18 26
Sample Output 2
182
Sample Input 3
21 10 10 5
1 10 21
3 4 16
1 1 7
3 11 21
3 1 16
3 3 3
2 1 17
3 5 18
1 7 11
2 3 14
Sample Output 3
210
Sample Input 4
21 15 8 7
2 12 21
2 1 2
3 6 13
2 13 17
1 11 19
3 3 5
1 12 13
3 2 2
1 12 15
1 5 17
1 2 3
1 1 9
1 8 12
3 8 9
3 2 9
Sample Output 4
153
Extracted Specification
An integer n (1 ≤ n ≤ 10^9), representing some quantity or size.
An integer m (1 ≤ m ≤ 2 * 10^5), representing another quantity or size.
Two integers x and y (1 ≤ x, y ≤ 10^5).
m pairs of integers (c_i, l_i, r_i):
- An integer c_i (c_i ∈ {1, 2, 3}), representing a category.
- Two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n).
### Example Input:
```
8 5 10 5
1 1 7
3 1 2
1 5 6
3 1 4
3 6 8
```
### Function Signature:
Write a function f(n, m, x, y, operations) that takes in the input.
def f(n: int, m: int, x: int, y: int, operations: List[Tuple[int, int, int]]):
'''
n: an integer
m: an integer
x: an integer
y: an integer
operations: a list of tuples, each tuple containing three integers
'''
Test Case Generator
Certainly! Here's a test case generator for the "Wall Painting" problem:
```python
import random
def generate_test_case():
# Generate `n` and `m`
n = random.randint(1, 10**9)
m = random.randint(1, 2 * 10**5)
# Generate `x` and `y`
x = random.randint(1, 10**5)
y = random.randint(1, 10**5)
# Generate robots' painting instructions
robots = []
for _ in range(m):
ci = random.randint(1, 3) # color
li = random.randint(1, n) # left position
ri = random.randint(li, n) # right position
robots.append((ci, li, ri))
return n, m, x, y, robots
def format_test_case(n, m, x, y, robots):
output = f"{n} {m} {x} {y}\n"
for robot in robots:
output += f"{robot[0]} {robot[1]} {robot[2]}\n"
return output
# Example usage:
random.seed(42) # For reproducibility in this example
n, m, x, y, robots = generate_test_case()
formatted_test_case = format_test_case(n, m, x, y, robots)
print(formatted_test_case)
```
### Explanation:
1. **`generate_test_case` function**:
- Generates random values for `n` (number of panels), `m` (number of robots), `x` (bonus value), and `y` (penalty value) within their specified ranges.
- For each of the `m` robots, it generates a random color (`ci`), a random left position (`li`), and a random right position (`ri`). The right position is guaranteed to be greater than or equal to the left position.
2. **`format_test_case` function**:
- Takes the generated test case values and formats them into a string that matches the input format specified in the problem statement.
3. **Example Usage**:
- The `random.seed(42)` line is added to ensure the generated test case is reproducible for demonstration purposes. Remove this line if you want different test cases each time you run the script.
- The generated test case is then printed out in the specified format.
### Notes:
- Given the large possible range of `n` (up to \(10^9\)), the generator may take a significant amount of time or memory if not constrained properly in a real-world setting. Adjust `n` to smaller values for practical testing if necessary.
- The generator ensures that every robot's painting range is valid (i.e., `1 ≤ li ≤ ri ≤ n`).
You can use this script to generate multiple test cases for the "Wall Painting" problem to test your solution's correctness and performance.
Extract Arguments
def extract_arguments(fh):
n, m, x, y = map(int, fh.readline().strip().split())
commands = []
for _ in range(m):
c, l, r = map(int, fh.readline().strip().split())
commands.append((c, l, r))
return n, m, x, y, commands
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# n, m, x, y, commands = extract_arguments(fh)
# f(n, m, x, y, commands)