Problem p02695 - Generation 2

Orig Description

Score : 300 points
Problem StatementGiven are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).
Consider a sequence A satisfying the following conditions:
A is a sequence of N positive integers.
1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.
Let us define a score of this sequence as follows:
The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)
Find the maximum possible score of A.
Constraints
All values in input are integers.
2 ≤ N ≤ 10
1 \leq M \leq 10
1 \leq Q \leq 50
1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )
0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )
(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)
1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )
InputInput is given from Standard Input in the following format:
N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q
OutputPrint the maximum possible score of A.
Sample Input 13 4 3
1 3 3 100
1 2 2 10
2 3 2 10
Sample Output 1110
When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.
Sample Input 24 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328
Sample Output 2357500
Sample Input 310 10 1
1 10 9 1
Sample Output 31

Extracted Specification

An integer N (2 ≤ N ≤ 10), an integer M (1 ≤ M ≤ 10), an integer Q (1 ≤ Q ≤ 50), and Q quadruples of integers (a_i, b_i, c_i, d_i).

### Example Input:

```
3 4 3
1 3 3 100
1 2 2 10
2 3 2 10
```

### Function Signature:
Write a function f(N, M, Q, inputs) that takes in the input. 
def f(N: int, M: int, Q: int, inputs: List[Tuple[int, int, int, int]]): 
    ''' 
    N: an integer 
    M: an integer 
    Q: an integer 
    inputs: a list of tuples of four integers
    '''

Test Case Generator

Sure, let's write a test case generator for the given problem statement. The generator will create random valid inputs based on the constraints provided.

```python
import random

def tcgen():
    # Generate N, M, and Q
    N = random.randint(2, 10)
    M = random.randint(1, 10)
    Q = random.randint(1, 50)

    # Generate Q quadruples of (a_i, b_i, c_i, d_i)
    quadruples = []
    for _ in range(Q):
        a_i = random.randint(1, N - 1)
        b_i = random.randint(a_i + 1, N)
        c_i = random.randint(0, M - 1)
        d_i = random.randint(1, 10**5)
        quadruples.append((a_i, b_i, c_i, d_i))
    
    # Return generated values in the required format
    return N, M, Q, quadruples

def format_test_case(N, M, Q, quadruples):
    formatted = f"{N} {M} {Q}\n"
    formatted += "\n".join(f"{a} {b} {c} {d}" for a, b, c, d in quadruples)
    return formatted

# Generate a test case
N, M, Q, quadruples = tcgen()
test_case = format_test_case(N, M, Q, quadruples)
print(test_case)
```

### Explanation:

1. **`tcgen` function:**
   - Generates random integers for `N`, `M`, and `Q` within specified constraints.
   - Creates a list of `Q` quadruples `(a_i, b_i, c_i, d_i)` with each value satisfying the given problem constraints.

2. **`format_test_case` function:**
   - Formats the generated test case according to the input format required by the problem statement.

3. **Generating and printing a test case:**
   - We call `tcgen` to get a random test case.
   - We then use `format_test_case` to format it and print it.

This generator ensures that all the constraints are adhered to, and it produces a variety of test cases for robust testing of your solution.

Extract Arguments

def extract_arguments(fh):
    N, M, Q = map(int, fh.readline().strip().split())
    queries = []
    for _ in range(Q):
        a, b, c, d = map(int, fh.readline().strip().split())
        queries.append((a, b, c, d))
    return N, M, Q, queries