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), representing some quantity or size.
An integer M (1 ≤ M ≤ 10), representing some upper limit.
An integer Q (1 ≤ Q ≤ 50), representing the number of quadruples.
Q quadruples of integers (a_i, b_i, c_i, d_i) where:
- 1 ≤ a_i < b_i ≤ N
- 0 ≤ c_i ≤ M - 1
- 1 ≤ d_i ≤ 10^5
### 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, quadruples) that takes in the input.
```python
def f(N: int, M: int, Q: int, quadruples: List[Tuple[int, int, int, int]]):
'''
N: an integer
M: an integer
Q: an integer
quadruples: a list of tuples, each containing four integers
'''
```
Test Case Generator
Sure! Here is a test case generator for the given problem statement:
```python
import random
def generate_test_case():
N = random.randint(2, 10)
M = random.randint(1, 10)
Q = random.randint(1, 50)
queries = []
for _ in range(Q):
# Since 1 <= a_i < b_i <= N, we generate a_i and b_i such that a_i < b_i
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)
queries.append((a_i, b_i, c_i, d_i))
return N, M, Q, queries
def format_test_case(N, M, Q, queries):
test_case = f"{N} {M} {Q}\n"
for a_i, b_i, c_i, d_i in queries:
test_case += f"{a_i} {b_i} {c_i} {d_i}\n"
return test_case
# Example usage:
N, M, Q, queries = generate_test_case()
test_case = format_test_case(N, M, Q, queries)
print(test_case)
```
### Explanation:
- **N**: The number of integers in the sequence \(A\). It's randomly chosen between 2 and 10.
- **M**: The maximum value for the integers in the sequence \(A\). It's randomly chosen between 1 and 10.
- **Q**: The number of queries. It's randomly chosen between 1 and 50.
- **Queries**: For each query, \(a_i\) and \(b_i\) are chosen such that \(1 \leq a_i < b_i \leq N\).
- \(a_i\): Randomly chosen from 1 to \(N-1\) to ensure \(a_i < b_i\).
- \(b_i\): Randomly chosen from \(a_i + 1\) to \(N\).
- \(c_i\): Randomly chosen from 0 to \(M-1\).
- \(d_i\): Randomly chosen from 1 to \(10^5\).
The `generate_test_case` function generates the random values, and `format_test_case` function formats these values into the required input format.
You can run this script multiple times to generate different test cases for your competitive programming problem.
Extract Arguments
def extract_arguments(fh):
N, M, Q = map(int, fh.readline().strip().split())
quadruples = []
for _ in range(Q):
a, b, c, d = map(int, fh.readline().strip().split())
quadruples.append((a, b, c, d))
return N, M, Q, quadruples