Problem p03008 - Generation 2

Orig Description

Score : 600 points
Problem StatementThe squirrel Chokudai has N acorns.
One day, he decides to do some trades in multiple precious metal exchanges to make more acorns.
His plan is as follows:
Get out of the nest with N acorns in his hands.
Go to Exchange A and do some trades.
Go to Exchange B and do some trades.
Go to Exchange A and do some trades.
Go back to the nest.
In Exchange X (X = A, B), he can perform the following operations any integer number of times (possibly zero) in any order:
Lose g_{X} acorns and gain 1 gram of gold.
Gain g_{X} acorns and lose 1 gram of gold.
Lose s_{X} acorns and gain 1 gram of silver.
Gain s_{X} acorns and lose 1 gram of silver.
Lose b_{X} acorns and gain 1 gram of bronze.
Gain b_{X} acorns and lose 1 gram of bronze.
Naturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.
What is the maximum number of acorns that he can bring to the nest?
Note that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.
Constraints
1 \leq N \leq 5000
1 \leq g_{X} \leq 5000
1 \leq s_{X} \leq 5000
1 \leq b_{X} \leq 5000
All values in input are integers.
InputInput is given from Standard Input in the following format:
N
g_A s_A b_A
g_B s_B b_B
OutputPrint the maximum number of acorns that Chokudai can bring to the nest.
Sample Input 123
1 1 1
2 1 1
Sample Output 146
He can bring 46 acorns to the nest, as follows:
In Exchange A, trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }
In Exchange B, trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }
In Exchange A, trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }
He cannot have 47 or more acorns, so the answer is 46.

Extracted Specification

An integer N (1 ≤ N ≤ 5000), representing some quantity.
Six integers g_A, s_A, b_A, g_B, s_B, b_B, each between 1 and 5000.

### Example Input:

```
23
1 1 1
2 1 1
```

### Function Signature:
Write a function f(N, g_A, s_A, b_A, g_B, s_B, b_B) that takes in the input. 
def f(N: int, g_A: int, s_A: int, b_A: int, g_B: int, s_B: int, b_B: int): 
    ''' 
    N: an integer 
    g_A: an integer 
    s_A: an integer 
    b_A: an integer 
    g_B: an integer 
    s_B: an integer 
    b_B: an integer 
    '''

Test Case Generator

Sure! Below is a Python function to generate test cases for the problem where Chokudai the squirrel is trying to maximize the number of acorns he can bring back to the nest after trading in two exchanges:

```python
import random

def tcgen():
    # Generate a random integer N in the range [1, 5000]
    N = random.randint(1, 5000)
    
    # Generate random integers for g_A, s_A, b_A, g_B, s_B, b_B in the range [1, 5000]
    g_A = random.randint(1, 5000)
    s_A = random.randint(1, 5000)
    b_A = random.randint(1, 5000)
    
    g_B = random.randint(1, 5000)
    s_B = random.randint(1, 5000)
    b_B = random.randint(1, 5000)
    
    # Return the generated values
    return N, (g_A, s_A, b_A), (g_B, s_B, b_B)

# Example usage
for _ in range(5):
    N, (g_A, s_A, b_A), (g_B, s_B, b_B) = tcgen()
    print(f"N: {N}\ng_A: {g_A}, s_A: {s_A}, b_A: {b_A}\ng_B: {g_B}, s_B: {s_B}, b_B: {b_B}\n")
```

This `tcgen` function generates a valid test case based on the constraints provided in the problem statement:
- \(1 \leq N \leq 5000\)
- \(1 \leq g_X \leq 5000\)
- \(1 \leq s_X \leq 5000\)
- \(1 \leq b_X \leq 5000\)

The output format is given in a way that matches the input requirements of the problem, where:
- `N` is the initial number of acorns.
- `g_A`, `s_A`, `b_A` are the parameters for Exchange A.
- `g_B`, `s_B`, `b_B` are the parameters for Exchange B.

You can use this function to generate multiple test cases to verify the correctness of your solution to the problem.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    g_A, s_A, b_A = map(int, fh.readline().strip().split())
    g_B, s_B, b_B = map(int, fh.readline().strip().split())
    return N, (g_A, s_A, b_A), (g_B, s_B, b_B)

# if __name__ == "__main__":
#     input_path = sys.argv[1]
#     with open(input_path, 'r') as fh: 
#     N, A, B = extract_arguments(fh)
#     f(N, A, B)