Problem p03008 - Generation 3

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).

A tuple (g_A, s_A, b_A) of three integers, each between 1 and 5000.

A tuple (g_B, s_B, b_B) of three integers, each between 1 and 5000.

### Example Input:

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

### Function Signature:
Write a function f(N, A, B) that takes in the input.
```python
def f(N: int, A: Tuple[int, int, int], B: Tuple[int, int, int]):
    '''
    N: an integer
    A: a tuple of three integers
    B: a tuple of three integers
    '''
```

Test Case Generator

Sure! To generate test cases for the given problem, we need to create a function that will randomly generate values for \(N\) (number of acorns), and the trading values for exchanges \(A\) and \(B\) (\(g_A\), \(s_A\), \(b_A\), \(g_B\), \(s_B\), and \(b_B\)) within the given constraints.

Here's the test case generator for the problem:

```python
import random

def tcgen():
    # Generate a random number of acorns N
    N = random.randint(1, 5000)
    
    # Generate random values for g_A, s_A, b_A within the given constraints
    g_A = random.randint(1, 5000)
    s_A = random.randint(1, 5000)
    b_A = random.randint(1, 5000)
    
    # Generate random values for g_B, s_B, b_B within the given constraints
    g_B = random.randint(1, 5000)
    s_B = random.randint(1, 5000)
    b_B = random.randint(1, 5000)
    
    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"Input:\n{N}\n{g_A} {s_A} {b_A}\n{g_B} {s_B} {b_B}\n")
```

This function `tcgen` will generate test cases as specified. Each call to `tcgen` will produce:

1. A random integer \(N\) representing the number of acorns Chokudai starts with.
2. Three random integers \(g_A\), \(s_A\), and \(b_A\) representing the number of acorns needed to gain 1 gram of gold, silver, and bronze respectively at Exchange A.
3. Three random integers \(g_B\), \(s_B\), and \(b_B\) representing the number of acorns needed to gain 1 gram of gold, silver, and bronze respectively at Exchange B.

The constraints ensure that \(N\) is between 1 and 5000, and each of \(g_A\), \(s_A\), \(b_A\), \(g_B\), \(s_B\), and \(b_B\) is between 1 and 5000. The example usage at the end demonstrates how to generate and print 5 test cases.

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)