Orig Description
Score : 300 points
Problem StatementWe have a 2 \times N grid. We will denote the square at the i-th row and j-th column (1 \leq i \leq 2, 1 \leq j \leq N) as (i, j).
You are initially in the top-left square, (1, 1).
You will travel to the bottom-right square, (2, N), by repeatedly moving right or down.
The square (i, j) contains A_{i, j} candies.
You will collect all the candies you visit during the travel.
The top-left and bottom-right squares also contain candies, and you will also collect them.
At most how many candies can you collect when you choose the best way to travel?
Constraints
1 \leq N \leq 100
1 \leq A_{i, j} \leq 100 (1 \leq i \leq 2, 1 \leq j \leq N)
InputInput is given from Standard Input in the following format:
N
A_{1, 1} A_{1, 2} ... A_{1, N}
A_{2, 1} A_{2, 2} ... A_{2, N}
OutputPrint the maximum number of candies that can be collected.
Sample Input 15
3 2 2 4 1
1 2 2 2 1
Sample Output 114
The number of collected candies will be maximized when you:
move right three times, then move down once, then move right once.
Sample Input 24
1 1 1 1
1 1 1 1
Sample Output 25
You will always collect the same number of candies, regardless of how you travel.
Sample Input 37
3 3 4 5 4 5 3
5 3 4 4 2 3 2
Sample Output 329
Sample Input 41
2
3
Sample Output 45
Extracted Specification
An integer N (1 ≤ N ≤ 100), representing some quantity or size.
A list of integers B of size N, where each integer is between 1 and 100.
A list of integers C of size N, where each integer is between 1 and 100.
### Example Input:
```
5
3 2 2 4 1
1 2 2 2 1
```
### Function Signature:
Write a function f(N, B, C) that takes in the input.
def f(N: int, B: List[int], C: List[int]):
'''
N: an integer
B: a list of integers
C: a list of integers
'''
Test Case Generator
Certainly! Below is a Python function to generate test cases for the given problem statement. This function will randomly generate values for \(N\), and the candy counts \(A\) for the 2xN grid, ensuring that all values follow the constraints specified:
```python
import random
def tcgen():
N = random.randint(1, 100)
# Generate the 2xN grid with candies, ensuring values are between 1 and 100
A_1 = [random.randint(1, 100) for _ in range(N)]
A_2 = [random.randint(1, 100) for _ in range(N)]
return N, A_1, A_2
# Example usage:
N, A_1, A_2 = tcgen()
print(N)
print(' '.join(map(str, A_1)))
print(' '.join(map(str, A_2)))
```
This function follows these steps:
1. Randomly selects \(N\) within the range [1, 100].
2. Generates two lists, \(A_1\) and \(A_2\), each of size \(N\) with random values between 1 and 100.
3. Returns \(N\), \(A_1\), and \(A_2\).
Here's an example of how the function might be used and what the output might look like:
```python
N, A_1, A_2 = tcgen()
print(N) # For example, might print: 5
print(' '.join(map(str, A_1))) # For example, might print: 3 2 2 4 1
print(' '.join(map(str, A_2))) # For example, might print: 1 2 2 2 1
```
This will generate a new test case each time it is called, providing a varied set of inputs to test the problem's solution thoroughly.
Extract Arguments
def extract_arguments(fh):
N = int(fh.readline().strip())
A = []
for _ in range(2):
A.append(list(map(int, fh.readline().strip().split())))
return N, A
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# N, A = extract_arguments(fh)
# f(N, A)