Problem p03254 - Generation 3

Orig Description

Score : 200 points
Problem StatementThere are N children, numbered 1, 2, ..., N.
Snuke has decided to distribute x sweets among them.
He needs to give out all the x sweets, but some of the children may get zero sweets.
For each i (1 \leq i \leq N), Child i will be happy if he/she gets exactly a_i sweets.
Snuke is trying to maximize the number of happy children by optimally distributing the sweets.
Find the maximum possible number of happy children.
Constraints
All values in input are integers.
2 \leq N \leq 100
1 \leq x \leq 10^9
1 \leq a_i \leq 10^9
InputInput is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
OutputPrint the maximum possible number of happy children.
Sample Input 13 70
20 30 10
Sample Output 12
One optimal way to distribute sweets is (20, 30, 20).
Sample Input 23 10
20 30 10
Sample Output 21
The optimal way to distribute sweets is (0, 0, 10).
Sample Input 34 1111
1 10 100 1000
Sample Output 34
The optimal way to distribute sweets is (1, 10, 100, 1000).
Sample Input 42 10
20 20
Sample Output 40
No children will be happy, no matter how the sweets are distributed.

Extracted Specification

An integer N (2 ≤ N ≤ 100), representing some quantity or size.
An integer x (1 ≤ x ≤ 10^9).
A list of integers A of size N, where each integer is between 1 and 10^9.

### Example Input:

```
3 70
20 30 10
```

### Function Signature:
Write a function f(N, x, A) that takes in the input.
def f(N: int, x: int, A: List[int]):
    '''
    N: an integer
    x: an integer
    A: a list of integers
    '''

Test Case Generator

Sure, let's write a test case generator for this problem. The generator will create random inputs that conform to the given constraints.

Here is the Python code for the test case generator:

```python
import random

def tcgen():
    # Generate N in the range [2, 100]
    N = random.randint(2, 100)
    
    # Generate x in the range [1, 10^9]
    x = random.randint(1, 10**9)
    
    # Generate list of a_i where each a_i is in the range [1, 10^9]
    A = [random.randint(1, 10**9) for _ in range(N)]
    
    return N, x, A

# Example of using the generator
if __name__ == "__main__":
    N, x, A = tcgen()
    print(N)
    print(x)
    print(" ".join(map(str, A)))
```

This code snippet will generate a random test case each time it runs, ensuring that all constraints are met:

1. `N` is a random integer between 2 and 100.
2. `x` is a random integer between 1 and \(10^9\).
3. `A` is a list of `N` integers, each between 1 and \(10^9\).

You can run the generator to produce various test cases, which can then be used to test your algorithm for correctness and performance.

Extract Arguments

def extract_arguments(fh):
    N, x = map(int, fh.readline().strip().split())
    A = list(map(int, fh.readline().strip().split()))
    return N, x, A

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