Problem p03910 - Generation 2

Orig Description

Score : 300 points
Problem StatementThe problem set at CODE FESTIVAL 20XX Finals consists of N problems.
The score allocated to the i-th (1≦i≦N) problem is i points.
Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.
As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.
Determine the set of problems that should be solved.
Constraints
1≦N≦10^7
Partial Score
200 points will be awarded for passing the test set satisfying 1≦N≦1000.
Additional 100 points will be awarded for passing the test set without additional constraints.
InputThe input is given from Standard Input in the following format:
N
OutputAmong the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.
If there exists more than one such set, any of them will be accepted.
Sample Input 14
Sample Output 11
3
Solving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.
Sample Input 27
Sample Output 21
2
4
The set \{3,4\} will also be accepted.
Sample Input 31
Sample Output 31

Extracted Specification

An integer N (1 ≤ N ≤ 10^7), representing some quantity or size.

### Example Input:

```
14
```

### Function Signature:
Write a function f(N) that takes in the input. 
def f(N: int): 
    ''' 
    N: an integer
    '''

Test Case Generator

Sure! Here is a test case generator for the given problem of selecting problems to solve with the minimum highest score:

```python
import random

def tcgen():
    # Generate a random integer N within the given constraint
    N = random.randint(1, 10**7)
    
    return N

# Example of using the test case generator
if __name__ == "__main__":
    test_case = tcgen()
    print(test_case)
```

This function generates a single random integer \( N \) within the constraint \( 1 \leq N \leq 10^7 \). You can run this script multiple times to generate different test cases.

Here are a few examples of how the function might generate test cases:
```
Example output:
1234567
```

```
Example output:
9876543
```

```
Example output:
10000000
```

For creating a comprehensive set of test cases and ensuring they cover a variety of scenarios, you may consider generating multiple test cases and possibly saving them in a file or another data structure for further testing.

```python
def generate_multiple_test_cases(num_cases):
    test_cases = []
    for _ in range(num_cases):
        test_cases.append(tcgen())
    return test_cases

# Example of generating multiple test cases
if __name__ == "__main__":
    num_cases = 5
    test_cases = generate_multiple_test_cases(num_cases)
    for test_case in test_cases:
        print(test_case)
```

This will generate and print 5 test cases, each being a random integer \( N \).

Remember, for competitive programming, the actual implementation of the problem-solving logic will need to ensure that the output meets the constraints and requirements specified in the problem statement. The test case generator helps in verifying the correctness and efficiency of your solution by providing diverse and edge test cases.

Extract Arguments

def extract_arguments(fh):
    N = int(fh.readline().strip())
    return N