Sum Over N Bound

from random import randint, shuffle


def size_split(typ=0, size=10**5, spli=2, minn=1):
    """
    Splits a given size into unknown number of random positive integers, ensuring
    that each integer is at least `minn`. The sum of the integers will equal
    the initial size.

    Parameters:
    typ (int): Type 0 means constant spliting while type 1 means random.
    size (int): The total size to be split (default is 100,000).
    spli (int): The number of parts to split the size into (default is 2).
    minn (int): The minimum value each integer in the split must have (default is 1).

    Returns:
    list: A list of known number in type 0 or unknown number of positive integers in type 1 that sum up to the
          original size.

    Notes:
    - If the size is less than n, an empty list will be returned.
    - The output will be shuffled randomly.
    """
    if typ == 0:
        if size % spli:
            raise ValueError("spli should divide size.")
        return [size // spli] * spli
    else:
        arr = []
        tsize = size
        while size >= spli:
            x = randint(1, size // spli)
            arr.append(x)
            size -= x
        arr.sort(reverse=True)
        sumi = size
        while arr and arr[-1] <= minn:
            sumi += arr.pop()
        if sumi>=minn:
            arr.append(sumi)
        else:
            arr[-1] += sumi
        assert sum(arr) == tsize
        shuffle(arr)
        return arr

# Example Usage
if __name__ == "__main__":
    result1 = size_split(typ=0, size=10**5, spli=1, minn=10)
    print(result1)
    result2 = size_split(typ=1, size=1000, spli=100, minn=1)
    print(result2)