"""
Given an array of integers, return a new array such that each element at index i of the new array is the product of all the numbers in the original array except the one at i.

For example, if the input is [1, 2, 3, 4, 5], the expected output is [120, 60, 40, 30, 24].

Follow-up: What if you can't use division?
"""

def product(arr: list[int]) -> list[int]:
    # first we calculate prefix/suffix. We add a spot with multiplicative identity (1) for convenience.
    prefix = [1]*len(arr)
    suffix = [1]*len(arr)

    p = 1
    for i in range(0, len(arr)-1):
        p *= arr[i]
        prefix[i+1] = p

    p = 1
    for i in range(len(arr)-1, 0, -1):
        p *= arr[i]
        suffix[i-1] = p

    ans = [1]*len(arr)
    for i in range(len(ans)):
        ans[i] = prefix[i] * suffix[i]
    return ans


# --- tests ---

assert product([2, 3, 4, 5]) == [60, 40, 30, 24]
assert product([1, 2, 3, 4, 5]) == [120, 60, 40, 30, 24]
assert product([1, 2]) == [2, 1]

# zero cases
assert product([0, 1, 2, 3]) == [6, 0, 0, 0]
assert product([0, 0, 2, 3]) == [0, 0, 0, 0]

# single element
assert product([5]) == [1]

print("All tests passed!")