Algorithm to get the longest sequential (consecutive set of numbers from the given unsorted list.

longest_consecutive_subsequence_algorithm.py

def longest_consecutive_subsequence(input_list):
    """
    Gets the longest sequential (consecutive set of numbers from the given unsorted list.

    Time complexity is O(n) and space complexity is O(n).

    This design uses Python's `range()` function to generate the list of sequential numbers.  To accomplish this,
    we iterate through the input list to find the least starting number and the number of sequential numbers.

    It works on all integers.

    :param input_list: given unsorted list of integers (positive and/or negative).
    :return: returns a list of the longest sequential numbers.
    """

    # Create a dictionary where number: visited.
    # Value of 1 means the number has been visited (processed).
    nums = {num: 0 for num in input_list}       # O(n)

    current_start = None
    current_count = 0
    longest_start = None
    longest_count = 0

    for num in input_list:                      # O(n)
        current_count = 1
        current_start = num
        nums[num] = -1

        # Check sequential n + 1.
        current = num + 1
        while current in nums and nums[current] == 0:
            current_count += 1
            nums[current] = 1           # Mark that this number has been visited.
            current += 1

        # Check sequential n - 1.
        current = num - 1
        while current in nums and nums[current] == 0:
            current_start = current
            current_count += 1
            nums[current] = 1           # Mark that this number has been visited.
            current -= 1

        if current_count == longest_count and current_start > longest_start:

            continue

        if current_count >= longest_count:
            longest_start = current_start
            longest_count = current_count

    return [num for num in range(longest_start, longest_start + longest_count)]
  
if __name__ == '__main__':
    test_case = [
        [[5, 4, 7, 10, 1, 3, 55, 2], [1, 2, 3, 4, 5]],
        [[2, 12, 9, 16, 10, 5, 3, 20, 25, 11, 1, 8, 6], [8, 9, 10, 11, 12]],
        [[0, 1, 2, 3, 4], [0, 1, 2, 3, 4]],
        [[25, 35, 45, 12, 26, 36, 13, 24, 44, 23], [23, 24, 25, 26]],
        [[0, -1, -2, -3, -10, 20, 30, -4], [-4, -3, -2, -1, 0]]
    ]

    for input, expected in test_case:
        actual = longest_consecutive_subsequence(input)
        if actual == expected:
            print("Passed")
        else:
            print("Failed. actual {} vs. expected {}".format(actual, expected)