###### Finding the Longest Consecutive Sequence in a List

In many programming scenarios, one might encounter the need to identify the longest consecutive sequence of integers within a list. This problem can be efficiently solved using a set for quick lookups, and the overall time complexity can be kept at O(n).
Below is a Python function that implements this logic:
def longest_consecutive_sequence(nums):
if not nums:
return []
# Convert the list to a set for O(1) lookups
num_set = set(nums)
longest_sequence = []
for num in num_set:
# Only check for sequences starting with the smallest number
if num - 1 not in num_set:
current_num = num
current_sequence = [current_num]
# Build the sequence from the current number
while current_num + 1 in num_set:
current_num += 1
current_sequence.append(current_num)
# Update the longest_sequence if current_sequence is longer
if len(current_sequence) > len(longest_sequence):
longest_sequence = current_sequence
return longest_sequence
# Example usage:
example_list = [100, 4, 200, 1, 3, 2]
print(longest_consecutive_sequence(example_list)) # Output: [1, 2, 3, 4]

###### Explanation of the Code

1. **Input Check**: First, the function checks if the input list is empty. If it is, an empty list is returned.
2. **Convert to Set**: The input list *nums* is converted to a set called *num_set*. This conversion allows for O(1) average time complexity for membership checks, which increases the efficiency of the algorithm.
3. **Iterate Over Unique Numbers**: The function iterates through each number in *num_set*. For each number, it checks whether it is the start of a sequence by verifying that *num - 1* is not present in *num_set*.
4. **Build Sequence**: If the number is the starting point, the function initializes *current_num* and *current_sequence*. It then enters a loop, checking for consecutive integers (*current_num + 1*). Each consecutive number is added to the *current_sequence*.
5. **Update Longest Sequence**: After building a complete sequence, the function compares the length of *current_sequence* with *longest_sequence*. If the current is longer, it updates *longest_sequence*.
6. **Return Result**: Finally, the function returns the longest found sequence.
###### Example Usage

The provided example demonstrates how to use the function. The list *[100, 4, 200, 1, 3, 2]* results in the longest consecutive sequence *[1, 2, 3, 4]*.
This function is efficient and handles sequences of varying sizes and orders, making it a useful tool for analyzing numeric datasets.