Implement a function to find the longest common prefix among a list of strings. Optimize for time and space complexity, and explain your approach.

To find the longest common prefix, first check if the input list is empty. If not, use the first string as a reference. Iterate through each character position of this string, comparing the character at that position with the corresponding character in all other strings. If all strings have the same character at the current position, add it to the prefix. If any string lacks the character or has a different one, return the prefix built so far. This approach ensures we stop early when a mismatch is found, optimizing time by avoiding unnecessary comparisons. Edge cases like empty strings or lists are handled explicitly.

The solution uses a character-by-character comparison approach. First, we check if the input list is empty or contains only one string, returning the appropriate result. We then take the first string as a reference and iterate through each character index. For each index, we compare the character in the reference string with the same index in all other strings. If any string is shorter than the current index or has a different character, we return the prefix up to that point. This method ensures we stop as soon as a mismatch is found, achieving a time complexity of O(n*m), where n is the number of strings and m is the length of the shortest string. Space complexity is O(1) if we ignore the input storage, or O(m) for the output prefix. This approach is efficient for most cases and avoids unnecessary operations.