Longest Common Prefix - Solution & Explanation

Problem Overview: Given an array of strings, return the longest prefix shared by every string. If the strings have no common starting characters, return an empty string. The challenge is efficiently comparing characters across multiple strings without unnecessary repeated work.

Approach 1: Horizontal Scanning (Time: O(S), Space: O(1))

Start with the first string as the candidate prefix. Iterate through the remaining strings and shrink the prefix until it matches the start of the current string. This works by repeatedly checking whether strs[i].startsWith(prefix); if not, remove the last character from the prefix and try again. The key insight: the prefix can only become shorter as you compare more strings. Since each character across all strings is examined at most once, the total cost is proportional to the total number of characters S. This approach uses simple iteration over the array and is the most practical solution for typical string interview problems.

Approach 2: Divide and Conquer (Time: O(S), Space: O(m log n))

Treat the problem similarly to merge operations. Split the array of strings into two halves, recursively compute the longest common prefix for each half, then merge the results by comparing characters of the two prefixes. The merge step scans character by character until a mismatch occurs. The insight is that computing prefixes for smaller groups reduces redundant comparisons across the entire list. This approach uses divide and conquer with recursion and performs the same total amount of character comparisons as horizontal scanning, resulting in O(S) time where S is the total number of characters across all strings.

Approach 3: Trie-Based Prefix Search (Time: O(S), Space: O(S))

Insert all strings into a Trie. After construction, walk down the Trie from the root while there is exactly one child and the node is not marked as the end of a word. Each step represents a shared prefix character. The traversal stops when branching occurs or a word terminates. The collected characters form the longest common prefix. While conceptually clean and useful when solving multiple prefix queries, it requires additional memory proportional to the total characters stored.

Recommended for interviews: Horizontal scanning is the expected answer in most interviews because it is simple, readable, and runs in optimal O(S) time with constant extra space. Divide and conquer demonstrates stronger algorithmic thinking and recursion skills. A Trie solution is rarely required but shows deeper knowledge of prefix-based data structures.