Longest Common Prefix

Finding the longest common prefix among an array of strings is a classic warm‑up. It pops up in real‑world scenarios like building autocomplete for URLs, grouping file paths, or merging similar entries in datasets. Let me talk through how I’d tackle this in a live interview.

Problem Statement

Given an array of strings strs, return the longest common prefix shared by all strings. If there is no common prefix, return an empty string.

1. Clarify Requirements Before Jumping Into Code

I’ll confirm a few details first

• Should the comparison be case‑sensitive? Yes, assume exact character matches.

• What should I return if the array is empty? Return an empty string.

• If there’s only one string, I can return it as the prefix.

• Are all inputs valid strings? Yes, no nulls, but some may be empty.

2. Identify the Category of the Question

This is a string problem involving prefix matching across multiple entries. It often uses scanning patterns (horizontal or vertical) or divide‑and‑conquer techniques. No complex data structures are needed—just systematic string comparisons.

3. Consider a Brute‑Force Approach to Understand the Problem

A naive method is to take the first string as a candidate prefix, then compare it against every other string, character by character, shrinking the prefix whenever there’s a mismatch. In the worst case, this takes O(n·m) time where n is number of strings and m is the length of the first string.

4. Brainstorm More Solutions

• Horizontal Scanning (Prefix Reduction): Start with the first string, iteratively trim it by comparing with each subsequent string.

• Vertical Scanning: Check each character position i across all strings; stop at the first mismatch.

• Divide & Conquer: Recursively split the array, find prefixes for halves, then merge by comparing those two prefixes.

• Binary Search on Length: Find the maximum length L such that the first L characters are common, using substring checks.

• Trie Construction: Build a trie of all strings and traverse until a node has more than one child or marks an end, but that’s overkill here.

5. Discuss Trade‑Offs Between Your Solutions

Approach	Time	Space	Pros	Cons
Brute-Force (horizontal)	O(n·m)	O(1)	Simple	May repeatedly compare same chars
Vertical Scanning	O(n·m)	O(1)	Stops early on mismatch	Scans one position at a time
Divide & Conquer	O(n·m)	O(m·log n)	Elegant recursion	Extra recursion overhead
Binary Search on Length	O(n·m·log m)	O(1)	Uses fewer string comparisons overall	More complex
Trie	O(n·m)	O(n·m)	Fast lookups, supports extensions	High space, complex to code

Vertical scanning is straightforward, stops early on mismatches, and uses minimal space.

6. Write Pseudocode to Structure Your Thoughts

function longestCommonPrefix(strs):
  if strs is empty:
    return ""

  for i from 0 to length of first string - 1:
    currentChar = firstString[i]
    for each string s in strs starting from second:
      if i == length(s) or s[i] != currentChar:
        return substring of firstString from 0 to i
  return firstString  // entire first string is a common prefix

7. Consider Edge Cases

• Empty array → returns ""

• Single-element array → returns that string

• No common prefix (e.g., ["dog","cat"]) → returns ""

• All strings identical → returns the full string

• Very short vs. long strings (e.g., ["a",""]) → returns ""

8. Write Full Code Syntax

def longest_common_prefix(strs):
    if not strs:
        return ""

    first = strs[0]
    for i, ch in enumerate(first):
        for other in strs[1:]:
            if i == len(other) or other[i] != ch:
                return first[:i]
    return first

9. Test Your Code

assert longest_common_prefix(["flower","flow","flight"]) == "fl"
assert longest_common_prefix(["dog","racecar","car"]) == ""
assert longest_common_prefix([]) == ""
assert longest_common_prefix(["single"]) == "single"
assert longest_common_prefix(["","prefix"]) == ""
assert longest_common_prefix(["prefix","prefix","prefix"]) == "prefix"

print("All tests passed!")

10. Key Lessons to Remember for Future Questions

• Vertical scanning stops as soon as any mismatch appears—great for early exits.

• Always handle empty or singleton inputs up front.

• Breaking the problem into simple loops and early returns makes code clear.

• Trade-offs: recursion or binary search can work but add complexity without big gains for small inputs. Talking through these trade-offs shows off your algorithmic thinking skills.

Good Luck and Happy Coding!