Longest Common Prefix

Dec 18, 2024 • 4 mins read

Problem Overview

The "Longest Common Prefix" is a classic problem in computer science which involves finding the longest common prefix string amongst an array of strings. If there is no common prefix, the function should return an empty string "".

Given an array of strings, you are tasked to write a function that returns the longest common prefix.

Example

For example, given the input ["flower","flow","flight"], the function should return "fl". Conversely, if given ["dog","racecar","car"], the function should return an empty string, since there is no common prefix among the strings.

Understanding the Problem

This problem involves iterating over a list of strings and analyzing each character index-wise to identify the longest sequence of characters shared by all strings at their respective beginning positions. The primary challenge is to efficiently find this sequence to avoid unnecessary computations and ensure optimal performance, especially with longer lists or longer strings.

Key DSA Concepts and Theory

Strings and Prefix

A string is a sequence of characters, and a prefix is a substring that occurs at the start of the string. For example, in the word "prefix", "pre" is a prefix.

Horizontal Scanning

One common approach is horizontal scanning where the algorithm starts by assuming the entire first string as a potential prefix and iteratively compares with every other string. This method reduces the prefix by removing the mismatched characters sequentially.

Vertical Scanning

Vertical scanning involves comparing characters column by column from a 2D matrix view of the list where each string represents a row. As soon as a mismatch is found, the length up to the previous character determines the longest common prefix.

Solution Approach

Horizontal Scanning Approach

The following is a step-by-step explanation of the horizontal scanning approach, combined with a code implementation in both C++ and Java.

Steps:

Edge Cases:
- If the input array is empty, return an empty string.
- If the input array contains just one string, return that string as the prefix itself.
Initialize the Prefix:
- Start with the entire first string as the initial prefix.
Iterate and Compare:
- For each subsequent string, compare the prefix with the current string character by character.
- If the current prefix does not match, shorten the prefix until a match is found or it becomes empty.
Result:
- If prefix remains non-empty after full iteration, it is the longest common prefix.

C++ Implementation:

#include <iostream>
#include <vector>
#include <string>

std::string longestCommonPrefix(std::vector<std::string>& strs) {
    if (strs.empty()) return "";
    
    std::string prefix = strs[0];
    for (int i = 1; i < strs.size(); ++i) {
        while (strs[i].find(prefix) != 0) {
            prefix = prefix.substr(0, prefix.length() - 1);
            if (prefix.empty()) return "";
        }
    }
    return prefix;
}

Java Implementation:

public class Solution {
    public String longestCommonPrefix(String[] strs) {
        if (strs == null || strs.length == 0) return "";
        
        String prefix = strs[0];
        for (int i = 1; i < strs.length; i++) {
            while (strs[i].indexOf(prefix) != 0) {
                prefix = prefix.substring(0, prefix.length() - 1);
                if (prefix.isEmpty()) return "";
            }
        }
        return prefix;
    }
}

Time and Space Complexity Analysis

Time Complexity: O(S), where S is the sum of all characters in all strings. In the worst-case scenario, the algorithm compares each character of the prefix with every character of all other strings.
Space Complexity: O(1) as no additional space proportional to input size is used. The space used for string manipulations is constant.

Common Mistakes to Avoid

Ignoring Edge Cases: Ensure your code handles cases where the input array might be empty or contains one string.
String Length Assumptions: Avoid assuming all strings have similar lengths; handle varying string lengths gracefully.

Additional Resources and References

To dive deeper into string manipulation and prefix-related algorithms, you might find these resources helpful:

Understanding these basics and exploring different approaches will bolster your ability to solve various string-manipulation challenges. Happy coding!