What is the time complexity of Longest Common Prefix?

The optimal solution has a time complexity of O(S).

What data structures are used to solve Longest Common Prefix?

This problem uses Array, String, Trie. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Longest Common Prefix?

The maximum possible common prefix cannot be longer than the first string in the input array. This allows us to initialize our candidate prefix with `strs[0]` and then only shorten it. Rather than comparing all strings simultaneously, we can iteratively reduce a candidate prefix by comparing it against *each subsequent string*. If a candidate `P` is a common prefix for `S1...Sn`, and `P'` is the common prefix for `P` and `Sn+1`, then `P'` must be the common prefix for `S1...Sn+1`.

Which companies ask LeetCode 14. Longest Common Prefix in interviews?

This problem is frequently asked at Accenture, Accolite, Adobe, Airbus SE, Amazon and 44 more companies.

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Longest Common Prefix - LeetCode 14 Solution

Q: How to solve Longest Common Prefix?

This solution takes an iterative, 'candidate reduction' approach. It intelligently initializes the `prefix` with the first string in the array. This makes sense because the longest possible common prefix can never be longer than the shortest string in the array, and by starting with one of the strings itself, we establish an upper bound. The algorithm then iterates through the *remaining* strings, one by one. For each string `strs[i]`, it checks if the current `prefix` is indeed a prefix of `strs[i]` using `strs[i].find(prefix) != 0`. The `find()` method returns the starting index of the substring if found; if it's a prefix, it *must* be found at index 0. If `prefix` is not a prefix of `strs[i]`, it means our current `prefix` is too long. The `while` loop then repeatedly shortens the `prefix` by one character from the end (`prefix = prefix[:-1]`) until it *does* become a prefix of `strs[i]`. If, during this shortening, the `prefix` becomes an empty string, it signifies that there's no common prefix among the strings processed so far, and we can immediately return `""`. This iterative pruning ensures that after checking each string, the `prefix` variable holds the longest common prefix *among all strings processed up to that point*. By the time the loop finishes, `prefix` will contain the longest common prefix of all strings in the entire input array.

Longest Common Prefix - Complete Solution Guide

Longest Common Prefix is LeetCode problem 14, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Write a function to find the longest common prefix string amongst an array of strings. If there is no common prefix, return an empty string "" . Example 1: Input: strs = ["flower","flow","flight"] Output: "fl" Example 2: Input: strs = ["dog","racecar","car"] Output: "" Explanation: There is no common prefix among the input strings. Constraints: 1 <= strs.length <= 200 0 <= strs[i].length <= 200 strs[i] consists of only lowercase English letters if it is non-empty.

Detailed Explanation

You're tasked with identifying the longest string that appears as the very beginning (prefix) of every single string within a given array. Imagine you have a list of words, and you need to find the largest common starting sequence of characters they all share. If even one character is different at a certain position among the words, that character (and everything after it) cannot be part of the common prefix. Consider the input `["flower","flow","flight"]`. The first two characters, 'f' and 'l', are present at the beginning of all three words. After 'l', "flower" has 'o', "flow" has 'o', but "flight" has 'i'. Since 'o' and 'i' are different, the common prefix cannot extend beyond 'fl', making "fl" the answer. Conversely, if you're given `["dog","racecar","car"]`, there isn't a single character that all three strings start with. 'd' is unique to "dog", 'r' to "racecar", and 'c' to "car". In such a scenario, the function should return an empty string. The core challenge isn't just finding *any* common prefix, but specifically the *longest* one. This implies a process of either building up a prefix character by character while checking all strings, or, as the provided solution demonstrates, starting with a maximal potential prefix and progressively shortening it until it satisfies the condition for all strings.

Solution Approach

This solution takes an iterative, 'candidate reduction' approach. It intelligently initializes the `prefix` with the first string in the array. This makes sense because the longest possible common prefix can never be longer than the shortest string in the array, and by starting with one of the strings itself, we establish an upper bound. The algorithm then iterates through the *remaining* strings, one by one. For each string `strs[i]`, it checks if the current `prefix` is indeed a prefix of `strs[i]` using `strs[i].find(prefix) != 0`. The `find()` method returns the starting index of the substring if found; if it's a prefix, it *must* be found at index 0. If `prefix` is not a prefix of `strs[i]`, it means our current `prefix` is too long. The `while` loop then repeatedly shortens the `prefix` by one character from the end (`prefix = prefix[:-1]`) until it *does* become a prefix of `strs[i]`. If, during this shortening, the `prefix` becomes an empty string, it signifies that there's no common prefix among the strings processed so far, and we can immediately return `""`. This iterative pruning ensures that after checking each string, the `prefix` variable holds the longest common prefix *among all strings processed up to that point*. By the time the loop finishes, `prefix` will contain the longest common prefix of all strings in the entire input array.

Step-by-Step Algorithm

Step 1: Handle edge cases: Check if the input array is empty or null. If so, return an empty string.
Step 2: Initialize: Assume the first string in the array is the initial common prefix.
Step 3: Iterate: Iterate through the remaining strings in the array.
Step 4: Compare: For each string, compare its characters with the current common prefix. If a mismatch is found at any position, shorten the common prefix by removing its last character.
Step 5: Repeat: Repeat step 4 until the end of the string is reached, or an empty prefix is found (no common prefix).
Step 6: Return: Return the final common prefix.

Key Insights

The maximum possible common prefix cannot be longer than the first string in the input array. This allows us to initialize our candidate prefix with `strs[0]` and then only shorten it.
Rather than comparing all strings simultaneously, we can iteratively reduce a candidate prefix by comparing it against *each subsequent string*. If a candidate `P` is a common prefix for `S1...Sn`, and `P'` is the common prefix for `P` and `Sn+1`, then `P'` must be the common prefix for `S1...Sn+1`.
An early exit condition vastly improves efficiency: if at any point our candidate prefix shrinks to an empty string (meaning no common prefix exists for the strings examined so far), we can immediately return `""` without checking the rest of the array.

Complexity Analysis

Time Complexity: O(S)

Space Complexity: O(1)

Topics

This problem involves: Array, String, Trie.

Companies

Asked at: Accenture, Accolite, Adobe, Airbus SE, Amazon, Apple, Bloomberg, CEDCOSS, CME Group, Capgemini, Cognizant, DXC Technology, Deloitte, Deutsche Bank, Disney, EPAM Systems, Google, HCL, HSBC, IBM, Infosys, Jane Street, Meta, Microsoft, Nokia, Nvidia, Oracle, PhonePe, PornHub, PubMatic, Pwc, Revolut, Roblox, Roche, SAP, Samsung, TikTok, Turing, Uber, VMware, Visa, Walmart Labs, Wells Fargo, Yahoo, Yelp, ZScaler, Zoho, eBay, tcs.

Longest Common Prefix | LeetCode 14

Easy

Array String Trie

Time: O(S)Space: O(1)

Solution Code

Available in:

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;
    }
}

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Problem Info

Description

Problem 14: Longest Common Prefix - Detailed explanation and solution approaches.

Topics

Array String Trie

Companies

AccentureAccoliteAdobeAirbus SEAmazonAppleBloombergCEDCOSS

Stats

Difficulty:Easy

Languages:4

Companies:49

Problem #:14

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Handle edge cases: Check if the input array is empty or null. If so, return an empty string.
2
Step 2: Initialize: Assume the first string in the array is the initial common prefix.
3
Step 3: Iterate: Iterate through the remaining strings in the array.
4
Step 4: Compare: For each string, compare its characters with the current common prefix. If a mismatch is found at any position, shorten the common prefix by removing its last character.
5
Step 5: Repeat: Repeat step 4 until the end of the string is reached, or an empty prefix is found (no common prefix).
6
Step 6: Return: Return the final common prefix.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(S)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm iterates through the strings character by character. In the worst case, it might traverse all characters in all strings once. The space complexity is constant because it only uses a few variables to store the prefix and indices, regardless of input size.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Trie-based approach

Build a Trie (prefix tree) with all input strings. The longest common prefix can then be found by traversing the Trie until a node with more than one child is encountered.

Time: O(S), where S is the sum of lengths of all stringsSpace: O(S), to store the Trie

Trade-offs: Trie-based approach can be more efficient if you need to perform multiple longest common prefix queries on the same set of strings, as it preprocesses the data. However, it uses more space than the character-by-character comparison approach.

Divide and Conquer

Recursively find the common prefix of the first half and the second half of the array, then recursively find the common prefix of the two results.

Time: O(S * log(n)) where n is the number of strings and S is sum of all string lengthsSpace: O(log n) due to recursive calls

Trade-offs: Might offer slight performance improvements on very large datasets by reducing some redundant comparisons, but introduces overhead from recursion.

✨

Key Insights

1The maximum possible common prefix cannot be longer than the first string in the input array. This allows us to initialize our candidate prefix with `strs[0]` and then only shorten it.
2Rather than comparing all strings simultaneously, we can iteratively reduce a candidate prefix by comparing it against *each subsequent string*. If a candidate `P` is a common prefix for `S1...Sn`, and `P'` is the common prefix for `P` and `Sn+1`, then `P'` must be the common prefix for `S1...Sn+1`.
3An early exit condition vastly improves efficiency: if at any point our candidate prefix shrinks to an empty string (meaning no common prefix exists for the strings examined so far), we can immediately return `""` without checking the rest of the array.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty input array `strs`: The solution correctly handles this by returning an empty string.
Edge case 2: Array containing empty string: The solution correctly identifies this as a case with no common prefix and returns an empty string.
Edge case 3: All strings are identical: The solution correctly returns the whole string as the common prefix.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the edge case of an empty input array or an array with an empty string.

✗Common mistake 2: Inefficient comparison methods. Instead of directly comparing characters, some solutions might use inefficient string comparison functions repeatedly, increasing the time complexity.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: File systems: Finding the longest common prefix of file names in a directory can be helpful for organizing and searching files.

🏦Real-world scenario 2: Autocompletion: In search engines or text editors, the longest common prefix algorithm can help suggest autocomplete options based on user input.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 15, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 11

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 4

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Longest Common Prefix"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether string techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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