What is the time complexity of Find the Length of the Longest Common Prefix?

The optimal solution has a time complexity of O(n*m).

What is the space complexity of Find the Length of the Longest Common Prefix?

The space complexity is O(n*m).

What data structures are used to solve Find the Length of the Longest Common Prefix?

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

What are the key insights for solving Find the Length of the Longest Common Prefix?

Insight 1: Converting integers to strings simplifies the prefix comparison because string comparison by character is a straightforward operation. Insight 2: Using a Trie data structure can efficiently store prefixes of numbers from one array, allowing for fast prefix searching when comparing with numbers from the other array.

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Find the Length of the Longest Common Prefix - LeetCode 3043 Solution

Q: Which companies ask LeetCode 3043. Find the Length of the Longest Common Prefix in interviews?

This problem is frequently asked at Capital One, Coinbase, Databricks, Roblox, The Trade Desk and 2 more companies.

Find the Length of the Longest Common Prefix - Complete Solution Guide

Find the Length of the Longest Common Prefix is LeetCode problem 3043, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given two arrays with positive integers arr1 and arr2 . A prefix of a positive integer is an integer formed by one or more of its digits, starting from its leftmost digit. For example, 123 is a prefix of the integer 12345 , while 234 is not . A common prefix of two integers a and b is an integer c , such that c is a prefix of both a and b . For example, 5655359 and 56554 have common prefixes 565 and 5655 while 1223 and 43456 do not have a common prefix. You need to find the length of the

Detailed Explanation

The problem asks us to find the length of the longest common prefix between pairs of numbers, where one number comes from the array `arr1` and the other from `arr2`. A prefix of a number is a substring that starts from the beginning of the number (e.g., '12' is a prefix of '1234', but '23' is not). The goal is to iterate through all possible pairs of numbers (one from `arr1` and one from `arr2`), find the longest common prefix for each pair, and then return the length of the *longest* of all these common prefixes. If no pair shares any prefix, the function should return 0. The input arrays contain positive integers, and the prefix must be composed of digits starting from the leftmost digit of each integer.

Solution Approach

The provided solution uses a Trie data structure to efficiently find the longest common prefix. First, the integer arrays `arr1` and `arr2` are converted into sets of strings. A Trie is then constructed using strings from the smaller set. After the Trie is built, each string from the larger set is searched within the Trie to find the longest matching prefix. The maximum length encountered during these searches is returned as the result.

Step-by-Step Algorithm

Step 1: Convert the integer arrays `arr1` and `arr2` into sets of strings (`build_set` and `search_set`). Using sets removes any duplicate entries.
Step 2: Check which set is smaller (`build_set` or `search_set`) and assign it to `build_set`. The smaller set is used to build the Trie for optimization as it generally results in smaller Trie structures.
Step 3: Create a Trie data structure. Each node in the Trie represents a digit, and paths from the root to other nodes represent prefixes.
Step 4: Insert all strings from `build_set` into the Trie. Each digit of each string is added as a child node in the Trie.
Step 5: Iterate through each string in `search_set` and search for the longest matching prefix within the Trie.
Step 6: During the Trie search, keep track of the length of the current matching prefix. If a character in the `search_set` string is not found in the Trie, the search for that string stops.
Step 7: Update the `max_length` with the maximum prefix length found so far.
Step 8: Return the `max_length`, which represents the length of the longest common prefix among all pairs.

Key Insights

Insight 1: Converting integers to strings simplifies the prefix comparison because string comparison by character is a straightforward operation.
Insight 2: Using a Trie data structure can efficiently store prefixes of numbers from one array, allowing for fast prefix searching when comparing with numbers from the other array.
Insight 3: Converting the input arrays to sets prevents duplicate calculations and allows to build the Trie with unique prefixes only

Complexity Analysis

Time Complexity: O(n*m)

Space Complexity: O(n*m)

Topics

This problem involves: Array, Hash Table, String, Trie.

Companies

Asked at: Capital One, Coinbase, Databricks, Roblox, The Trade Desk, Visa, ZipRecruiter.

Find the Length of the Longest Common Prefix | LeetCode 3043

Medium

Array Hash Table String Trie

Time: O(n*m)Space: O(n*m)

Solution Code

Available in:

import java.util.HashSet;
import java.util.Set;
import java.util.HashMap;
import java.util.Map;

class Solution {
    public int longestCommonPrefix(int[] arr1, int[] arr2) {
        Set<String> build_set = new HashSet<>();
        Set<String> search_set = new HashSet<>();

        for (int x : arr1) {
            build_set.add(String.valueOf(x));
        }

        for (int x : arr2) {
            search_set.add(String.valueOf(x));
        }

        if (build_set.size() > search_set.size()) {
            Set<String> temp = build_set;
            build_set = search_set;
            search_set = temp;
        }

        class TrieNode {
            Map<Character, TrieNode> children;

            public TrieNode() {
                this.children = new HashMap<>();
            }
        }

        TrieNode root = new TrieNode();

        for (String s_num : build_set) {
            TrieNode curr = root;
            for (char char_ : s_num.toCharArray()) {
                if (!curr.children.containsKey(char_)) {
                    curr.children.put(char_, new TrieNode());
                }
                curr = curr.children.get(char_);
            }
        }

        int max_length = 0;

        for (String s_num : search_set) {
            TrieNode curr = root;
            int current_length = 0;
            for (char char_ : s_num.toCharArray()) {
                if (curr.children.containsKey(char_)) {
                    curr = curr.children.get(char_);
                    current_length += 1;
                } else {
                    break;
                }
            }
            max_length = Math.max(max_length, current_length);
        }

        return max_length;
    }
}

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Problem Info

Description

Problem 3043: Find the Length of the Longest Common Prefix - Detailed explanation and solution approaches.

Topics

Array Hash Table String Trie

Companies

Capital OneCoinbaseDatabricksRobloxThe Trade DeskVisaZipRecruiter

Stats

Difficulty:Medium

Languages:4

Companies:7

Problem #:3043

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

8 steps

1
Step 1: Convert the integer arrays `arr1` and `arr2` into sets of strings (`build_set` and `search_set`). Using sets removes any duplicate entries.
2
Step 2: Check which set is smaller (`build_set` or `search_set`) and assign it to `build_set`. The smaller set is used to build the Trie for optimization as it generally results in smaller Trie structures.
3
Step 3: Create a Trie data structure. Each node in the Trie represents a digit, and paths from the root to other nodes represent prefixes.
4
Step 4: Insert all strings from `build_set` into the Trie. Each digit of each string is added as a child node in the Trie.
5
Step 5: Iterate through each string in `search_set` and search for the longest matching prefix within the Trie.
6
Step 6: During the Trie search, keep track of the length of the current matching prefix. If a character in the `search_set` string is not found in the Trie, the search for that string stops.
7
Step 7: Update the `max_length` with the maximum prefix length found so far.
8
Step 8: Return the `max_length`, which represents the length of the longest common prefix among all pairs.

💡

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(n*m)

💾

Space Complexity

O(n*m)

📝

Why?

The time complexity is driven by set creation and the Trie operations (insertion and search). The space complexity is determined by the Trie's size, which depends on the number and length of the prefixes stored within it. Using sets before building the trie improves both the average and worst case performance and reduces the number of trie nodes.

📖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

Brute Force

Iterate through all pairs of numbers (one from each array) and compare their prefixes character by character to find the longest common prefix for each pair. Then, find the maximum of these lengths.

Time: O(N*M*K), where N and M are the sizes of the arrays, and K is the maximum length of a number (as a string).Space: O(1). Constant extra space is used.

Trade-offs: The brute force approach is simpler to implement but less efficient than the Trie-based approach for larger input sizes. It avoids the overhead of building and maintaining a Trie data structure, but has a significantly higher time complexity.

✨

Key Insights

1Insight 1: Converting integers to strings simplifies the prefix comparison because string comparison by character is a straightforward operation.
2Insight 2: Using a Trie data structure can efficiently store prefixes of numbers from one array, allowing for fast prefix searching when comparing with numbers from the other array.
3Insight 3: Converting the input arrays to sets prevents duplicate calculations and allows to build the Trie with unique prefixes only

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

String

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

Edge Cases

Edge case 1: One or both arrays are empty. The sets will be empty, and the Trie will not be built, leading to a max_length of 0, which is the correct result.
Edge case 2: No common prefixes exist between any pair of numbers. The Trie search will always fail, and `max_length` will remain 0.
Edge case 3: Overlapping values in the arrays. The conversion to sets ensures that we only process unique values. For instance arr1 = [1,1,1] and arr2=[10, 100]. The sets will become arr1={1} and arr2={10, 100} so Trie will only contain 1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not converting the integers to strings. String-based prefix comparison is much easier than trying to manipulate integers to extract prefixes.

✗Common mistake 2: Incorrectly calculating prefix length during the Trie search. It's essential to increment the length only when a matching character is found.

✗Common mistake 3: Forgetting to handle the case where no common prefix exists (returning 0).

✅

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: Autocompletion in search bars. The Trie data structure can be used to store a dictionary of words, and as the user types, the Trie can quickly suggest words with matching prefixes.

🏦Real-world scenario 2: Routing tables in networking. IP addresses often share common prefixes, and Trie-like structures can be used to efficiently store and search for the longest matching prefix to route network packets.

🎮Real-world scenario 3: Data compression algorithms. Prefix coding (like Huffman coding) relies on finding common prefixes to represent data more efficiently.

💡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

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ 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: November 11, 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

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 14

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

@TechLeadJul 7

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

@DevExpert92Jun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find the Length of the Longest Common Prefix"?

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

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