What is the time complexity of Repeated DNA Sequences?

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

What data structures are used to solve Repeated DNA Sequences?

This problem uses Hash Table, String, Bit Manipulation, Sliding Window, Rolling Hash, Hash Function. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Repeated DNA Sequences?

Insight 1: A sliding window of size 10 can be used to iterate through all possible 10-letter sequences in the DNA string. Insight 2: Hashing can be used to efficiently store and check for repeated sequences. Using a direct string comparison for every substring would lead to higher time complexity. A rolling hash helps update the hash value in O(1) time.

Which companies ask LeetCode 187. Repeated DNA Sequences in interviews?

This problem is frequently asked at Grammarly, LinkedIn, Tesla.

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Repeated DNA Sequences - LeetCode 187 Solution

Repeated DNA Sequences - Complete Solution Guide

Repeated DNA Sequences is LeetCode problem 187, 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

The DNA sequence is composed of a series of nucleotides abbreviated as 'A' , 'C' , 'G' , and 'T' . For example, "ACGAATTCCG" is a DNA sequence . When studying DNA , it is useful to identify repeated sequences within the DNA. Given a string s that represents a DNA sequence , return all the 10 -letter-long sequences (substrings) that occur more than once in a DNA molecule. You may return the answer in any order . Example 1: Input: s = "AAAAACCCCCAAAAACCCCCCAAAAAGGGTTT" Output: ["AAAAACCCCC","CCCCC

Detailed Explanation

The problem requires us to find all 10-letter-long sequences (substrings) that occur more than once in a given DNA sequence (string) consisting of characters 'A', 'C', 'G', and 'T'. The function should return a list of these repeated sequences, and the order of the sequences in the output list doesn't matter.

Solution Approach

The solution utilizes a sliding window of length 10 and a hash set to efficiently identify repeated DNA sequences. Each 10-letter sequence is converted into an integer representation using bit manipulation. The algorithm iterates through the DNA string, calculating the hash value for each 10-letter sequence. If a sequence's hash value is already present in the `seen` set, it means the sequence has been encountered before, and it's added to the `output` set. Otherwise, the sequence's hash value is added to the `seen` set. Using sets ensures that each repeated sequence is added to the result only once.

Step-by-Step Algorithm

Step 1: Initialize variables: `L = 10` (length of sequences to find), `n` (length of the input string), `to_int` (a mapping of nucleotides to integers: A->0, C->1, G->2, T->3), `seen` (a set to store encountered sequences' hash values), `output` (a set to store the repeated sequences themselves), and `mask` (used for the rolling hash).
Step 2: Handle the edge case where the input string's length is less than or equal to `L`. If so, return an empty list.
Step 3: Calculate the initial hash value for the first 10-letter sequence.
Step 4: Add the initial hash value to the `seen` set.
Step 5: Iterate through the remaining characters of the string (from index 10 to the end). For each character:
Step 6: Update the hash value using a rolling hash technique. This involves left-shifting the current hash value by 2 bits, applying the `mask` to keep the hash within the required bit range, and then adding the integer representation of the current character.
Step 7: Check if the current hash value is already present in the `seen` set. If it is, add the corresponding sequence (substring) to the `output` set.
Step 8: If the hash value is not in `seen`, add it to the `seen` set.
Step 9: Convert the `output` set to a list and return the list of repeated DNA sequences.

Key Insights

Insight 1: A sliding window of size 10 can be used to iterate through all possible 10-letter sequences in the DNA string.
Insight 2: Hashing can be used to efficiently store and check for repeated sequences. Using a direct string comparison for every substring would lead to higher time complexity. A rolling hash helps update the hash value in O(1) time.
Insight 3: Bit manipulation can be used to represent each nucleotide (A, C, G, T) with 2 bits (00, 01, 10, 11 respectively), which allows us to represent a 10-letter sequence with a 20-bit integer.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, String, Bit Manipulation, Sliding Window, Rolling Hash, Hash Function.

Companies

Asked at: Grammarly, LinkedIn, Tesla.

Repeated DNA Sequences | LeetCode 187

Medium

Hash Table String Bit Manipulation Sliding Window Rolling Hash Hash Function

Time: O(n)Space: O(n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

class Solution {
    public List<String> findRepeatedDnaSequences(String s) {
        int L = 10;
        int n = s.length();
        if (n <= L) {
            return new ArrayList<>();
        }

        java.util.Map<Character, Integer> to_int = new java.util.HashMap<>();
        to_int.put('A', 0);
        to_int.put('C', 1);
        to_int.put('G', 2);
        to_int.put('T', 3);

        Set<Integer> seen = new HashSet<>();
        Set<String> output = new HashSet<>();

        int mask = (1 << (2 * L)) - 1;

        int current_hash = 0;
        for (int i = 0; i < L; i++) {
            current_hash = (current_hash << 2) | to_int.get(s.charAt(i));
        }
        seen.add(current_hash);

        for (int i = L; i < n; i++) {
            current_hash = ((current_hash << 2) & mask) | to_int.get(s.charAt(i));

            if (seen.contains(current_hash)) {
                output.add(s.substring(i - L + 1, i + 1));
            } else {
                seen.add(current_hash);
            }
        }

        return new ArrayList<>(output);
    }
}

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Problem Info

Description

Problem 187: Repeated DNA Sequences - Detailed explanation and solution approaches.

Topics

Hash Table String Bit Manipulation Sliding Window Rolling Hash Hash Function

Companies

GrammarlyLinkedInTesla

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:187

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

9 steps

1
Step 1: Initialize variables: `L = 10` (length of sequences to find), `n` (length of the input string), `to_int` (a mapping of nucleotides to integers: A->0, C->1, G->2, T->3), `seen` (a set to store encountered sequences' hash values), `output` (a set to store the repeated sequences themselves), and `mask` (used for the rolling hash).
2
Step 2: Handle the edge case where the input string's length is less than or equal to `L`. If so, return an empty list.
3
Step 3: Calculate the initial hash value for the first 10-letter sequence.
4
Step 4: Add the initial hash value to the `seen` set.
5
Step 5: Iterate through the remaining characters of the string (from index 10 to the end). For each character:
6
Step 6: Update the hash value using a rolling hash technique. This involves left-shifting the current hash value by 2 bits, applying the `mask` to keep the hash within the required bit range, and then adding the integer representation of the current character.
7
Step 7: Check if the current hash value is already present in the `seen` set. If it is, add the corresponding sequence (substring) to the `output` set.
8
Step 8: If the hash value is not in `seen`, add it to the `seen` set.
9
Step 9: Convert the `output` set to a list and return the list of repeated DNA sequences.

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the single loop that iterates through the input string. Each operation within the loop (bit manipulation, hash set lookups, and insertions) takes constant time on average. The space complexity stems from the sets `seen` and `output`, which in the worst case may store a number of unique sequences proportional to the length of the input string.

📖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

Direct String Comparison

Instead of using hashing, one could directly compare each 10-letter sequence with all other 10-letter sequences in the string.

Time: O(n^2), where n is the length of the input string, because we need to compare n-9 sequences against each other.Space: O(n) to store the result. Potentially O(1) if done in-place, but that would complicate the algorithm significantly.

Trade-offs: This approach is simpler to implement but has a significantly higher time complexity, making it less efficient for large input strings. Should be avoided if the input string can be large.

Using a HashMap to count occurrences

Store the count of each 10 letter sequence in a hashmap and iterate through the map to find the ones whose count is greater than 1.

Time: O(n), where n is the length of the input stringSpace: O(n), where n is the length of the input string because we will store all possible 10-letter sequence

Trade-offs: This approach is fairly easy to implement compared to the bit manipulation one. The bit manipulation technique is used as optimization here.

✨

Key Insights

1Insight 1: A sliding window of size 10 can be used to iterate through all possible 10-letter sequences in the DNA string.
2Insight 2: Hashing can be used to efficiently store and check for repeated sequences. Using a direct string comparison for every substring would lead to higher time complexity. A rolling hash helps update the hash value in O(1) time.
3Insight 3: Bit manipulation can be used to represent each nucleotide (A, C, G, T) with 2 bits (00, 01, 10, 11 respectively), which allows us to represent a 10-letter sequence with a 20-bit integer.

📚

Key Terms Explained

For Students

Hash Table

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

Sliding Window

A moving "window" over data to process subsets efficiently.

String

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

Edge Cases

Edge case 1: Input string length is less than 10. The solution correctly handles this by returning an empty list.
Edge case 2: The input string contains only one unique 10-letter sequence. The solution will return an empty list since the sequence needs to appear *more than once*.
Edge case 3: The input string is very long, potentially causing hash collisions. While the sets provide constant average time, hash collisions could degrade performance towards O(n^2) in a pathological case; however, well-distributed hash functions generally mitigate this concern in practice.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the edge case where the input string's length is less than 10, leading to incorrect behavior or errors.

✗Common mistake 2: Using string comparison directly without hashing, leading to a quadratic time complexity which will time out for larger inputs.

✗Common mistake 3: Not using a rolling hash, which makes the solution less efficient than it could be. Recalculating hash value for each substring requires recomputing the hash from scratch each time.

✅

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: Bioinformatics research, where identifying repeated DNA sequences can help understand gene function, identify genetic markers, or analyze viral genomes.

🏦Real-world scenario 2: Data compression algorithms, where identifying repeated patterns in data can be used to reduce the storage space required.

💡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

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

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

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

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 8, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

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

@CodeNinjaJul 6

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

@TechLeadJun 29

❓

Frequently Asked Questions

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.

What is the sliding window technique for string problems?

Sliding window maintains a "window" of characters with two pointers. Expand the right pointer to include characters, shrink from left when window violates constraints. Useful for substring problems, anagrams, and longest/shortest substring with properties.

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 "Repeated DNA Sequences"?

For this medium-level Hash Table 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.

🤖 Need help with this problem?