What is the time complexity of Letter Combinations of a Phone Number?

The optimal solution has a time complexity of O(4^n).

What data structures are used to solve Letter Combinations of a Phone Number?

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

What are the key insights for solving Letter Combinations of a Phone Number?

Insight 1: Backtracking is suitable for generating combinations. Since we need to explore all possible combinations, backtracking is a natural choice. Insight 2: A hash table (or map) is useful for mapping digits to their corresponding letters. This allows for quick and easy access to the letters associated with each digit.

Which companies ask LeetCode 17. Letter Combinations of a Phone Number in interviews?

This problem is frequently asked at Adobe, Amazon, Apple, Autodesk, Bloomberg and 29 more companies.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Letter Combinations of a Phone Number - LeetCode 17 Solution

Q: How to solve Letter Combinations of a Phone Number?

The solution uses a backtracking algorithm to explore all possible letter combinations. It iterates through the digits of the input string. For each digit, it retrieves the corresponding letters from a predefined mapping. It then recursively calls itself, adding each possible letter to the current combination. When the recursion reaches the end of the digit string, the current combination is added to the result list.

Letter Combinations of a Phone Number - Complete Solution Guide

Letter Combinations of a Phone Number is LeetCode problem 17, 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

Given a string containing digits from 2-9 inclusive, return all possible letter combinations that the number could represent. Return the answer in any order . A mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters. Example 1: Input: digits = "23" Output: ["ad","ae","af","bd","be","bf","cd","ce","cf"] Example 2: Input: digits = "" Output: [] Example 3: Input: digits = "2" Output: ["a","b","c"] Constraints: 0 <= digits.length <=

Detailed Explanation

The problem asks us to generate all possible letter combinations from a given string of digits, where each digit corresponds to a set of letters according to a standard telephone keypad. The input is a string of digits from '2' to '9', and the output is a list of all possible letter combinations that can be formed by mapping each digit to its corresponding letters and concatenating them. The order of the combinations in the output doesn't matter. The constraints specify that the input digit string can be empty or have a length between 1 and 4.

Solution Approach

The solution uses a backtracking algorithm to explore all possible letter combinations. It iterates through the digits of the input string. For each digit, it retrieves the corresponding letters from a predefined mapping. It then recursively calls itself, adding each possible letter to the current combination. When the recursion reaches the end of the digit string, the current combination is added to the result list.

Step-by-Step Algorithm

Step 1: Create a mapping (hash table) that stores the letters corresponding to each digit from '2' to '9'.
Step 2: Initialize an empty list (or array) to store the resulting letter combinations.
Step 3: Define a recursive backtracking function that takes an index and a current path (combination) as input.
Step 4: The base case for the recursion is when the index reaches the length of the input digit string. In this case, add the current path (combination) to the result list and return.
Step 5: For the current digit at the given index, retrieve the corresponding letters from the mapping.
Step 6: Iterate through each letter in the retrieved set of letters.
Step 7: Recursively call the backtracking function with the index incremented by 1 and the current path extended by the current letter.
Step 8: Start the backtracking process with an initial index of 0 and an empty path (combination).
Step 9: Return the list of resulting letter combinations.

Key Insights

Insight 1: Backtracking is suitable for generating combinations. Since we need to explore all possible combinations, backtracking is a natural choice.
Insight 2: A hash table (or map) is useful for mapping digits to their corresponding letters. This allows for quick and easy access to the letters associated with each digit.
Insight 3: The depth of the backtracking tree will be equal to the length of the input digit string.

Complexity Analysis

Time Complexity: O(4^n)

Space Complexity: O(n)

Topics

This problem involves: Hash Table, String, Backtracking.

Companies

Asked at: Adobe, Amazon, Apple, Autodesk, Bloomberg, Chime, Cisco, Citadel, DE Shaw, Dropbox, Epic Systems, Flexport, FreshWorks, Goldman Sachs, IBM, J.P. Morgan, LinkedIn, Meta, Microsoft, Morgan Stanley, Nextdoor, Oracle, Pinterest, ServiceNow, Siemens, Swiggy, Tesla, Trexquant, Twilio, Twitch, Uber, Yahoo, Zoho, Zopsmart.

Letter Combinations of a Phone Number | LeetCode 17

Medium

Hash Table String Backtracking

Time: O(4^n)Space: O(n)

Solution Code

Available in:

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

class Solution {
    public List<String> letterCombinations(String digits) {
        if (digits == null || digits.length() == 0) {
            return new ArrayList<>();
        }

        Map<String, String> phoneMap = new HashMap<>();
        phoneMap.put("2", "abc");
        phoneMap.put("3", "def");
        phoneMap.put("4", "ghi");
        phoneMap.put("5", "jkl");
        phoneMap.put("6", "mno");
        phoneMap.put("7", "pqrs");
        phoneMap.put("8", "tuv");
        phoneMap.put("9", "wxyz");

        List<String> result = new ArrayList<>();

        backtrack(0, "", digits, phoneMap, result);

        return result;
    }

    private void backtrack(int index, String path, String digits, Map<String, String> phoneMap, List<String> result) {
        if (index == digits.length()) {
            result.add(path);
            return;
        }

        String possibleLetters = phoneMap.get(String.valueOf(digits.charAt(index)));
        for (int i = 0; i < possibleLetters.length(); i++) {
            backtrack(index + 1, path + possibleLetters.charAt(i), digits, phoneMap, result);
        }
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 17: Letter Combinations of a Phone Number - Detailed explanation and solution approaches.

Topics

Hash Table String Backtracking

Companies

AdobeAmazonAppleAutodeskBloombergChimeCiscoCitadel

Stats

Difficulty:Medium

Languages:4

Companies:34

Problem #:17

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: Create a mapping (hash table) that stores the letters corresponding to each digit from '2' to '9'.
2
Step 2: Initialize an empty list (or array) to store the resulting letter combinations.
3
Step 3: Define a recursive backtracking function that takes an index and a current path (combination) as input.
4
Step 4: The base case for the recursion is when the index reaches the length of the input digit string. In this case, add the current path (combination) to the result list and return.
5
Step 5: For the current digit at the given index, retrieve the corresponding letters from the mapping.
6
Step 6: Iterate through each letter in the retrieved set of letters.
7
Step 7: Recursively call the backtracking function with the index incremented by 1 and the current path extended by the current letter.
8
Step 8: Start the backtracking process with an initial index of 0 and an empty path (combination).
9
Step 9: Return the list of resulting letter combinations.

💡

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(4^n)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is O(4^n) because, in the worst case (digits string consisting only of 7 and 9), each digit has 4 possible letters and we explore all combinations. The space complexity is O(n) mainly from the recursion depth, which cannot exceed the number of digits. Each recursive call stores the path, which has a length of at most n.

📖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

Iterative Approach (using a queue)

An iterative approach can be used by employing a queue. Start with an empty string in the queue. Iterate through the digits. For each digit, dequeue each element in the queue, and append each possible letter of the current digit to it, enqueuing the new string. Repeat this process until all digits are processed.

Time: O(4^n)Space: O(4^n)

Trade-offs: The iterative approach avoids recursion, which can be useful for very long input strings to avoid stack overflow errors. However, it might be slightly less intuitive to implement and can have a higher constant factor in space complexity due to storing intermediate combinations in the queue.

✨

Key Insights

1Insight 1: Backtracking is suitable for generating combinations. Since we need to explore all possible combinations, backtracking is a natural choice.
2Insight 2: A hash table (or map) is useful for mapping digits to their corresponding letters. This allows for quick and easy access to the letters associated with each digit.
3Insight 3: The depth of the backtracking tree will be equal to the length of the input digit string.

📚

Key Terms Explained

For Students

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: Empty input string. The solution correctly handles this by returning an empty list.
Edge case 2: Input string containing '0' or '1'. The problem states digits are in the range '2'-'9', the provided solutions assume the input is valid based on constraints.
Edge case 3: Input string with length 1. The solution correctly generates the letters corresponding to the single digit.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting the base case in the backtracking recursion. This can lead to infinite recursion and a stack overflow error.

✗Common mistake 2: Not properly handling the edge case of an empty input string, leading to incorrect results or errors.

✗Common mistake 3: Failing to create a copy of the current combination when adding it to the result list in languages like C. Modifying the `combination` string after adding it can corrupt the result.

✅

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 mobile keyboards. When typing a number on a phone keyboard, the system can use this algorithm to suggest possible words or phrases that could be formed from the number sequence.

🏦Real-world scenario 2: Password generation. While not cryptographically secure, this algorithm could be used to generate a set of possible passwords based on a sequence of digits and their corresponding letters.

💡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

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ 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 18, 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 14

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

@CodeNinjaJul 7

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

@TechLeadJun 30

❓

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 "Letter Combinations of a Phone Number"?

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?