What is the time complexity of Reconstruct Original Digits from English?

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

What data structures are used to solve Reconstruct Original Digits from English?

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

What are the key insights for solving Reconstruct Original Digits from English?

Insight 1: Recognize unique letters that identify certain digits. For instance, 'z' is unique to 'zero', 'w' is unique to 'two', 'u' is unique to 'four', 'x' is unique to 'six', and 'g' is unique to 'eight'. Insight 2: After identifying the counts of digits using unique letters, use the remaining letters to deduce counts for the other digits. Subtract the counts of digits with shared letters.

Which companies ask LeetCode 423. Reconstruct Original Digits from English in interviews?

This problem is frequently asked at NetApp, Salesforce, Wix.

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Reconstruct Original Digits from English - LeetCode 423 Solution

Q: How to solve Reconstruct Original Digits from English?

The solution uses a counting approach. It first counts the frequency of each character in the input string. Then, it uses the unique characteristics of the English spellings of digits to determine the count of each digit. By identifying unique letters in certain digit names, we can calculate the counts of those digits directly. Then we subtract counts of digits with shared letters from the remaining letters to deduce the remaining digit counts. Finally, we construct the output string by appending each digit according to its calculated frequency and ordering it numerically.

Reconstruct Original Digits from English - Complete Solution Guide

Reconstruct Original Digits from English is LeetCode problem 423, 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 s containing an out-of-order English representation of digits 0-9 , return the digits in ascending order . Example 1: Input: s = "owoztneoer" Output: "012" Example 2: Input: s = "fviefuro" Output: "45" Constraints: 1 <= s.length <= 10 5 s[i] is one of the characters ["e","g","f","i","h","o","n","s","r","u","t","w","v","x","z"] . s is guaranteed to be valid.

Detailed Explanation

The problem asks us to reconstruct the original digits (0-9) from a given string `s`. The string `s` contains an out-of-order English representation of these digits. We need to return the digits in ascending order. The input string `s` is guaranteed to be valid, meaning it will always contain a valid combination of letters that can form digits from zero to nine. The constraints also tell us the string length and the allowed characters.

Solution Approach

The solution uses a counting approach. It first counts the frequency of each character in the input string. Then, it uses the unique characteristics of the English spellings of digits to determine the count of each digit. By identifying unique letters in certain digit names, we can calculate the counts of those digits directly. Then we subtract counts of digits with shared letters from the remaining letters to deduce the remaining digit counts. Finally, we construct the output string by appending each digit according to its calculated frequency and ordering it numerically.

Step-by-Step Algorithm

Step 1: Initialize a character count map (or array) to store the frequencies of each character in the input string `s`.
Step 2: Initialize an array `digit_counts` of size 10 to store the frequency of each digit (0-9).
Step 3: Identify and count digits with unique letters: zero ('z'), two ('w'), four ('u'), six ('x'), eight ('g'). Update the `digit_counts` array accordingly.
Step 4: Calculate the counts of the remaining digits by subtracting the counts of the already identified digits that share letters: three ('h' - 'eight'), five ('f' - 'four'), seven ('s' - 'six').
Step 5: Calculate the counts of the remaining digits: one ('o' - 'zero' - 'two' - 'four'), nine ('i' - 'five' - 'six' - 'eight').
Step 6: Build the resulting string by iterating through the `digit_counts` array. For each digit, append it to the result string as many times as its frequency indicates.
Step 7: Return the resulting string.

Key Insights

Insight 1: Recognize unique letters that identify certain digits. For instance, 'z' is unique to 'zero', 'w' is unique to 'two', 'u' is unique to 'four', 'x' is unique to 'six', and 'g' is unique to 'eight'.
Insight 2: After identifying the counts of digits using unique letters, use the remaining letters to deduce counts for the other digits. Subtract the counts of digits with shared letters.
Insight 3: Use a consistent order of deduction to avoid circular dependencies and incorrect counts. For example, calculate the counts of digits 0, 2, 4, 6, and 8 first because they have unique characters. After that derive 3, 5, and 7. Then finally find digits 1 and 9

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Hash Table, Math, String.

Companies

Asked at: NetApp, Salesforce, Wix.

Reconstruct Original Digits from English | LeetCode 423

Medium

Hash Table Math String

Time: O(n)Space: O(1)

Solution Code

Available in:

import java.util.HashMap;
import java.util.Map;

class Solution {
    public String originalDigits(String s) {
        Map<Character, Integer> charCounts = new HashMap<>();
        for (char c : s.toCharArray()) {
            charCounts.put(c, charCounts.getOrDefault(c, 0) + 1);
        }

        int[] digitCounts = new int[10];

        // Unique letters for certain digits
        digitCounts[0] = charCounts.getOrDefault('z', 0);  // "zero"
        digitCounts[2] = charCounts.getOrDefault('w', 0);  // "two"
        digitCounts[4] = charCounts.getOrDefault('u', 0);  // "four"
        digitCounts[6] = charCounts.getOrDefault('x', 0);  // "six"
        digitCounts[8] = charCounts.getOrDefault('g', 0);  // "eight"

        // Deriving counts for other digits based on letters that become unique
        digitCounts[3] = charCounts.getOrDefault('h', 0) - digitCounts[8];                 // "three" has 'h', "eight" also has 'h'
        digitCounts[5] = charCounts.getOrDefault('f', 0) - digitCounts[4];                 // "five" has 'f', "four" also has 'f'
        digitCounts[7] = charCounts.getOrDefault('s', 0) - digitCounts[6];                 // "seven" has 's', "six" also has 's'

        // Deriving counts for the remaining digits
        digitCounts[1] = charCounts.getOrDefault('o', 0) - digitCounts[0] - digitCounts[2] - digitCounts[4]; // "one"
        digitCounts[9] = charCounts.getOrDefault('i', 0) - digitCounts[5] - digitCounts[6] - digitCounts[8]; // "nine"

        StringBuilder result = new StringBuilder();
        for (int i = 0; i < 10; i++) {
            for (int j = 0; j < digitCounts[i]; j++) {
                result.append(i);
            }
        }

        return result.toString();
    }
}

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Problem Info

Description

Problem 423: Reconstruct Original Digits from English - Detailed explanation and solution approaches.

Topics

Hash Table Math String

Companies

NetAppSalesforceWix

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:423

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

7 steps

1
Step 1: Initialize a character count map (or array) to store the frequencies of each character in the input string `s`.
2
Step 2: Initialize an array `digit_counts` of size 10 to store the frequency of each digit (0-9).
3
Step 3: Identify and count digits with unique letters: zero ('z'), two ('w'), four ('u'), six ('x'), eight ('g'). Update the `digit_counts` array accordingly.
4
Step 4: Calculate the counts of the remaining digits by subtracting the counts of the already identified digits that share letters: three ('h' - 'eight'), five ('f' - 'four'), seven ('s' - 'six').
5
Step 5: Calculate the counts of the remaining digits: one ('o' - 'zero' - 'two' - 'four'), nine ('i' - 'five' - 'six' - 'eight').
6
Step 6: Build the resulting string by iterating through the `digit_counts` array. For each digit, append it to the result string as many times as its frequency indicates.
7
Step 7: Return the resulting string.

💡

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(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is dominated by the initial character counting loop which iterates through the input string of length n. Other operations like creating and filling the digit_counts array, performing arithmetic operations on character frequencies, and building the result string take O(1) or O(n) which becomes O(n) in total. The space complexity does not depend on the length of the input string, which uses constant space.

📖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

Sorting the string

An alternative approach would be to sort the input string alphabetically. This might make it easier to group the characters belonging to the same digits. However, you'd still need to deduce the digits and their counts based on the sorted character sequence.

Time: O(n log n), where n is the length of the string, due to the sorting operation.Space: O(1) or O(n) depending on the sorting algorithm (in-place vs. creating a new sorted string).

Trade-offs: This approach is generally less efficient than the counting approach because sorting takes O(n log n) time. The counting approach is more efficient with its O(n) time complexity. This sorting might be useful if further operations besides character counting need to be performed, but in this particular problem, the counting-based solution is superior.

✨

Key Insights

1Insight 1: Recognize unique letters that identify certain digits. For instance, 'z' is unique to 'zero', 'w' is unique to 'two', 'u' is unique to 'four', 'x' is unique to 'six', and 'g' is unique to 'eight'.
2Insight 2: After identifying the counts of digits using unique letters, use the remaining letters to deduce counts for the other digits. Subtract the counts of digits with shared letters.
3Insight 3: Use a consistent order of deduction to avoid circular dependencies and incorrect counts. For example, calculate the counts of digits 0, 2, 4, 6, and 8 first because they have unique characters. After that derive 3, 5, and 7. Then finally find digits 1 and 9

📚

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 code gracefully handles this case because the character counts will all be zero, resulting in an empty output string, which is a valid result.
Edge case 2: Input string with characters other than the allowed characters. The problem statement specifies that input is guaranteed to be valid, which will only contain letters that construct valid digits from 0 to 9. If the string contains invalid character, the frequencies will be affected, which may produce the wrong answer. The solution doesn't handle such invalid input, as it's assumed to be compliant with the constraints.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly deducting counts for digits sharing letters. For instance, forgetting to subtract the count of 'eight' from the count of 'h' when calculating the count of 'three'.

✗Common mistake 2: Not handling the order of deduction properly, which can lead to circular dependencies. For example, calculating count of digit 'one' prior to digits zero, two and four that affects the letter 'o'.

✗Common mistake 3: Forgetting to sort the final output numerically. Ensure the generated digits are in ascending order, which is a critical requirement of the problem.

✅

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: Data analysis and statistics: analyzing text-based data where character frequencies can indicate meaningful patterns or trends.

🏦Real-world scenario 2: Cryptography: Character frequency analysis can be used in simple cryptanalysis to break substitution ciphers.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: August 3, 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 13

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

@TechLeadJul 6

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

@DevExpert92Jun 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.

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 "Reconstruct Original Digits from English"?

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 math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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