What is the time complexity of Largest Number?

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

What data structures are used to solve Largest Number?

This problem uses Array, String, Greedy, Sorting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Largest Number?

Insight 1: A standard sorting algorithm won't work directly because we need to compare numbers based on how they would appear when concatenated. For example, 30 should come after 3 because '330' is larger than '303'. Insight 2: The core idea is to treat the numbers as strings and define a custom comparison function. This function compares two strings `x` and `y` by concatenating them in both orders (`x+y` and `y+x`) and comparing the resulting strings. The string that results in a larger concatenation should come first.

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Largest Number - LeetCode 179 Solution

Q: Which companies ask LeetCode 179. Largest Number in interviews?

This problem is frequently asked at Accenture, Goldman Sachs, Graviton, Huawei, Myntra and 12 more companies.

Largest Number - Complete Solution Guide

Largest Number is LeetCode problem 179, 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 list of non-negative integers nums , arrange them such that they form the largest number and return it. Since the result may be very large, so you need to return a string instead of an integer. Example 1: Input: nums = [10,2] Output: "210" Example 2: Input: nums = [3,30,34,5,9] Output: "9534330" Constraints: 1 <= nums.length <= 100 0 <= nums[i] <= 10 9

Detailed Explanation

The problem asks us to take a list of non-negative integers and arrange them in such a way that they form the largest possible number. The result needs to be returned as a string because the resulting number might be very large and exceed the maximum value representable by integer data types. For example, given `[10, 2]`, we should return "210" because 210 > 102. Given `[3, 30, 34, 5, 9]`, we should return "9534330".

Solution Approach

The solution involves converting the integer array to an array of strings. Then, it sorts the array of strings using a custom comparison function. The comparison function determines the order based on whether concatenating two strings in one order results in a larger number than concatenating them in the reverse order. Finally, the sorted strings are joined together to form the largest possible number. A final check ensures that if the resulting string starts with '0', then the string represents 0, which is then returned.

Step-by-Step Algorithm

Step 1: Convert the array of integers `nums` into an array of strings `numsStr`.
Step 2: Sort the `numsStr` array using a custom comparison function. This function compares two strings `x` and `y` by checking if `x + y` is greater than `y + x`. This custom sorting orders the numbers so they produce the largest possible number when concatenated.
Step 3: Concatenate the sorted strings in `numsStr` into a single string `largestNumStr`.
Step 4: Check if the resulting `largestNumStr` starts with '0'. If it does, it means all the input numbers were essentially zeros (e.g., [0,0,0]). In this case, return '0'. Otherwise, return the `largestNumStr`.

Key Insights

Insight 1: A standard sorting algorithm won't work directly because we need to compare numbers based on how they would appear when concatenated. For example, 30 should come after 3 because '330' is larger than '303'.
Insight 2: The core idea is to treat the numbers as strings and define a custom comparison function. This function compares two strings `x` and `y` by concatenating them in both orders (`x+y` and `y+x`) and comparing the resulting strings. The string that results in a larger concatenation should come first.
Insight 3: Handle the edge case where all numbers are zero. In this case, the output should be '0', not a string of multiple zeros.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, String, Greedy, Sorting.

Companies

Asked at: Accenture, Goldman Sachs, Graviton, Huawei, Myntra, Nykaa, Oracle, Paytm, Salesforce, ServiceNow, Siemens, Visa, Works Applications, Zalando, Zoho, josh technology, tcs.

Largest Number | LeetCode 179

Medium

Array String Greedy Sorting

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

Solution Code

Available in:

import java.util.Arrays;
import java.util.Comparator;

class Solution {
    public String largestNumber(int[] nums) {
        String[] numsStr = new String[nums.length];
        for (int i = 0; i < nums.length; i++) {
            numsStr[i] = String.valueOf(nums[i]);
        }

        Arrays.sort(numsStr, new Comparator<String>() {
            @Override
            public int compare(String x, String y) {
                String order1 = x + y;
                String order2 = y + x;
                return order2.compareTo(order1);
            }
        });

        StringBuilder largestNumStr = new StringBuilder();
        for (String numStr : numsStr) {
            largestNumStr.append(numStr);
        }

        if (largestNumStr.charAt(0) == '0') {
            return "0";
        } else {
            return largestNumStr.toString();
        }
    }
}

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Problem Info

Description

Problem 179: Largest Number - Detailed explanation and solution approaches.

Topics

Array String Greedy Sorting

Companies

AccentureGoldman SachsGravitonHuaweiMyntraNykaaOraclePaytm

Stats

Difficulty:Medium

Languages:4

Companies:17

Problem #:179

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

4 steps

1
Step 1: Convert the array of integers `nums` into an array of strings `numsStr`.
2
Step 2: Sort the `numsStr` array using a custom comparison function. This function compares two strings `x` and `y` by checking if `x + y` is greater than `y + x`. This custom sorting orders the numbers so they produce the largest possible number when concatenated.
3
Step 3: Concatenate the sorted strings in `numsStr` into a single string `largestNumStr`.
4
Step 4: Check if the resulting `largestNumStr` starts with '0'. If it does, it means all the input numbers were essentially zeros (e.g., [0,0,0]). In this case, return '0'. Otherwise, return the `largestNumStr`.

💡

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 log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by sorting the array of strings, which typically uses a comparison-based sorting algorithm like mergesort or quicksort, resulting in O(n log n) time. The space complexity stems from creating a new string array of size `n` to store the string representations of the numbers. String concatenation can also require O(n) space in some implementations as well.

📖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

Radix Sort

Instead of using comparison sort, radix sort could be used which in some scenarios can perform better for specific input ranges. However implementing the comparator for concatenations for Radix sort is complex

Time: O(kn) in the best case where k is the average string lengthSpace: O(n + k)

Trade-offs: The advantage would be potentially better performance with highly specific input distributions. Disadvantage is far greater code complexity

✨

Key Insights

1Insight 1: A standard sorting algorithm won't work directly because we need to compare numbers based on how they would appear when concatenated. For example, 30 should come after 3 because '330' is larger than '303'.
2Insight 2: The core idea is to treat the numbers as strings and define a custom comparison function. This function compares two strings `x` and `y` by concatenating them in both orders (`x+y` and `y+x`) and comparing the resulting strings. The string that results in a larger concatenation should come first.
3Insight 3: Handle the edge case where all numbers are zero. In this case, the output should be '0', not a string of multiple zeros.

📚

Key Terms Explained

For Students

Array

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

Greedy Algorithm

Making the best choice at each step without looking ahead.

String

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

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: All numbers are zero (e.g., `[0, 0, 0]`). The solution correctly handles this case by returning '0' instead of '000'. The check at the end ensures that if the result starts with zero, '0' is returned if the entire number is zero.
Edge case 2: Single-digit numbers mixed with multi-digit numbers (e.g., `[3, 30, 34, 5, 9]`). The custom comparison function ensures that numbers are ordered correctly to maximize the resulting concatenated string.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Using a standard sorting algorithm without the custom comparison function. This will lead to incorrect results because the numbers are not compared based on their concatenated values.

✗Common mistake 2: Not handling the edge case where all numbers are zero. This will lead to a result with leading zeros.

✗Common mistake 3: Integer overflow. When the resulting number is very large, it may exceed the maximum value that can be represented by an integer. This is why the solution returns a string.

✅

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: Creating a unique identifier by combining multiple numerical attributes. For example, generating a unique ID for a product by concatenating its category code, manufacturer ID, and serial number, where the order is determined by the largest possible ID.

🏦Real-world scenario 2: Forming the largest possible version number from a list of version components. For instance, constructing a software version number by combining major, minor, and patch versions to represent the latest stable release.

💡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

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

⚠️ 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 27, 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.

@TechLeadJul 13

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

@DevExpert92Jul 6

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 29

❓

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.

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 "Largest Number"?

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

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