What is the time complexity of Add to Array-Form of Integer?

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

What is the space complexity of Add to Array-Form of Integer?

The space complexity is O(max(n, log(k))).

What data structures are used to solve Add to Array-Form of Integer?

This problem uses Array, Math. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Add to Array-Form of Integer?

Insight 1: Simulating addition like we do it by hand, starting from the least significant digit (rightmost part of the array) is crucial. Insight 2: Handling the carry-over from each digit addition is essential for obtaining the correct sum.

Which companies ask LeetCode 989. Add to Array-Form of Integer in interviews?

This problem is frequently asked at Avito, ByteDance, Zoho.

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Add to Array-Form of Integer - LeetCode 989 Solution

Add to Array-Form of Integer - Complete Solution Guide

Add to Array-Form of Integer is LeetCode problem 989, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

The array-form of an integer num is an array representing its digits in left to right order. For example, for num = 1321 , the array form is [1,3,2,1] . Given num , the array-form of an integer, and an integer k , return the array-form of the integer num + k . Example 1: Input: num = [1,2,0,0], k = 34 Output: [1,2,3,4] Explanation: 1200 + 34 = 1234 Example 2: Input: num = [2,7,4], k = 181 Output: [4,5,5] Explanation: 274 + 181 = 455 Example 3: Input: num = [2,1,5], k = 806 Output: [1,0,2,1] Expl

Detailed Explanation

The problem asks us to add an integer `k` to an integer represented as an array of digits `num`. The `num` array represents the number in array form, meaning each digit is stored in the array from left to right (most significant to least significant digit). We need to return the array form of the sum of `num` and `k`. For instance, if `num = [1, 2, 0, 0]` and `k = 34`, we treat `num` as the integer 1200. The sum is 1200 + 34 = 1234. The desired output is the array form of 1234, which is `[1, 2, 3, 4]`. The constraints are that the array `num` has between 1 and 10000 elements, each element is a digit between 0 and 9, `num` doesn't have leading zeros (except if the number is 0), and `k` is between 1 and 10000.

Solution Approach

The solution simulates the manual addition process. We iterate through the array `num` from right to left (least significant digit to most significant digit) and simultaneously process the digits of `k` (also from right to left). At each step, we add the corresponding digit from `num`, the last digit of `k`, and the carry-over from the previous addition. The sum's last digit becomes part of the result, and the carry-over is updated. We continue this process until we've processed all digits of `num`, all digits of `k`, and there's no carry-over left.

Step-by-Step Algorithm

Step 1: Initialize an empty list (or array) to store the result.
Step 2: Initialize a carry variable to 0.
Step 3: Iterate from the end of the `num` array towards the beginning (right to left).
Step 4: In each iteration, extract the current digit from `num` (if there are digits left in `num`, otherwise, use 0).
Step 5: Extract the last digit from `k` (if `k` is greater than 0, otherwise, use 0). This can be done by taking `k % 10`.
Step 6: Add the digit from `num`, the last digit of `k`, and the carry together.
Step 7: Append the last digit of the sum (sum % 10) to the beginning of the result list.
Step 8: Update the carry by taking the integer division of the sum by 10 (sum // 10).
Step 9: Divide `k` by 10 (integer division) to move to the next digit of `k`.
Step 10: Repeat steps 4-9 until all digits in `num` have been processed, `k` is 0, and there is no remaining carry.
Step 11: If there's a remaining carry after the loop, append it to the beginning of the result list.
Step 12: Return the result list.

Key Insights

Insight 1: Simulating addition like we do it by hand, starting from the least significant digit (rightmost part of the array) is crucial.
Insight 2: Handling the carry-over from each digit addition is essential for obtaining the correct sum.
Insight 3: We need to account for cases where `k` has more digits than `num` or vice versa, and for any remaining carry after processing both `num` and `k`.

Complexity Analysis

Time Complexity: O(max(n, log(k)))

Space Complexity: O(max(n, log(k)))

Topics

This problem involves: Array, Math.

Companies

Asked at: Avito, ByteDance, Zoho.

Add to Array-Form of Integer | LeetCode 989

Easy

Array Math

Time: O(max(n, log(k)))Space: O(max(n, log(k)))

Solution Code

Available in:

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

class Solution {
    public List<Integer> addToArrayForm(int[] num, int k) {
        List<Integer> result = new ArrayList<>();
        int n = num.length;
        int carry = 0;
        for (int i = n - 1; i >= 0; i--) {
            int sum = num[i] + k % 10 + carry;
            k /= 10;
            carry = sum / 10;
            result.add(sum % 10);
        }
        while (k > 0) {
            int sum = k % 10 + carry;
            k /= 10;
            carry = sum / 10;
            result.add(sum % 10);
        }
        if (carry > 0) {
            result.add(carry);
        }
        Collections.reverse(result);
        return result;
    }
}

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Problem Info

Description

Problem 989: Add to Array-Form of Integer - Detailed explanation and solution approaches.

Topics

Array Math

Companies

AvitoByteDanceZoho

Stats

Difficulty:Easy

Languages:4

Companies:3

Problem #:989

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

12 steps

1
Step 1: Initialize an empty list (or array) to store the result.
2
Step 2: Initialize a carry variable to 0.
3
Step 3: Iterate from the end of the `num` array towards the beginning (right to left).
4
Step 4: In each iteration, extract the current digit from `num` (if there are digits left in `num`, otherwise, use 0).
5
Step 5: Extract the last digit from `k` (if `k` is greater than 0, otherwise, use 0). This can be done by taking `k % 10`.
6
Step 6: Add the digit from `num`, the last digit of `k`, and the carry together.
7
Step 7: Append the last digit of the sum (sum % 10) to the beginning of the result list.
8
Step 8: Update the carry by taking the integer division of the sum by 10 (sum // 10).
9
Step 9: Divide `k` by 10 (integer division) to move to the next digit of `k`.
10
Step 10: Repeat steps 4-9 until all digits in `num` have been processed, `k` is 0, and there is no remaining carry.
11
Step 11: If there's a remaining carry after the loop, append it to the beginning of the result list.
12
Step 12: Return the result list.

💡

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(max(n, log(k)))

💾

Space Complexity

O(max(n, log(k)))

📝

Why?

The time complexity is determined by the while loop, which iterates at most `max(n, log(k))` times because we are iterating through either the array `num` or the digits of `k`. Similarly, the space complexity is determined by the size of the `result` list, which in the worst case will be equal to the number of digits of the final sum, which is at most `max(n, log(k)) + 1`.

📖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

Convert Array to Integer, Add, and Convert Back

Convert the array `num` to an integer, add it to `k`, and then convert the sum back to an array of digits.

Time: O(n) to convert array to integer, O(log(sum)) to convert the sum to an array (where sum is num + k). Potentially O(n) or O(log10(sum)) if the conversion from number to array is carefully implementedSpace: O(log(sum)), since we are creating a new array of size equal to the number of digits in the sum.

Trade-offs: This approach is conceptually simpler, but it's not practical due to potential integer overflow issues if `num` represents a large number. It is best to avoid this approach.

✨

Key Insights

1Insight 1: Simulating addition like we do it by hand, starting from the least significant digit (rightmost part of the array) is crucial.
2Insight 2: Handling the carry-over from each digit addition is essential for obtaining the correct sum.
3Insight 3: We need to account for cases where `k` has more digits than `num` or vice versa, and for any remaining carry after processing both `num` and `k`.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: `num` is [0] and `k` is a non-zero number. The algorithm correctly adds `k` to 0 and returns the array form of `k`.
Edge case 2: `k` has more digits than `num`. The algorithm handles this by continuing the addition process until `k` becomes 0.
Edge case 3: There is a carry-over after processing all digits of `num` and `k`. The algorithm correctly adds the remaining carry to the beginning of the result array.
Edge case 4: num is very large (e.g., 10000 digits) and k is also large. The solution handles this efficiently without converting num to an integer, which would lead to integer overflow.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle the carry-over properly, which can lead to incorrect sums.

✗Common mistake 2: Not considering the case where `k` has more digits than `num` or there's a remaining carry after processing both.

✗Common mistake 3: Attempting to convert the array `num` to an integer directly, which can lead to integer overflow issues for large arrays.

✗Common mistake 4: Incorrectly reversing the result list/array.

✅

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: Implementing arithmetic operations on very large numbers that exceed the capacity of standard integer data types in programming languages. Libraries for big integer arithmetic often use similar techniques.

🏦Real-world scenario 2: Cryptography algorithms often involve arithmetic operations on large numbers represented as arrays of digits or bits. This problem demonstrates a fundamental building block for such algorithms.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ 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: August 29, 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 should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

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 "Add to Array-Form of Integer"?

For this easy-level Array 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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