What is the time complexity of Keep Multiplying Found Values by Two?

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

What data structures are used to solve Keep Multiplying Found Values by Two?

This problem uses Array, Hash Table, Sorting, Simulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Keep Multiplying Found Values by Two?

Insight 1: Using a HashSet (or set in Python) to efficiently check for the presence of a number in the array is crucial for optimizing the search time. Linear search in each iteration would lead to a less efficient solution. Insight 2: The problem's iterative nature lends itself well to a `while` loop, where the loop continues as long as the current `original` value is found in the array.

Which companies ask LeetCode 2154. Keep Multiplying Found Values by Two in interviews?

This problem is frequently asked at Goldman Sachs.

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Keep Multiplying Found Values by Two - LeetCode 2154 Solution

Keep Multiplying Found Values by Two - Complete Solution Guide

Keep Multiplying Found Values by Two is LeetCode problem 2154, 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

You are given an array of integers nums . You are also given an integer original which is the first number that needs to be searched for in nums . You then do the following steps: If original is found in nums , multiply it by two (i.e., set original = 2 * original ). Otherwise, stop the process. Repeat this process with the new number as long as you keep finding the number. Return the final value of original . Example 1: Input: nums = [5,3,6,1,12], original = 3 Output: 24 Explanation: - 3 is fou

Detailed Explanation

The problem asks you to simulate a process where you start with an integer `original` and repeatedly search for it in an array `nums`. If found, you double `original`; otherwise, you stop. The final value of `original` after this process is the output. The input consists of an integer array `nums` and an integer `original`. The output is a single integer representing the final value of `original` after the described process.

Solution Approach

The solution uses a HashSet (or set) to store the elements of the input array `nums`. This allows for O(1) lookup time when checking if `original` exists in the array. The `while` loop continues as long as `original` is present in the HashSet. Inside the loop, `original` is multiplied by 2, and the process repeats. Once `original` is no longer found in the HashSet, the loop terminates, and the final value of `original` is returned.

Step-by-Step Algorithm

Step 1: Create a HashSet (or set) and insert all elements of the `nums` array into it.
Step 2: Initialize a `while` loop condition that checks if `original` is present in the HashSet.
Step 3: Inside the loop, multiply `original` by 2.
Step 4: After the multiplication, check again if the updated `original` is present in the HashSet. Continue the loop if it's present.
Step 5: If the loop terminates (meaning `original` is not found in the HashSet), return the final value of `original`.

Key Insights

Insight 1: Using a HashSet (or set in Python) to efficiently check for the presence of a number in the array is crucial for optimizing the search time. Linear search in each iteration would lead to a less efficient solution.
Insight 2: The problem's iterative nature lends itself well to a `while` loop, where the loop continues as long as the current `original` value is found in the array.
Insight 3: No significant edge cases exist. The constraints ensure the input values are positive integers, preventing issues with negative numbers or zero.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, Sorting, Simulation.

Companies

Asked at: Goldman Sachs.

Keep Multiplying Found Values by Two | LeetCode 2154

Easy

Array Hash Table Sorting Simulation

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

Solution Code

Available in:

class Solution {
    public int findFinalValue(int[] nums, int original) {
        java.util.HashSet<Integer> set = new java.util.HashSet<>();
        for (int num : nums) {
            set.add(num);
        }
        while (set.contains(original)) {
            original *= 2;
        }
        return original;
    }
}

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Problem Info

Description

Problem 2154: Keep Multiplying Found Values by Two - Detailed explanation and solution approaches.

Topics

Array Hash Table Sorting Simulation

Companies

Goldman Sachs

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2154

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

5 steps

1
Step 1: Create a HashSet (or set) and insert all elements of the `nums` array into it.
2
Step 2: Initialize a `while` loop condition that checks if `original` is present in the HashSet.
3
Step 3: Inside the loop, multiply `original` by 2.
4
Step 4: After the multiplication, check again if the updated `original` is present in the HashSet. Continue the loop if it's present.
5
Step 5: If the loop terminates (meaning `original` is not found in the HashSet), return the final value of `original`.

💡

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?

Building the HashSet takes O(n) time, where n is the length of `nums`. The while loop iterates at most log₂(1000) ≈ 10 times (as original can at most be multiplied by 2 ten times to reach the upper bound of 1000). The lookup in the HashSet within the while loop takes O(1) time. Therefore, the overall time complexity is dominated by the HashSet creation, resulting in O(n). The space complexity is O(n) due to the HashSet storing all elements of `nums`.

📖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

Linear Search (without HashSet)

Iterate through `nums` in each iteration of the `while` loop to check for the presence of `original`. This approach avoids using a HashSet.

Time: O(n^2)Space: O(1)

Trade-offs: This approach is less efficient due to the nested loop structure, leading to a quadratic time complexity. It's only preferable if memory is extremely constrained and the input array is relatively small.

✨

Key Insights

1Insight 1: Using a HashSet (or set in Python) to efficiently check for the presence of a number in the array is crucial for optimizing the search time. Linear search in each iteration would lead to a less efficient solution.
2Insight 2: The problem's iterative nature lends itself well to a `while` loop, where the loop continues as long as the current `original` value is found in the array.
3Insight 3: No significant edge cases exist. The constraints ensure the input values are positive integers, preventing issues with negative numbers or zero.

📚

Key Terms Explained

For Students

Array

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

Hash Table

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

Sorting

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

Edge Cases

Edge case 1: The `original` value is not found in `nums`. The solution correctly handles this by exiting the `while` loop and returning the initial `original` value.
Edge case 2: `original` is found multiple times in `nums`, and successive doublings keep it within `nums`. The solution correctly handles this by repeatedly doubling until it's no longer found.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to check for the presence of `original` in the array before multiplying it by 2. This could lead to incorrect results.

✗Common mistake 2: Using inefficient searching (like linear search repeatedly) which leads to O(n^2) time complexity instead of using a hash table (set) for O(n) time complexity

✅

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: Simulating a process of doubling a value based on certain conditions (e.g., doubling the investment amount if a certain condition is met in a financial model).

🏦Real-world scenario 2: Modeling a system where a quantity is updated based on its presence in a set of available resources (e.g., doubling the production rate of an item if sufficient raw materials are available).

💡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

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ 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 22, 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.

@TechLeadMay 29

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

@DevExpert92May 22

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Keep Multiplying Found Values by Two"?

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

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