What is the time complexity of Shuffle an Array?

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

What data structures are used to solve Shuffle an Array?

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

What are the key insights for solving Shuffle an Array?

Insight 1: The Fisher-Yates shuffle algorithm is the standard algorithm for generating a random permutation of a finite set in linear time. Insight 2: Preserving the original array is crucial to implementing the `reset()` function correctly. This requires storing a copy of the initial array.

Which companies ask LeetCode 384. Shuffle an Array in interviews?

This problem is frequently asked at J.P. Morgan, LinkedIn, Nvidia.

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Shuffle an Array - LeetCode 384 Solution

Shuffle an Array - Complete Solution Guide

Shuffle an Array is LeetCode problem 384, 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 an integer array nums , design an algorithm to randomly shuffle the array. All permutations of the array should be equally likely as a result of the shuffling. Implement the Solution class: Solution(int[] nums) Initializes the object with the integer array nums . int[] reset() Resets the array to its original configuration and returns it. int[] shuffle() Returns a random shuffling of the array. Example 1: Input ["Solution", "shuffle", "reset", "shuffle"] [[[1, 2, 3]], [], [], []] Output [n

Detailed Explanation

The problem requires designing a class that can shuffle an array of integers randomly, reset the array to its original state, and do both efficiently. The core requirement is that all permutations of the array must have an equal probability of being generated by the shuffle function. The input is an integer array `nums`. The class should have three methods: `Solution(nums)` to initialize the object, `reset()` to return the original array, and `shuffle()` to return a randomly shuffled array.

Solution Approach

The provided solution implements the Fisher-Yates shuffle algorithm within the `shuffle()` method and maintains a copy of the original array to implement the `reset()` method. The `Solution` class stores two copies of the input array: `_original` (the initial configuration) and `_array` (the current configuration, which gets shuffled). The `reset()` method restores `_array` from `_original`. The `shuffle()` method iterates through the array, swapping each element with a randomly chosen element from the remaining unsorted portion of the array.

Step-by-Step Algorithm

Step 1: In the constructor, `Solution(nums)`, create a copy of the input array `nums` and store it in `_original`. Also, create another copy and store it in `_array`. This ensures the original array remains unchanged and `_array` can be shuffled and reset.
Step 2: The `reset()` method simply copies the content of `_original` back into `_array` and returns `_array`.
Step 3: The `shuffle()` method implements the Fisher-Yates shuffle. Iterate from the end of the array to the beginning.
Step 4: For each index `i`, generate a random index `j` between `0` and `i` (inclusive).
Step 5: Swap the elements at indices `i` and `j` in `_array`.
Step 6: After iterating through the entire array, return the shuffled `_array`.

Key Insights

Insight 1: The Fisher-Yates shuffle algorithm is the standard algorithm for generating a random permutation of a finite set in linear time.
Insight 2: Preserving the original array is crucial to implementing the `reset()` function correctly. This requires storing a copy of the initial array.
Insight 3: Using a separate `_array` to store the current state enables efficient shuffling and resetting without modifying the original input array directly.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Math, Design, Randomized.

Companies

Asked at: J.P. Morgan, LinkedIn, Nvidia.

Shuffle an Array | LeetCode 384

Medium

Array Math Design Randomized

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

Solution Code

Available in:

import java.util.Arrays;
import java.util.Random;

class Solution {

    private int[] _original;
    private int[] _array;
    private Random random;

    public Solution(int[] nums) {
        _original = Arrays.copyOf(nums, nums.length);
        _array = Arrays.copyOf(nums, nums.length);
        random = new Random();
    }
    
    public int[] reset() {
        _array = Arrays.copyOf(_original, _original.length);
        return _array;
    }
    
    public int[] shuffle() {
        int n = _array.length;
        for (int i = 0; i < n; i++) {
            int randomIndex = random.nextInt(n);
            int temp = _array[i];
            _array[i] = _array[randomIndex];
            _array[randomIndex] = temp;
        }
        return _array;
    }
}

/**
 * Your Solution object will be instantiated and called as such:
 * Solution obj = new Solution(nums);
 * int[] param_1 = obj.reset();
 * int[] param_2 = obj.shuffle();
 */

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Problem Info

Description

Problem 384: Shuffle an Array - Detailed explanation and solution approaches.

Topics

Array Math Design Randomized

Companies

J.P. MorganLinkedInNvidia

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:384

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

6 steps

1
Step 1: In the constructor, `Solution(nums)`, create a copy of the input array `nums` and store it in `_original`. Also, create another copy and store it in `_array`. This ensures the original array remains unchanged and `_array` can be shuffled and reset.
2
Step 2: The `reset()` method simply copies the content of `_original` back into `_array` and returns `_array`.
3
Step 3: The `shuffle()` method implements the Fisher-Yates shuffle. Iterate from the end of the array to the beginning.
4
Step 4: For each index `i`, generate a random index `j` between `0` and `i` (inclusive).
5
Step 5: Swap the elements at indices `i` and `j` in `_array`.
6
Step 6: After iterating through the entire array, return the shuffled `_array`.

💡

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?

The time complexity is derived from the single loop used in `shuffle()` and the element-by-element copy in `reset()`. The space complexity stems from storing two arrays that are copies of the input. These arrays occupy space proportional to the input size '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

Using Collections.shuffle in Java/ std::random_shuffle in C++ / random.shuffle in Python

Leverage the built-in shuffle functions provided by the language's standard library. This would involve copying the original array and then using the standard library function to shuffle the copy.

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

Trade-offs: This approach simplifies the code and potentially leverages optimized implementations of shuffle in the standard library. However, it might not provide as much control over the random number generation process.

Generating Random Indices and Sorting

Assign a random number to each element in the array and then sort the array based on these random numbers. This creates a random order.

Time: O(n log n) due to the sorting operationSpace: O(n) to store the random numbers or potentially in-place depending on sort.

Trade-offs: Simpler to conceptualize, but less efficient than Fisher-Yates shuffle. Avoid this approach due to the higher time complexity.

✨

Key Insights

1Insight 1: The Fisher-Yates shuffle algorithm is the standard algorithm for generating a random permutation of a finite set in linear time.
2Insight 2: Preserving the original array is crucial to implementing the `reset()` function correctly. This requires storing a copy of the initial array.
3Insight 3: Using a separate `_array` to store the current state enables efficient shuffling and resetting without modifying the original input array directly.

📚

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: Empty input array. The code works correctly for an empty array as the loops won't execute, and the methods will return the empty arrays accordingly.
Edge case 2: Array with one element. The Fisher-Yates shuffle will not change the array in this case, which is the desired behavior.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Modifying the original input array directly instead of making a copy. This would prevent the `reset()` method from functioning correctly.

✗Common mistake 2: Generating random numbers outside the correct range for the Fisher-Yates shuffle. This could lead to biased shuffles, where some permutations are more likely than others.

✗Common mistake 3: Forgetting to re-seed the random number generator when using `rand()` in C, which can result in the same shuffle being generated every time the program runs.

✅

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: Shuffling a deck of cards in a card game simulation. The algorithm ensures a fair and random distribution of cards.

🏦Real-world scenario 2: Randomizing a playlist of songs in a music player. The shuffle algorithm guarantees that the songs are played in a random order without repetition until all songs have been played.

🎮Real-world scenario 3: Randomly assigning users to different experimental groups in A/B testing.

💡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

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

⚠️ 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: June 25, 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

❓

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 techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

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 "Shuffle an Array"?

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

🤖 Need help with this problem?