What is the time complexity of Sort an Array?

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

What data structures are used to solve Sort an Array?

This problem uses Array, Divide and Conquer, Sorting, Heap (Priority Queue), Merge Sort, Bucket Sort, Radix Sort, Counting Sort. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Sort an Array?

Insight 1: The problem asks for O(n log n) sorting, which eliminates options like bubble sort, insertion sort, and selection sort which are O(n^2). Insight 2: Heap sort can be implemented in-place, satisfying the requirement of smallest space complexity.

Which companies ask LeetCode 912. Sort an Array in interviews?

This problem is frequently asked at Hive, Infosys.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Sort an Array - LeetCode 912 Solution

Sort an Array - Complete Solution Guide

Sort an Array is LeetCode problem 912, 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 array of integers nums , sort the array in ascending order and return it. You must solve the problem without using any built-in functions in O(nlog(n)) time complexity and with the smallest space complexity possible. Example 1: Input: nums = [5,2,3,1] Output: [1,2,3,5] Explanation: After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5). Example 2: Input: nums = [5,1,1,2,0,0] O

Detailed Explanation

The problem requires sorting an array of integers in ascending order. The constraint is to achieve this in O(n log n) time complexity without using built-in sorting functions. The input is an array `nums` of integers, and the output should be the sorted array. The length of the array and the range of numbers within the array are also specified in the constraints.

Solution Approach

The provided solution utilizes the Heap Sort algorithm to sort the array. Heap sort involves two main phases: building a max heap from the input array and then repeatedly extracting the maximum element from the heap and placing it at the end of the array. This process effectively sorts the array in ascending order because each time we extract the maximum element, we are left with a smaller heap, and the extracted element is placed at its correct position in the sorted array.

Step-by-Step Algorithm

Step 1: Build a max heap from the input array. This is done by iterating through the array from the middle towards the beginning and calling the `heapify` function on each element.
Step 2: The `heapify` function ensures that the subtree rooted at a given index satisfies the max heap property (the parent is greater than or equal to its children).
Step 3: After building the max heap, repeatedly extract the maximum element (which is at the root of the heap) and swap it with the last element of the unsorted portion of the array.
Step 4: Reduce the size of the heap by one and call `heapify` on the root to maintain the max heap property.
Step 5: Repeat steps 3 and 4 until the entire array is sorted.

Key Insights

Insight 1: The problem asks for O(n log n) sorting, which eliminates options like bubble sort, insertion sort, and selection sort which are O(n^2).
Insight 2: Heap sort can be implemented in-place, satisfying the requirement of smallest space complexity.
Insight 3: Understanding the heapify process is crucial for building and maintaining the heap structure.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Divide and Conquer, Sorting, Heap (Priority Queue), Merge Sort, Bucket Sort, Radix Sort, Counting Sort.

Companies

Asked at: Hive, Infosys.

Sort an Array | LeetCode 912

Medium

Array Divide and Conquer Sorting Heap (Priority Queue)Merge Sort Bucket Sort Radix Sort Counting Sort

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

Solution Code

Available in:

class Solution {
    public int[] sortArray(int[] nums) {
        
        int n = nums.length;

        // Build a max heap
        for (int i = n / 2 - 1; i >= 0; i--) {
            heapify(nums, n, i);
        }

        // One by one extract an element from the heap
        for (int i = n - 1; i > 0; i--) {
            // Move current root to end
            int temp = nums[0];
            nums[0] = nums[i];
            nums[i] = temp;

            // call max heapify on the reduced heap
            heapify(nums, i, 0);
        }
        return nums;
    }

    void heapify(int arr[], int n, int i) {
        int largest = i; // Initialize largest as root
        int l = 2 * i + 1; // left = 2*i + 1
        int r = 2 * i + 2; // right = 2*i + 2

        // If left child is larger than root
        if (l < n && arr[l] > arr[largest])
            largest = l;

        // If right child is larger than largest so far
        if (r < n && arr[r] > arr[largest])
            largest = r;

        // If largest is not root
        if (largest != i) {
            int swap = arr[i];
            arr[i] = arr[largest];
            arr[largest] = swap;

            // Recursively heapify the affected sub-tree
            heapify(arr, n, largest);
        }
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 912: Sort an Array - Detailed explanation and solution approaches.

Topics

Array Divide and Conquer Sorting Heap (Priority Queue)Merge Sort Bucket Sort Radix Sort Counting Sort

Companies

HiveInfosys

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:912

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: Build a max heap from the input array. This is done by iterating through the array from the middle towards the beginning and calling the `heapify` function on each element.
2
Step 2: The `heapify` function ensures that the subtree rooted at a given index satisfies the max heap property (the parent is greater than or equal to its children).
3
Step 3: After building the max heap, repeatedly extract the maximum element (which is at the root of the heap) and swap it with the last element of the unsorted portion of the array.
4
Step 4: Reduce the size of the heap by one and call `heapify` on the root to maintain the max heap property.
5
Step 5: Repeat steps 3 and 4 until the entire array is sorted.

💡

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(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

Building the max heap takes O(n) time. Extracting the maximum element and heapifying takes O(log n) time, and this is repeated n times. Therefore, the overall time complexity is O(n + n log n) which simplifies to O(n log n). The space complexity is O(1) because heap sort is performed in-place, meaning it does not require any extra space proportional to the input size. The `heapify` function uses recursion, but the depth of the recursion is logarithmic, contributing only O(log n) stack space which is generally considered negligible for in-place sorting algorithms.

📖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

Merge Sort

Merge sort is a divide-and-conquer algorithm that recursively divides the array into smaller subarrays, sorts them, and then merges them back together. It provides a guaranteed O(n log n) time complexity.

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

Trade-offs: Merge sort has a guaranteed O(n log n) time complexity but requires O(n) extra space for the merging process. Heap sort, on the other hand, has the same time complexity but operates in-place (O(1) space). Therefore, if space is a major concern, heap sort is preferable. If a stable sort is needed, merge sort is preferred.

Quick Sort

Quick sort is also a divide-and-conquer algorithm, but it sorts the array in-place by partitioning it around a pivot element. Its average-case time complexity is O(n log n).

Time: O(n log n) average, O(n^2) worst caseSpace: O(log n) average, O(n) worst case

Trade-offs: Quick sort is generally faster than heap sort in practice due to lower constant factors, but it has a worst-case time complexity of O(n^2), while heap sort guarantees O(n log n). Quick sort's space complexity depends on the pivot selection strategy and recursion depth.

✨

Key Insights

1Insight 1: The problem asks for O(n log n) sorting, which eliminates options like bubble sort, insertion sort, and selection sort which are O(n^2).
2Insight 2: Heap sort can be implemented in-place, satisfying the requirement of smallest space complexity.
3Insight 3: Understanding the heapify process is crucial for building and maintaining the heap structure.

📚

Key Terms Explained

For Students

Array

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

Sorting

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

Edge Cases

Edge case 1: Empty array or an array with only one element. The code handles this correctly since the loops won't execute, and the array is returned as is.
Edge case 2: Array with duplicate elements. The code correctly sorts arrays with duplicate elements because the heapify process ensures the heap property is maintained even with duplicates.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect implementation of the `heapify` function, leading to an incorrect heap structure and, consequently, an incorrect sorted array.

✗Common mistake 2: Building a min heap instead of a max heap. This would result in sorting the array in descending order instead of ascending order.

✅

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: Priority queues are often implemented using heaps, which are fundamental to heap sort. They are used in task scheduling, Dijkstra's algorithm (shortest path), and Huffman coding (data compression).

🏦Real-world scenario 2: Heap sort can be used in situations where memory is limited and guaranteed O(n log n) sorting is needed, like embedded systems or certain database sorting operations.

💡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 13, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

❓

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 "Sort 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 divide and conquer techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?