What is the time complexity of Minimum Right Shifts to Sort the Array?

The optimal solution has a time complexity of O(n^2).

What data structures are used to solve Minimum Right Shifts to Sort the Array?

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

What are the key insights for solving Minimum Right Shifts to Sort the Array?

Insight 1: The problem involves cyclical shifts. We need to consider the wrap-around effect when shifting elements. Insight 2: Brute-force is a viable approach for smaller input sizes (as indicated by constraints). We can iterate through all possible numbers of shifts and check if the resulting array is sorted.

Which companies ask LeetCode 2855. Minimum Right Shifts to Sort the Array in interviews?

This problem is frequently asked at Accenture.

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Minimum Right Shifts to Sort the Array - LeetCode 2855 Solution

Minimum Right Shifts to Sort the Array - Complete Solution Guide

Minimum Right Shifts to Sort the Array is LeetCode problem 2855, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3.

Problem Statement

You are given a 0-indexed array nums of length n containing distinct positive integers. Return the minimum number of right shifts required to sort nums and -1 if this is not possible. A right shift is defined as shifting the element at index i to index (i + 1) % n , for all indices. Example 1: Input: nums = [3,4,5,1,2] Output: 2 Explanation: After the first right shift, nums = [2,3,4,5,1]. After the second right shift, nums = [1,2,3,4,5]. Now nums is sorted; therefore the answer is 2. Example 2:

Detailed Explanation

The problem asks you to find the minimum number of right shifts needed to sort a given array of distinct positive integers. A right shift moves each element one position to the right, wrapping around from the last position to the first. The goal is to determine the smallest number of such shifts that result in a sorted array. If it's impossible to sort the array using right shifts, the function should return -1.

Solution Approach

The provided Python code uses a brute-force approach. It iterates through a range of possible right shifts (from 0 up to the array length). For each shift count, it creates a copy of the original array and performs the specified number of right shifts. Finally, it checks if the shifted array is sorted. If a sorted array is found, the corresponding shift count is returned. If no sorted array is found after trying all possible shift counts, it returns -1.

Step-by-Step Algorithm

Step 1: Iterate through possible shift counts (from 0 to n-1, where n is the array length).
Step 2: For each shift count, create a copy of the input array.
Step 3: Perform the right shifts: Move the last element to the beginning, and shift all other elements one position to the right.
Step 4: Check if the shifted array is sorted using `all(temp[i] <= temp[i+1] for i in range(n-1))`.
Step 5: If the array is sorted, return the current shift count.
Step 6: If no sorted array is found after trying all shift counts, return -1.

Key Insights

Insight 1: The problem involves cyclical shifts. We need to consider the wrap-around effect when shifting elements.
Insight 2: Brute-force is a viable approach for smaller input sizes (as indicated by constraints). We can iterate through all possible numbers of shifts and check if the resulting array is sorted.
Insight 3: The array contains distinct elements. This simplifies the check for sorted order – we only need to verify that each element is less than or equal to its successor.

Complexity Analysis

Time Complexity: O(n^2)

Space Complexity: O(n)

Topics

This problem involves: Array.

Companies

Asked at: Accenture.

Minimum Right Shifts to Sort the Array | LeetCode 2855

Easy

Array

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

Solution Code

Available in:

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Problem Info

Description

Problem 2855: Minimum Right Shifts to Sort the Array - Detailed explanation and solution approaches.

Topics

Array

Companies

Accenture

Stats

Difficulty:Easy

Languages:2

Companies:1

Problem #:2855

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: Iterate through possible shift counts (from 0 to n-1, where n is the array length).
2
Step 2: For each shift count, create a copy of the input array.
3
Step 3: Perform the right shifts: Move the last element to the beginning, and shift all other elements one position to the right.
4
Step 4: Check if the shifted array is sorted using `all(temp[i] <= temp[i+1] for i in range(n-1))`.
5
Step 5: If the array is sorted, return the current shift count.
6
Step 6: If no sorted array is found after trying all shift counts, return -1.

💡

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^2)

🐢 Quadratic - Gets slow with large inputs. Consider optimization!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The outer loop iterates n times (for each possible shift). The inner loop (shifting the array) takes O(n) time in each iteration of the outer loop. Therefore, the overall time complexity is O(n * n) = O(n^2). The space complexity is O(n) because we create a copy of the array in each iteration.

📖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

Optimized Approach (using a sorted copy)

Create a sorted copy of the input array. Then, for each possible shift, compare the shifted array with the sorted copy to see if they match. This avoids the need for a separate sorted check in each iteration.

Time: O(n log n + n^2)Space: O(n)

Trade-offs: While sorting adds O(n log n) complexity initially, this approach might be slightly faster for large n if the cost of the comparison outweighs the repeated sorted checks in the original solution.

✨

Key Insights

1Insight 1: The problem involves cyclical shifts. We need to consider the wrap-around effect when shifting elements.
2Insight 2: Brute-force is a viable approach for smaller input sizes (as indicated by constraints). We can iterate through all possible numbers of shifts and check if the resulting array is sorted.
3Insight 3: The array contains distinct elements. This simplifies the check for sorted order – we only need to verify that each element is less than or equal to its successor.

📚

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: The array is already sorted. The solution correctly returns 0 shifts.
Edge case 2: It's impossible to sort the array using right shifts. The solution correctly returns -1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect implementation of the right shift operation. Failing to handle the wrap-around correctly.

✗Common mistake 2: Not handling the case where the array cannot be sorted with right shifts. Forgetting to return -1 in this scenario.

✅

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: Circular buffer management: Optimizing data arrangement in a circular buffer to improve access times.

🏦Real-world scenario 2: Cryptography: Analyzing the effects of cyclical shifts on data sequences to understand the strength of certain encryption 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.

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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 3, 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

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

@DevExpert92Jul 14

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

@AlgoMasterJul 7

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

@InterviewProJun 30

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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 "Minimum Right Shifts to Sort the Array"?

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

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