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[Solved] Sort the Circular Rotated Array in O(n) Time| Algorithm | Code

Aniruddha Chaudhari/2838/0
CodePython

Problem statement: You have given a circular rotated array. Write a program to sort the circular rotated array.

Example

Input (Circular Rotated Array): [3, 4, 5, 1, 2] 

Output (Sorted Array): [1, 2, 3, 4, 5]

This question was asked in one of Byju’s coding interview. Basically, they asked to find the given element in a circular rotated array in order of O(log(n) time.

To solve this problem, you have to rotate the array and then do the binary search.

Let’s continue with the sorting circular rotated array.

Table of Contents

  • Algorithm
  • Explanation
  • Python Program
  • Complexity

Algorithm

  • Find the index of the smallest element in the array (says index_smallest).
  • Reverse all the left side elements of the smallest element in the array (excluding element at index_smallest)
  • Reverse all the right side elements of the smallest element in the array (including element at index_smallest)
  • Now, reverse the complete array.

Explanation

  • Let’s take an example of a circular rotated array [3, 4, 5, 1, 2].
  • Smallest element is at position “3” (index_smallest = 3).
  • Reverse all elements from index “0” to “2”. The resultant array will be [5, 4, 3, 1, 2].
  • Reverse all elements from index “3” to “4”. The resultant array will be [5, 4, 3, 2, 1].
  • Now reverse all the elements in the array. You will get a complete sorted array as [1, 2, 3, 4, 5].

You can solve this problem in any programming language of your choice.

Python Program

In Python, you can reverse the list using extended slice syntax (just one line code). But, in competitive programming, you will be encourage to write your own logic.

Code

# function to reverse the array list
def reverse_array(arr, start=0, end=0):
    if end == 0:
        end = len(arr)-1
    while start<=end:
        temp = arr[start]
        arr[start] = arr[end]
        arr[end] = temp
        start += 1
        end -= 1
    
# function to sort cicular roated array list
def sort_circular_rotated_array(arr):
    index_smallest = 0
    for i in range(len(arr)-1):
        if arr[i]>arr[i+1]:
            index_smallest = i+1
            break

    reverse_array(arr=arr, end=index_smallest-1)
    reverse_array(arr=arr, start=index_smallest)
    reverse_array(arr=arr)
    return arr


arr = [3, 4, 5, 1, 2]
print(sort_circular_rotated_array(arr))

Output

[1, 2, 3, 4, 5]

Complexity

It takes O(n) time to find the smallest element in the array. For reversing array it will take O(n) times in worst-case scenario.

We are calling the reverse array function thrice but each element will get displaced twice so the overall complexity for reversing array is 2*O(n).

Total complexity is O(n)+2*O(3) which is equivalent to O(n). So, the overall time complexity of this algorithm is O(n).

We are not creating any new array and all the elements in the array are getting changed in place. So, the space complexity is O(1) i.e. constant space.

Hope you learned a new trick to sort the circular rotated array and to find the element in the circular rotated array in minimum time.

Python Interview Questions eBook

coding challenge
Aniruddha Chaudhari
I am complete Python Nut, love Linux and vim as an editor. I hold a Master of Computer Science from NIT Trichy. I dabble in C/C++, Java too. I keep sharing my coding knowledge and my own experience on CSEstack.org portal.

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Why?

Why Competitive Programming Important?

Coding Challenges for Practice

  1. Count Common Factor
  2. Does it Divide
  3. Sum of Sub Arrays
  4. Pair of Desired Sum
  5. Remove Duplicate Char from String
  6. Sort String by Char Freq (Python)
  7. Sort String by Char Freq (Java)
  8. Split Array into Equal Sum Subarray
  9. Validate IP Address
  10. Validate PAN Card Number
  11. Validate Sudoku
  12. Sort Circular Rotated Array
  13. Min Arrow to Burst Bubbles
  14. Min Cost to Paint All Houses [Amazon]
  15. HourGlass with Largest Sum
  16. Max Profit by Buying/Selling Stocks
  17. Hailstone Sequence
  18. Reverse String without affecting Special Characters
  19. Secure Conversation by Encry/Decry
  20. Special Elements in Matrix
  21. Next Greater No with Same set of Digits
  22. Smallest Subarray with Sum Greater than Given Number
  23. Group Anagrams
  24. Find Duplicates in Array in O(n)
  25. Find Two Unique Numbers from Array in O(n)
  26. Number Patterns & Finding Smallest Number
  27. First Unique Element in a Stream
  28. Flip Equivalent Binary Trees [TeachMint]
  29. Minimum Cost of Merging Files [Amazon]
  30. Minimum Distance for Truck to Deliver Order [Amazon]
  31. Order Task for Given Dependencies
  32. Multilevel Parking System Design
  33. Minimum Coins Required
  34. Max Sum Subarray
  35. Max Avg Sum of Two Subsequences
  36. Merge Overlapping Intervals
  37. Longest Balanced Subarray
  38. Longest Path in a Weighted Tree
  39. Generate Balanced Parentheses
  40. PostOrder Traversal Without Recursion

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