Javascript Program to Count of rotations required to generate a sorted array
Last Updated :
25 Jan, 2022
Given an array arr[], the task is to find the number of rotations required to convert the given array to sorted form.
Examples:
Input: arr[] = {4, 5, 1, 2, 3}Â
Output: 2Â
Explanation:Â
Sorted array {1, 2, 3, 4, 5} after 2 anti-clockwise rotations.
Input: arr[] = {2, 1, 2, 2, 2}Â
Output: 1Â
Explanation:Â
Sorted array {1, 2, 2, 2, 2} after 1 anti-clockwise rotations.
Naive Approach:
To solve the problem mentioned above the first observation is if we have n elements in the array then after sorting, the largest element is at (n - 1)th position. After k number of anti-clockwise rotations, the largest element will be at index (k - 1) (kth element from start). Another thing to note here is that, after rotation, the next element of the largest element will always be the smallest element, (unless the largest element is at last index, possible if there was no rotation).Â
Hence,
Number of rotations (k) = index of smallest element (k) in the array
Below is the implementation of the above approach:
JavaScript
<script>
// JavaScript program to find the
// count of rotations
// Function to return the count of
// rotations
function countRotation(arr, n)
{
for(let i = 1; i < n; i++)
{
// Find the smallest element
if (arr[i] < arr[i - 1])
{
// Return its index
return i;
}
}
// If array is not
// rotated at all
return 0;
}
// Driver Code
let arr1 = [ 4, 5, 1, 2, 3 ];
document.write(countRotation(
arr1, arr1.length));
// This code is contributed by sanjoy_62
</script>
Time Complexity: O(N)Â
Auxiliary Space: O(1)
Efficient Approach:Â
To optimize the above approach, we will use Binary Search. We can notice that, after being sorted and rotated, the given array is divided into two halves with non-decreasing elements, which is the only pre-requisite for binary search. Perform a recursive binary search in the array to find the index of the smallest element.
Below is the implementation of the above approach:
JavaScript
<script>
// Javascript Program to implement
// the above approach
// Function to return the
// count of rotations
function countRotation(arr,low,high)
{
// If array is not rotated
if (low > high) {
return 0;
}
let mid = low + Math.floor((high - low) / 2);
// Check if current element is
// greater than the next
// element
if (mid < high
&& arr[mid] > arr[mid + 1]) {
// the next element is
// the smallest
return mid + 1;
}
// Check if current element is
// smaller than it's previous
// element
if (mid > low
&& arr[mid] < arr[mid - 1]) {
// Current element is
// the smallest
return mid;
}
// Check if current element is
// greater than lower bound
if (arr[mid] > arr[low]) {
// The sequence is increasing
// so far
// Search for smallest
// element on the right
// subarray
return countRotation(arr,
mid + 1,
high);
}
if (arr[mid] < arr[high])
{
// Smallest element lies on the
// left subarray
return countRotation(arr,
low,
mid - 1);
}
else
{
// Search for the smallest
// element on both subarrays
let rightIndex = countRotation(arr,
mid + 1,
high);
let leftIndex = countRotation(arr,
low,
mid - 1);
if (rightIndex == 0) {
return leftIndex;
}
return rightIndex;
}
}
// Driver Program
let arr1=[4, 5, 1, 2, 3 ];
document.write(
countRotation(
arr1,
0, arr1.length
- 1));
// This code is contributed by avanitrachhadiya2155
</script>
Time Complexity: O(N)Â
The complexity will be O(logN) for an array without duplicates. But if the array contains duplicates, then it will recursively call the search for both halves. So the worst-case complexity will be O(N).
Auxiliary Space:O(N)Â
At worst case, the recursion call stack will have N/2 recursion calls at a time.
Â
Please refer complete article on
Count of rotations required to generate a sorted array for more details!
Similar Reads
Count of rotations required to generate a sorted array Given an array arr[], the task is to find the number of rotations required to convert the given array to sorted form.Examples: Input: arr[] = {4, 5, 1, 2, 3} Output: 2 Explanation: Sorted array {1, 2, 3, 4, 5} after 2 anti-clockwise rotations. Input: arr[] = {2, 1, 2, 2, 2} Output: 1 Explanation: So
11 min read
Javascript Program to Count rotations required to sort given array in non-increasing order Given an array arr[] consisting of N integers, the task is to sort the array in non-increasing order by minimum number of anti-clockwise rotations. If it is not possible to sort the array, then print "-1". Otherwise, print the count of rotations. Examples: Input: arr[] = {2, 1, 5, 4, 3}Output: 2Expl
3 min read
Count rotations required to sort given array in non-increasing order Given an array arr[] consisting of N integers, the task is to sort the array in non-increasing order by minimum number of anti-clockwise rotations. If it is not possible to sort the array, then print "-1". Otherwise, print the count of rotations. Examples: Input: arr[] = {2, 1, 5, 4, 3}Output: 2Expl
7 min read
Find the Rotation Count in Rotated Sorted array in JavaScript A Rotated Sorted Array is an array type in JavaScript that has been rotated to the left or right by some random number of positions. In this article, we will understand how to find the count of rotations performed on the original sorted array to obtain the given sorted array using JavaScript languag
5 min read
Javascript Program to Check if it is possible to sort the array after rotating it Given an array of size N, the task is to determine whether its possible to sort the array or not by just one shuffle. In one shuffle, we can shift some contiguous elements from the end of the array and place it in the front of the array.For eg: A = {2, 3, 1, 2}, we can shift {1, 2} from the end of t
3 min read
Javascript Program to Find the Mth element of the Array after K left rotations Given non-negative integers K, M, and an array arr[] with N elements find the Mth element of the array after K left rotations. Examples: Input: arr[] = {3, 4, 5, 23}, K = 2, M = 1Output: 5Explanation:Â The array after first left rotation a1[ ] = {4, 5, 23, 3}The array after second left rotation a2[ ]
2 min read
Javascript Program to Find Mth element after K Right Rotations of an Array Given non-negative integers K, M, and an array arr[ ] consisting of N elements, the task is to find the Mth element of the array after K right rotations. Examples: Input: arr[] = {3, 4, 5, 23}, K = 2, M = 1 Output: 5 Explanation: The array after first right rotation a1[ ] = {23, 3, 4, 5} The array a
8 min read
Javascript Program For Counting Rotations In Sorted And Rotated Linked List Given a linked list of n nodes which is first sorted, then rotated by k elements. Find the value of k.The idea is to traverse singly linked list to check condition whether current node value is greater than value of next node. If the given condition is true, then break the loop. Otherwise increase t
3 min read
Rotation Count in a Rotated Sorted array Given an array arr[] having distinct numbers sorted in increasing order and the array has been right rotated (i.e, the last element will be cyclically shifted to the starting position of the array) k number of times, the task is to find the value of k.Examples: Input: arr[] = {15, 18, 2, 3, 6, 12}Ou
12 min read
Javascript Program to Print array after it is right rotated K times Given an Array of size N and a values K, around which we need to right rotate the array. How to quickly print the right rotated array?Examples :Â Â Input: Array[] = {1, 3, 5, 7, 9}, K = 2. Output: 7 9 1 3 5 Explanation: After 1st rotation - {9, 1, 3, 5, 7} After 2nd rotation - {7, 9, 1, 3, 5} Input:
2 min read