Skip to content
Related Articles

Related Articles

Find the Rotation Count in Rotated Sorted array

View Discussion
Improve Article
Save Article
  • Difficulty Level : Easy
  • Last Updated : 08 Sep, 2022
View Discussion
Improve Article
Save Article

Given an array arr[] of size N 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}
Output: 2
Explanation: Initial array must be {2, 3, 6, 12, 15, 18}. 
We get the given array after rotating the initial array twice.

Input: arr[] = {7, 9, 11, 12, 5}
Output: 4

Input: arr[] = {7, 9, 11, 12, 15};
Output: 0

Recommended Practice

Approach 1 (Using linear search): This problem can be solved using linear search.

If we take a closer look at examples, we can notice that the number of rotations is equal to the index of the minimum element. A simple linear solution is to find the minimum element and returns its index. 

Illustration:

Consider the array arr[]={15, 18, 2, 3, 6, 12};
Initially minimum = 15, min_index = 0

At i = 1: min = 15, min_index = 0
At i = 2: min = min(2, 15) = 2, min_index = 2
At i = 3: min = 2, min_index = 2
At i = 4: min = 2, min_index = 2
At i = 5: min = 2, min_index = 2

The array is rotated twice to the right

Follow the steps mentioned below to implement the idea:

  • Initialize two variables to store the minimum value and the index of that value.
  • Traverse the array from start to the end:
    • Find the minimum value and index where the minimum value is stored.
  • Return the index of the minimum value.

Below is the code implementation of the above idea. 

C++




// C++ program to find number of rotations
// in a sorted and rotated array.
#include <bits/stdc++.h>
using namespace std;
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
int countRotations(int arr[], int n)
{
    // We basically find index of minimum
    // element
    int min = arr[0], min_index = 0;
    for (int i = 0; i < n; i++) {
        if (min > arr[i]) {
            min = arr[i];
            min_index = i;
        }
    }
    return min_index;
}
 
// Driver code
int main()
{
    int arr[] = { 15, 18, 2, 3, 6, 12 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << countRotations(arr, n);
    return 0;
}
 
// This code is contributed by Adutya Kumar(adityakumar129)


C




// C program to find number of rotations
// in a sorted and rotated array.
#include <stdio.h>
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
int countRotations(int arr[], int n)
{
    // We basically find index of minimum
    // element
    int min = arr[0], min_index = 0;
    for (int i = 0; i < n; i++) {
        if (min > arr[i]) {
            min = arr[i];
            min_index = i;
        }
    }
    return min_index;
}
 
// Driver code
int main()
{
    int arr[] = { 15, 18, 2, 3, 6, 12 };
    int n = sizeof(arr) / sizeof(arr[0]);
    printf("%d", countRotations(arr, n));
    return 0;
}
 
// This code is contributed by Adutya Kumar(adityakumar129)


Java




// Java program to find number of
// rotations in a sorted and rotated
// array.
import java.io.*;
import java.lang.*;
import java.util.*;
 
class LinearSearch {
    // Returns count of rotations for an
    // array which is first sorted in
    // ascending order, then rotated
    static int countRotations(int arr[], int n)
    {
        // We basically find index of minimum
        // element
        int min = arr[0], min_index = 0;
        for (int i = 0; i < n; i++) {
            if (min > arr[i]) {
                min = arr[i];
                min_index = i;
            }
        }
        return min_index;
    }
 
    // Driver program to test above functions
    public static void main(String[] args)
    {
        int arr[] = { 15, 18, 2, 3, 6, 12 };
        int n = arr.length;
 
        System.out.println(countRotations(arr, n));
    }
}
 
// This code is contributed by Adutya Kumar(adityakumar129)


Python3




# Python3 program to find number
# of rotations in a sorted and
# rotated array.
 
# Returns count of rotations for
# an array which is first sorted
# in ascending order, then rotated
def countRotations(arr, n):
 
    # We basically find index
    # of minimum element
    min = arr[0]
    min_index = 0
    for i in range(0, n):
     
        if (min > arr[i]):
         
            min = arr[i]
            min_index = i
         
    return min_index;
 
 
# Driver code
arr = [15, 18, 2, 3, 6, 12]
n = len(arr)
print(countRotations(arr, n))
 
# This code is contributed by Smitha Dinesh Semwal


C#




// c# program to find number of
// rotations in a sorted and rotated
// array.
using System;
 
class LinearSearch
{
    // Returns count of rotations for an
    // array which is first sorted in
    // ascending order, then rotated
    static int countRotations(int []arr, int n)
    {
        // We basically find index of minimum
        // element
        int min = arr[0], min_index = 0;
        for (int i = 0; i < n; i++)
        {
            if (min > arr[i])
            {
                min = arr[i];
                min_index = i;
            }
        }
        return min_index;
    }
 
    // Driver program to test above functions
    public static void Main ()
    {
        int []arr = {15, 18, 2, 3, 6, 12};
        int n = arr.Length;
     
    Console.WriteLine(countRotations(arr, n));
    }
}
// This code is contributed by vt_m.


PHP




<?php
// PHP program to find number
// of rotations in a sorted
// and rotated array.
 
// Returns count of rotations
// for an array which is first
// sorted in ascending order,
// then rotated
function countRotations($arr, $n)
{
    // We basically find index
    // of minimum element
    $min = $arr[0];
    $min_index = 0;
    for ($i = 0; $i < $n; $i++)
    {
        if ($min > $arr[$i])
        {
            $min = $arr[$i];
            $min_index = $i;
        }
    }
    return $min_index;
}
 
// Driver code
$arr = array(15, 18, 2,
             3, 6, 12);
$n = sizeof($arr);
echo countRotations($arr, $n);
 
// This code is contributed
// by ajit
?>


Javascript




<script>
 
// Javascript program to find number of rotations
// in a sorted and rotated array.
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
  
    function countRotations(arr, n)
    {
        // We basically find index of minimum
        // element
        let min = arr[0], min_index = 0
        for (let i = 0; i < n; i++)
        {
            if (min > arr[i])
            {
                min = arr[i];
                min_index = i;
            }
        }
        return min_index;
    }
 
// Driver Code
     
    let arr = [15, 18, 2, 3, 6, 12];
    let n = arr.length;
     
    document.write(countRotations(arr, n));
 
</script>


Output

2

Time Complexity: O(N) 
Auxiliary Space: O(1) 

Approach 2: (Efficient Using Binary Search) 

A better approach would be to perform binary searching, in place of linear search to find the position of the smallest element in the array.

Follow the steps mentioned below to implement the idea: 

  • The minimum element is the only element whose previous is greater than it. If there is no previous element, then there is no rotation (the first element is minimum). 
  • Check this condition for the middle element by comparing it with the (mid-1)th and (mid+1)th elements.
  • If the minimum element is not at the middle (neither mid nor mid + 1), then 
    • If the middle element is smaller than the last element, then the minimum element lies in the left half
    • Else minimum element lies in the right half.

Illustration:

Let the array be arr[]={15, 18, 2, 3, 6, 12}
low = 0 , high = 5.
            =>  mid = 2
            =>  arr[mid]=2 , arr[mid-1] > arr[mid] , hence condition is matched
            =>  The required index = mid = 2

So the element is  found at index 2.

Below is the implementation of the above approach.

C++




// Binary Search based C++ program to find number
// of rotations in a sorted and rotated array.
#include <bits/stdc++.h>
using namespace std;
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
int countRotations(int arr[], int low, int high)
{
    // This condition is needed to handle the case
    // when the array is not rotated at all
    if (high < low)
        return 0;
 
    // If there is only one element left
    if (high == low)
        return low;
 
    // Find mid
    int mid = low + (high - low) / 2; /*(low + high)/2;*/
 
    // Check if element (mid+1) is minimum element.
    // Consider the cases like {3, 4, 5, 1, 2}
    if (mid < high && arr[mid + 1] < arr[mid])
        return (mid + 1);
 
    // Check if mid itself is minimum element
    if (mid > low && arr[mid] < arr[mid - 1])
        return mid;
 
    // Decide whether we need to go to left half or
    // right half
    if (arr[high] > arr[mid])
        return countRotations(arr, low, mid - 1);
 
    return countRotations(arr, mid + 1, high);
}
 
// Driver code
int main()
{
    int arr[] = { 15, 18, 2, 3, 6, 12 };
    int N = sizeof(arr) / sizeof(arr[0]);
    cout << countRotations(arr, 0, N - 1);
    return 0;
}


Java




// Java program to find number of
// rotations in a sorted and rotated
// array.
import java.io.*;
import java.lang.*;
import java.util.*;
 
class BinarySearch {
    // Returns count of rotations for an array
    // which is first sorted in ascending order,
    // then rotated
    static int countRotations(int arr[], int low, int high)
    {
        // This condition is needed to handle
        // the case when array is not rotated
        // at all
        if (high < low)
            return 0;
 
        // If there is only one element left
        if (high == low)
            return low;
 
        // Find mid
        // /*(low + high)/2;*/
        int mid = low + (high - low) / 2;
 
        // Check if element (mid+1) is minimum
        // element. Consider the cases like
        // {3, 4, 5, 1, 2}
        if (mid < high && arr[mid + 1] < arr[mid])
            return (mid + 1);
 
        // Check if mid itself is minimum element
        if (mid > low && arr[mid] < arr[mid - 1])
            return mid;
 
        // Decide whether we need to go to left
        // half or right half
        if (arr[high] > arr[mid])
            return countRotations(arr, low, mid - 1);
 
        return countRotations(arr, mid + 1, high);
    }
 
    // Driver program to test above functions
    public static void main(String[] args)
    {
        int arr[] = { 15, 18, 2, 3, 6, 12 };
        int N = arr.length;
 
        System.out.println(countRotations(arr, 0, N - 1));
    }
}
// This code is contributed by Chhavi


Python3




# Binary Search based Python3
# program to find number of
# rotations in a sorted and
# rotated array.
 
# Returns count of rotations for
# an array which is first sorted
# in ascending order, then rotated
 
def countRotations(arr, n):
    start = 0
    end = n-1
 
    # Finding the index of minimum of the array
    # index of min would be equal to number to rotation
    while start<=end:
        mid = start+(end-start)//2
         
        # Calculating the previous(prev)
        # and next(nex) index of mid
        prev = (mid-1+n)%n
        nex = (mid+1)%n
 
        # Checking if mid is minimum
        if arr[mid]<arr[prev]\
           and arr[mid]<=arr[nex]:
          return mid
       
        # if not selecting the unsorted part of array
        elif arr[mid]<arr[start]: end = mid-1
        elif arr[mid]>arr[end]: start = mid+1
        else: return 0
 
# Driver code
if __name__ == '__main__':
    arr = [15, 18, 2, 3, 6, 12]
    N = len(arr)
    print(countRotations(arr, N))
 
# This code is contributed by Smitha Dinesh Semwal


C#




// C# program to find number of
// rotations in a sorted and rotated
// array.
using System;
 
class BinarySearch {
    // Returns count of rotations for an array
    // which is first sorted in ascending order,
    // then rotated
    static int countRotations(int[] arr, int low, int high)
    {
        // This condition is needed to handle
        // the case when array is not rotated
        // at all
        if (high < low)
            return 0;
 
        // If there is only one element left
        if (high == low)
            return low;
 
        // Find mid
        // /*(low + high)/2;*/
        int mid = low + (high - low) / 2;
 
        // Check if element (mid+1) is minimum
        // element. Consider the cases like
        // {3, 4, 5, 1, 2}
        if (mid < high && arr[mid + 1] < arr[mid])
            return (mid + 1);
 
        // Check if mid itself is minimum element
        if (mid > low && arr[mid] < arr[mid - 1])
            return mid;
 
        // Decide whether we need to go to left
        // half or right half
        if (arr[high] > arr[mid])
            return countRotations(arr, low, mid - 1);
 
        return countRotations(arr, mid + 1, high);
    }
 
    // Driver program to test above functions
    public static void Main()
    {
        int[] arr = { 15, 18, 2, 3, 6, 12 };
        int N = arr.Length;
 
        Console.WriteLine(countRotations(arr, 0, N - 1));
    }
}
// This code is contributed by vt_m.


PHP




<?php
// Binary Search based PHP
// program to find number
// of rotations in a sorted
// and rotated array.
 
// Returns count of rotations
// for an array which is
// first sorted in ascending
// order, then rotated
function countRotations($arr,
                        $low, $high)
{
    // This condition is needed
    // to handle the case when
    // array is not rotated at all
    if ($high < $low)
        return 0;
 
    // If there is only
    // one element left
    if ($high == $low)
        return $low;
 
    // Find mid
    $mid = $low + ($high -
                   $low) / 2;
 
    // Check if element (mid+1)
    // is minimum element. Consider
    // the cases like {3, 4, 5, 1, 2}
    if ($mid < $high &&
        $arr[$mid + 1] < $arr[$mid])
    return (int)($mid + 1);
 
    // Check if mid itself
    // is minimum element
    if ($mid > $low &&
        $arr[$mid] < $arr[$mid - 1])
    return (int)($mid);
 
    // Decide whether we need
    // to go to left half or
    // right half
    if ($arr[$high] > $arr[$mid])
    return countRotations($arr, $low,
                          $mid - 1);
 
    return countRotations($arr,
                          $mid + 1,
                          $high);
}
 
// Driver code
$arr = array(15, 18, 2, 3, 6, 12);
$N = sizeof($arr);
echo countRotations($arr, 0, $N - 1);
 
// This code is contributed bu ajit
?>


Javascript




<script>
// Binary Search based C++ program to find number
// of rotations in a sorted and rotated array.
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
function countRotations(arr, low, high)
{
    // This condition is needed to handle the case
    // when the array is not rotated at all
    if (high < low)
        return 0;
 
    // If there is only one element left
    if (high == low)
        return low;
 
    // Find mid
    let mid = Math.floor(low + (high - low)/2); /*(low + high)/2;*/
 
    // Check if element (mid+1) is minimum element.
    // Consider the cases like {3, 4, 5, 1, 2}
    if (mid < high && arr[mid+1] < arr[mid])
    return (mid+1);
 
    // Check if mid itself is minimum element
    if (mid > low && arr[mid] < arr[mid - 1])
    return mid;
 
    // Decide whether we need to go to left half or
    // right half
    if (arr[high] > arr[mid])
    return countRotations(arr, low, mid-1);
 
    return countRotations(arr, mid+1, high);
}
 
// Driver code
    let arr = [15, 18, 2, 3, 6, 12];
    let N = arr.length;
    document.write(countRotations(arr, 0, N-1));
 
 
 
 
// This code is contributed by Surbhi Tyagi.
</script>


Output

2

Time Complexity: O(log N) 
Auxiliary Space: O(log N)  [this is the space of recursion stack]

Iterative Code (Binary Search):

C++




#include <bits/stdc++.h>
using namespace std;
 
// Returns count of rotations
// for an array which is first sorted
// in ascending order, then rotated
 
// Observation: We have to return
// index of the smallest element
int countRotations(int arr[], int n)
{
    int low = 0, high = n - 1;
    while (low <= high) {
 
        // if first element is mid or
        // last element is mid
        // then simply use modulo so it
        // never goes out of bound.
        int mid = low + (high - low) / 2;
        int prev = (mid - 1 + n) % n;
        int next = (mid + 1) % n;
 
        if (arr[mid] <= arr[prev] && arr[mid] <= arr[next])
            return mid;
        else if (arr[mid] <= arr[high])
            high = mid - 1;
        else if (arr[mid] >= arr[low])
            low = mid + 1;
    }
    return 0;
}
 
// Driver code
int main()
{
    int arr[] = { 15, 18, 2, 3, 6, 12 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << countRotations(arr, n);
    return 0;
}


Java




/*package whatever //do not write package name here */
import java.io.*;
 
class GFG {
    // Returns count of rotations
    // for an array which is first sorted
    // in ascending order, then rotated
 
    // Observation: We have to return
    // index of the smallest element
    static int countRotations(int[] arr, int n)
    {
        int low = 0, high = n - 1;
        while (low <= high) {
 
            // if first element is mid or
            // last element is mid
            // then simply use modulo so it
            // never goes out of bound.
            int mid = low + (high - low) / 2;
            int prev = (mid - 1 + n) % n;
            int next = (mid + 1) % n;
 
            if (arr[mid] <= arr[prev]
                && arr[mid] <= arr[next])
                return mid;
            else if (arr[mid] <= arr[high])
                high = mid - 1;
            else if (arr[mid] >= arr[low])
                low = mid + 1;
        }
        return 0;
    }
 
    // Driver Code
    public static void main(String args[])
    {
 
        int[] arr = { 15, 18, 2, 3, 6, 12 };
        int n = arr.length;
        System.out.println(countRotations(arr, n));
    }
}
 
// This code is contributed by shinjanpatra


Python3




# Returns count of rotations for an array which
# is first sorted in ascending order, then rotated
 
# Observation: We have to return index of the smallest element
 
 
def countRotations(arr, n):
 
    low = 0
    high = n - 1
    while(low <= high):
 
        # if first element is mid or
        # last element is mid
        # then simply use modulo
        # so it never goes out of bound.
        mid = low + ((high - low) // 2)
        prev = (mid - 1 + n) % n
        next = (mid + 1) % n
 
        if(arr[mid] <= arr[prev]
           and arr[mid] <= arr[next]):
            return mid
        elif (arr[mid] <= arr[high]):
            high = mid - 1
        elif (arr[mid] >= arr[low]):
            low = mid + 1
    return 0
 
# Driver code
 
 
arr = [15, 18, 2, 3, 6, 12]
n = len(arr)
print(countRotations(arr, n))
 
# This code is contributed by shinjanpatra.


C#




// C# program for the above approach
 
using System;
 
class GFG {
    // Returns count of rotations
    // for an array which is first sorted
    // in ascending order, then rotated
 
    // Observation: We have to return
    // index of the smallest element
    static int countRotations(int[] arr, int n)
    {
        int low = 0, high = n - 1;
        while (low <= high) {
 
            // if first element is mid or
            // last element is mid
            // then simply use modulo so it
            // never goes out of bound.
            int mid = low + (high - low) / 2;
            int prev = (mid - 1 + n) % n;
            int next = (mid + 1) % n;
 
            if (arr[mid] <= arr[prev]
                && arr[mid] <= arr[next])
                return mid;
            else if (arr[mid] <= arr[high])
                high = mid - 1;
            else if (arr[mid] >= arr[low])
                low = mid + 1;
        }
        return 0;
    }
 
    // Driver Code
    public static void Main()
    {
 
        int[] arr = { 15, 18, 2, 3, 6, 12 };
        int n = arr.Length;
        Console.Write(countRotations(arr, n));
    }
}
 
// This code is contributed by saurabh_jaiswal.


Javascript




<script>
 
// Returns count of rotations for an array which
// is first sorted in ascending order, then rotated
 
//Observation: We have to return index of the smallest element
function countRotations(arr, n)
{     
      let low =0 , high = n-1;
      while(low<=high){
          let mid = low + Math.floor((high-low)/2) ;
          let prev = (mid-1 + n)  %n , next = (mid+1)%n;//if first element is mid or
        //last element is mid then simply use modulo so it never goes out of bound.
          if(arr[mid]<=arr[prev] && arr[mid]<=arr[next])
            return mid;
          else if (arr[mid]<=arr[high])
            high = mid-1 ;
          else if (arr[mid]>=arr[low])
            low=mid+1;
      }
      return 0;
}
 
// Driver code
 
let arr = [15, 18, 2, 3, 6, 12];
let n = arr.length;
document.write(countRotations(arr, n));
    
// This code is contributed by shinjanpatra.
</script>


Output

2

Time Complexity: O(log N)
Auxiliary Space: O(1), since no extra space has been taken.

This article is contributed by Rakesh Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!