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We can do this using the binary search approach as following:

int rotatedSorted(int[] arr, int target){
  int left = 0;
  int right = arr.length-1;
  while(left<=right){
    int mid = left+(right-left)/2;
    if(arr[mid]==target)
      return arr[mid]
    if(arr[left]<=arr[mid]){
      if(arr[left]<=target && target<arr[mid]){
        right=mid-1;
      }else{
        left=mid+1;
      }
    }else{
      if(arr[mid]<target && target <= arr[right]){
        left=mid+1;
      }else{
        right=mid-1;
      }
    }
  }
  return -1;
}

Find the smallest elements in the array using binary search. We need to find the element which is smaller than previous element.

If the required element is greater than last element, then we need to do binary search in arr[0, min-1] else binary search in arr[min+1, n-1]

This could be sollution whith O(logn) efficency

public static int SearchRotatedSortedArray(int l, int d, int[] array, int toFind) {
		if (l >= d) {
			return -1;
		}
		if (array[l] == toFind) {
			return l;
		}
		if (array[d] == toFind) {
			return d;
		}

		int mid = (l + d) / 2;
		if (array[mid] == toFind) {
			return mid;
		}

		if ((array[mid] > toFind && toFind > array[l]) || (array[mid] < toFind && array[d] < toFind)) {
			return SearchRotatedSortedArray(l, mid - 1, array, toFind);
		} else {
			return SearchRotatedSortedArray(mid + 1, d, array, toFind);
		}

	}

public class RotatedSortedArray {

static int findMin(int arr[], int low, int high) {


if (high == low) return low;
if (high < low) return low;

int mid = low + (high - low) / 2;

if (arr[mid + 1] < arr[mid] && high > mid) {
return mid + 1;
}
if (arr[mid - 1] > arr[mid] && mid > low) {
return mid;
}
if (arr[high] > arr[mid]) {
return findMin(arr, low, mid);
} else {
return findMin(arr, mid, high);
}
}

static int findPosRotatedArray(int arr[], int low, int high, int num) {
int pos = findMin(arr, low, high);
if (arr[pos] < num && num > arr[high]) {
return binarySearch(arr, num, pos - 1, low);
} else {
return binarySearch(arr, num, high, pos);
}
}

static int binarySearch(int arr[], int num, int high, int low) {
if (high < low) {
return -1;
}
int mid = low + (high - low) / 2;

if (num == arr[mid]) {
return mid;
} else if (num > arr[mid]) {
return binarySearch(arr, num, high, mid + 1);
} else {
return binarySearch(arr, num, mid - 1, low);
}

}

public static void main(String[] args) {
int arr1[] = {5, 6, -2, -1, 1, 2, 3, 4};
System.out.println(findMin(arr1, 0, arr1.length - 1));
System.out.println(findPosRotatedArray(arr1, 0, arr1.length - 1, 2));


}


}

package algorithms.sorting;

import java.util.Arrays;

public class P2 {

    public static void main(String[] args) {
        Integer[] words = new Integer[]{
                5, 6, -2, -1, 1, 2, 3, 4
        };

        int foundIndex = findElement(words, -2);

        if(foundIndex == -1) {
            System.out.println("Not Found");
        }
        else {
            System.out.println("Found at : " + String.valueOf(foundIndex) + " : Word : " + words[foundIndex]);
        }

    }

    private static int findElement(Integer[] words, Integer element) {
        int mid = words.length / 2;
        if(words[mid].equals(element)) {
            return mid;
        }
        if(words.length == 1) {
            return -1;
        }
        if(words[mid] > element && (words[mid] < words[0] || element > words[0])) {
            return findElement(Arrays.copyOfRange(words, 0, mid), element);
        }
        else {
            return findElement(Arrays.copyOfRange(words, mid + 1, words.length), element);
        }
    }
}