Search in an almost sorted array

• Difficulty Level : Medium
• Last Updated : 16 Jul, 2021

Given an array which is sorted, but after sorting some elements are moved to either of the adjacent positions, i.e., arr[i] may be present at arr[i+1] or arr[i-1]. Write an efficient function to search an element in this array. Basically the element arr[i] can only be swapped with either arr[i+1] or arr[i-1].
For example consider the array {2, 3, 10, 4, 40}, 4 is moved to next position and 10 is moved to previous position.
Example :

Input: arr[] =  {10, 3, 40, 20, 50, 80, 70}, key = 40
Output: 2
Output is index of 40 in given array

Input: arr[] =  {10, 3, 40, 20, 50, 80, 70}, key = 90
Output: -1
-1 is returned to indicate element is not present

A simple solution is to linearly search the given key in given array. Time complexity of this solution is O(n). We can modify binary search to do it in O(Logn) time.
The idea is to compare the key with middle 3 elements, if present then return the index. If not present, then compare the key with middle element to decide whether to go in left half or right half. Comparing with middle element is enough as all the elements after mid+2 must be greater than element mid and all elements before mid-2 must be smaller than mid element.
Following is the implementation of this approach.

C++

 // C++ program to find an element// in an almost sorted array#include  // A recursive binary search based function.// It returns index of x in given array// arr[l..r] is present, otherwise -1int binarySearch(int arr[], int l, int r, int x){if (r >= l){        int mid = l + (r - l) / 2;         // If the element is present at        // one of the middle 3 positions        if (arr[mid] == x)            return mid;        if (mid > l && arr[mid - 1] == x)            return (mid - 1);        if (mid < r && arr[mid + 1] == x)            return (mid + 1);         // If element is smaller than mid, then        // it can only be present in left subarray        if (arr[mid] > x)            return binarySearch(arr, l, mid - 2, x);         // Else the element can only be present        // in right subarray        return binarySearch(arr, mid + 2, r, x);} // We reach here when element is not present in arrayreturn -1;} // Driver Codeint main(void){int arr[] = {3, 2, 10, 4, 40};int n = sizeof(arr) / sizeof(arr);int x = 4;int result = binarySearch(arr, 0, n - 1, x);(result == -1) ? printf("Element is not present in array")               : printf("Element is present at index %d",                         result);return 0;}

Java

 // Java program to find an element// in an almost sorted arrayclass GFG{    // A recursive binary search based function.    // It returns index of x in given array    // arr[l..r] is present, otherwise -1    int binarySearch(int arr[], int l, int r, int x)    {        if (r >= l)        {            int mid = l + (r - l) / 2;             // If the element is present at            // one of the middle 3 positions            if (arr[mid] == x)                return mid;            if (mid > l && arr[mid - 1] == x)                return (mid - 1);            if (mid < r && arr[mid + 1] == x)                return (mid + 1);             // If element is smaller than mid, then            // it can only be present in left subarray            if (arr[mid] > x)                return binarySearch(arr, l, mid - 2, x);             // Else the element can only be present            // in right subarray            return binarySearch(arr, mid + 2, r, x);        }         // We reach here when element is        // not present in array        return -1;    }     // Driver code    public static void main(String args[])    {        GFG ob = new GFG();        int arr[] = {3, 2, 10, 4, 40};        int n = arr.length;        int x = 4;        int result = ob.binarySearch(arr, 0, n - 1, x);        if(result == -1)            System.out.println("Element is not present in array");        else            System.out.println("Element is present at index " +                                result);    }} // This code is contributed by Rajat Mishra

Python3

 # Python 3 program to find an element# in an almost sorted array # A recursive binary search based function.# It returns index of x in given array arr[l..r]# is present, otherwise -1def binarySearch(arr, l, r, x):     if (r >= l):                 mid = int(l + (r - l) / 2)                 # If the element is present at one        # of the middle 3 positions        if (arr[mid] == x): return mid        if (mid > l and arr[mid - 1] == x):            return (mid - 1)        if (mid < r and arr[mid + 1] == x):            return (mid + 1)                     # If element is smaller than mid, then        # it can only be present in left subarray        if (arr[mid] > x):            return binarySearch(arr, l, mid - 2, x)                 # Else the element can only        # be present in right subarray        return binarySearch(arr, mid + 2, r, x)     # We reach here when element    # is not present in array    return -1 # Driver Codearr = [3, 2, 10, 4, 40]n = len(arr)x = 4result = binarySearch(arr, 0, n - 1, x)if (result == -1):    print("Element is not present in array")else:    print("Element is present at index", result) # This code is contributed by Smitha Dinesh Semwal.

C#

 // C# program to find an element// in an almost sorted arrayusing System; class GFG{    // A recursive binary search based function.    // It returns index of x in given array    // arr[l..r] is present, otherwise -1    int binarySearch(int []arr, int l, int r, int x)    {        if (r >= l)        {            int mid = l + (r - l) / 2;             // If the element is present at            // one of the middle 3 positions            if (arr[mid] == x)                return mid;            if (mid > l && arr[mid - 1] == x)                return (mid - 1);            if (mid < r && arr[mid + 1] == x)                return (mid + 1);             // If element is smaller than mid, then            // it can only be present in left subarray            if (arr[mid] > x)                return binarySearch(arr, l, mid - 2, x);             // Else the element can only be present            // in right subarray            return binarySearch(arr, mid + 2, r, x);        }         // We reach here when element is        // not present in array        return -1;    }     // Driver code    public static void Main()    {        GFG ob = new GFG();        int []arr = {3, 2, 10, 4, 40};        int n = arr.Length;        int x = 4;        int result = ob.binarySearch(arr, 0, n - 1, x);        if(result == -1)            Console.Write("Element is not present in array");        else            Console.Write("Element is present at index " +                           result);    }} // This code is contributed by nitin mittal.

PHP

 = \$l)    {        \$mid = \$l + (\$r - \$l) / 2;         // If the element is present at        // one of the middle 3 positions        if (\$arr[\$mid] == \$x)            return \$mid;        if (\$mid > \$l && \$arr[\$mid - 1] == \$x)            return (\$mid - 1);        if (\$mid < \$r && \$arr[\$mid + 1] == \$x)            return (\$mid + 1);         // If element is smaller than mid, then        // it can only be present in left subarray        if (\$arr[\$mid] > \$x)            return binarySearch(\$arr, \$l,                           \$mid - 2, \$x);         // Else the element can only be present        // in right subarray        return binarySearch(\$arr, \$mid + 2,                                    \$r, \$x);} // We reach here when element// is not present in arrayreturn -1;} // Driver Code\$arr = array(3, 2, 10, 4, 40);\$n = sizeof(\$arr);\$x = 4;\$result = binarySearch(\$arr, 0, \$n - 1, \$x);if(\$result == -1)    echo("Element is not present in array");else    echo("Element is present at index \$result"); //This code is contributed by nitin mittal?>

Javascript



Output :

Element is present at index 3

Time complexity of the above function is O(Logn).