Magic Index – Find Index In Sorted Array Such That A[i] = i.

by SJ · February 22, 2015

Objective: Given a sorted array of distinct integers, Find the Magic index or Fixed point in the array.

Magic Index or Fixed Point: Magic index or a Fixed point in an array is an index i in the array such that A[i] = i.

Example :

int[] A = { -1, 0, 1, 2, 4, 10 };

Magic index or fixed point is : 4

Approach:

Naive approach is to do the linear scan and find the magic index in O(n).

Better solution would Modify the Binary Search – Time Complexity O(logN).

Check mid = (start+end)/2, with A[mid], check if A[mid] = mid. if yes then return mid.
If mid>A[mid] means fixed point might be on the right half of the array, make a recursive call to search(A, mid + 1, end).
If mid<A[mid] means fixed point might be on the left half of the array, make a recursive call to search(A, start, mid – 1).

Code:

Output:

Magic index 4

Kamal

in the example you have given, the array is not sorted
- tutorialhorizon
  
  Thanks kamal for pointing it out, corrected it.
Sai Yashodhar Vinay

this algorithm is wrong

Here the counter example :
array={1,2,3,3,4,5,6,7,8,9,10}
will return -1 not 3
Please check it out
- tutorialhorizon
  
  The program is works for distinct integers, My bad the objective of the problem was confusing, i have corrected it. Thanks for finding it out.
Aishwarya Parasuram

Is there a similar binary search method for arrays with repeated elements or is linear scan the only way?
http://tkachuko.info Oleksii Tkachuk

Thanks for post! Did you look into the case when elements are not distinct?