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

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:

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

A better solution would Modify the Binary SearchTime 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 a 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 a 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
```

### 6 thoughts on “Magic Index – Find Index In Sorted Array Such That A[i] = i.”

1. in the example you have given, the array is not sorted

• Thanks kamal for pointing it out, corrected it.

2. 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