128. 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: A 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 be to 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 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).

Output:

Magic index 4