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Loop over the array and check the first index i such A[i] == i
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Yes, variations of the Fixed Point problem appear in technical interviews. It tests understanding of binary search patterns and recognizing monotonic relationships within arrays.
The optimal approach uses binary search. Since the array is sorted with distinct integers, the expression A[i] - i is monotonic, allowing us to eliminate half of the search space each step and find the fixed point in O(log n) time.
The problem primarily uses a simple array. The key idea is leveraging the sorted property of the array to apply binary search rather than relying on additional data structures.
Binary search works because the array is sorted and all values are distinct. This makes the function A[i] - i non-decreasing, which provides a predictable direction to move the search when comparing A[mid] with mid.