You are given an array A of $n$ distinct integers sorted in ascending order. You need to find a fixed point in the array if one exists. A fixed point in an array is an index i such that $A[i]=i.$ You decide to use a binary search algorithm to efficiently find a fixed point. The algorithm works as follows:

Initialize two indices, low larr$0$ and high larrn$-1.$

While low $$ high, do the following:

Compute mid larr $($low $+$ high$)/2.$

If $A[$mid$]=$ mid, then mid is a fixed point, and you return mid.

If $A[$mid$]$ mid, then you search the right half of the array by setting low $=$ mid $+1.$

Otherwise, you search the left half of the array by setting high $=$ mid $1.$

If no fixed point is found, return $-1.$

Which of the following statements is correct about the above algorithm?

The algorithm can find a fixed point in $0(n)$ time complexity.

The algorithm guarantees to find all fixed points in the array.

The algorithm works correctly only if the array contains non$-$negative integers.

The algorithm can find a fixed point in $0(logn)$ time complexity and works correctly for any array of distinct integers sorted in ascending order.