Hello,
I hope you’re doing well.
This function is designed to find a “fixed point” in an array nums
, which is an index i
such that nums[i] == i
. Here’s a stepbystep explanation of what the code does:
 Initialize two variables:

left
to 0, indicating the leftmost index.

right
to the number of elements in the array, indicating the rightmost index.
 Enter a
while
loop with the condition left + 1 < right
, which means the loop continues until there are at least two elements to search between.
 Inside the loop:
 Calculate the middle index
mid
as (right + left) / 2
.
 Check if
nums[mid]
is equal to mid
and left
is less than nums[left]
. If true, return mid
because it’s the fixed point.
 If
nums[mid] < mid
, it means that we need to look for the fixed point in the right half of the array, so update left = mid
.
 Otherwise, if
nums[mid] > mid
, it means we need to look for the fixed point in the left half of the array, so update right = mid
.
 After the loop, if
left
points to a fixed point (nums[left] == left
), return left
.
 Also, if
right
is within the bounds of the array and it points to a fixed point (nums[right] == right
), return right
.
 If no fixed point is found, return 1 to indicate that there’s no such element in the array.
The algorithm use binary search to locate the fixed point within the array, using the fact that the array is sorted and the target value (the index) exhibits a specific relationship with the values in the array.