# Question

Formatted question description: https://leetcode.ca/all/1064.html

 1064. Fixed Point

Given an array A of distinct integers sorted in ascending order,
return the smallest index i that satisfies A[i] == i.  Return -1 if no such i exists.

Example 1:

Input: [-10,-5,0,3,7]
Output: 3
Explanation:
For the given array, A[0] = -10, A[1] = -5, A[2] = 0, A[3] = 3, thus the output is 3.

Example 2:

Input: [0,2,5,8,17]
Output: 0
Explanation:
A[0] = 0, thus the output is 0.

Example 3:

Input: [-10,-5,3,4,7,9]
Output: -1
Explanation:
There is no such i that A[i] = i, thus the output is -1.

Note:

1 <= A.length < 10^4
-10^9 <= A[i] <= 10^9


# Algorithm

The basic idea of ​​binary search is to divide n elements into two roughly equal parts, and compare a[n/2] with x.

• If x=a[n/2], then find x and the algorithm stops;
• if x<a[n/2], as long as you continue to search for x in the left half of array a,
• if x>a[n/2], then as long as you search for x in the right half of array a.

Java