#### Binary Search

The binary search algorithm returns the index of the target value if it exists in the array, or -1 if it does not.

#### Problem

```Given a sorted array of integers, write a function that returns the index of the target value if it exists in the array, or -1 if it does not.
Example input: [0, 1, 2, 3, 4, 5, 6], 4
Example output: 4```

#### Solution

This solution is in Python. Our A.I. can create solutions in multiple languages.
by kayakane
```def find_index(array, target):
# Binary search is the optimal solution for this problem.
# It is optimal because it is O(log n) time complexity.
# This is because the array is sorted and we can use the
# divide and conquer approach to find the target value.
# We can do this by finding the midpoint of the array and
# comparing the target value to the value at the midpoint.
# If the target value is less than the value at the midpoint,
# we can search the left half of the array. If the target value
# is greater than the value at the midpoint, we can search the
# right half of the array. We can repeat this process until we
# find the target value or until we have searched the entire array.
# If we have searched the entire array and have not found the target
# value, we can return -1.
left = 0
right = len(array) - 1
while left <= right:
mid = (left + right) // 2
if array[mid] == target: return mid
elif array[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1

print(find_index([0, 1, 2, 3, 4, 5, 6], 4))```

A.I. Evaluation of the Solution

The candidate's solution is a binary search, which is the optimal solution for this problem. The time complexity of a binary search is O(log n), which is better than the time complexity of a linear search, which is O(n). The candidate's solution correctly returns the index of the target value if it exists in the array, or -1 if it does not.

Evaluated at: 2022-11-27 00:15:54