To implement a binary search algorithm, you can follow these steps:

  1. Define the search range: Initially, the search range will be the entire array or list you want to search in. For example, if you're searching in an array of integers, the initial range would be from index 0 to index n-1, where n is the size of the array.

  2. Find the midpoint: Calculate the midpoint of the search range by taking the average of the lower and upper bounds. If the lower bound is represented by the variable "low" and the upper bound by "high," then the midpoint can be calculated as "mid = (low + high) / 2".

  3. Compare the target value: Compare the value at the midpoint with the target value you are searching for. If they are equal, the search is successful, and you can return the index of the midpoint. If the value at the midpoint is greater than the target value, update the upper bound to be one less than the midpoint (high = mid - 1). If the value at the midpoint is less than the target value, update the lower bound to be one more than the midpoint (low = mid + 1).

  4. Repeat the process: Continue steps 2 and 3 until the search range is empty (i.e., low > high). In this case, the target value is not present in the array, and you can return a predefined value to indicate that.

  Here is a sample implementation of binary search in Python:

  python

  def binary_search(arr, target):

   low = 0

   high = len(arr) - 1

   while low <= high:

   mid = (low + high) // 2

   if arr[mid] == target:

   return mid

   elif arr[mid] < target:

   low = mid + 1

   else:

   high = mid - 1

   return -1 # Target value not found

  # Example usage:

  arr = [2, 5, 8, 12, 16, 23, 38, 56, 72, 91]

  target = 23

  result = binary_search(arr, target)

  print(f"Index of {target}: {result}")

  It's important to note that binary search works only on sorted arrays, as it relies on the "divide and conquer" approach by continuously halving the search range.