They let fast lookup, addition and removal of items, and can be used to implement either dynamic sets of items, or lookup tables that let finding an item by its key (e.g., finding the telephone number of a person by name).Binary search trees keep their keys in sorted order, so that lookup and other operations can use the principle of binary search: when looking for a key in a tree (or a place to insert a new key), they traverse the tree from root to leaf, make comparisons to keys stored in the nodes of the tree and deciding, on the basis of the comparison, to continue searching in the left or right subtrees.

COMING SOON!

```
=begin
Searches through a list for a value in O(log(n)) time.
The list must be sorted.
=end
def binary_search(array, key)
front = 0
back = array.length - 1
while front <= back
middle = (front + back) / 2
return middle if array[middle] == key
key < array[middle] ?
back = middle - 1 : front = middle + 1
end
nil
end
puts "Enter a sorted space-separated list:"
arr = gets.chomp.split(' ').map(&:to_i)
puts "Enter the value to be searched:"
value = gets.chomp.to_i
puts binary_search(arr, value) != nil ?
"Found at index #{binary_search(arr, value)}" :
"Not found"
```