Trees

BST Search

Search a binary search tree for one present and one absent value.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this Python DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.py 
class Node:
    def __init__(self, value, left=None, right=None):
        self.value = value
        self.left = left
        self.right = right

def render(node):
    if node is None:
        return "_"
    if node.left is None and node.right is None:
        return str(node.value)
    return f"{node.value}({render(node.left)},{render(node.right)})"

def sample_tree():
    n1 = Node(1)
    n3 = Node(3)
    n2 = Node(2, n1, n3)
    n5 = Node(5)
    n7 = Node(7)
    n6 = Node(6, n5, n7)
    return Node(4, n2, n6)

root = sample_tree()
def search(root, target):
    node = root
    while node is not None:
        if target == node.value:
            return True
        node = node.left if target < node.value else node.right
    return False
print("5 found" if search(root, 5) else "5 not found")
print("8 found" if search(root, 8) else "8 not found")

Complexity

  • Time: O(h) per search
  • Space: O(1) iterative

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.
search path A comparison chooses one subtree at each step, so whole branches are skipped.