Binary Search Tree is a sorted binary tree meaning given a root node all the values to the left are less than it and all the values to the right are greater it. This property enables Binary Search to be performed on the tree.
Let exploit this capability, Given a target value let's find a number that is the closest to it in the tree. First we create our BST node which has a value and two pointers. One to the right and one to the left.
# A BST node class BST: def __init__(self, value): self.value = value self.left = None self.right = None
Now we create our tree by attaching our nodes together
# 7 <-- Root Node # 5 12 <-- Depth One # 3 6 9 15 <-- Depth Two # 1 4 8 10 13 17 <-- Depth Three # Create the tree tree = BST(7) # depth one tree.right = BST(5) tree.left = BST(12) # Right node --> depth two tree.right.right = BST(15) tree.right.left = BST(9) # Right node --> depth three (right node) tree.right.right.right = BST(17) tree.right.right.left = BST(13) # Right node --> depth three (left node) tree.right.left.right = BST(10) tree.right.right.left = BST(8) # Left node --> depth two tree.left.right = BST(6) tree.left.left = BST(3) # Left node --> depth three (left node) tree.left.left.right = BST(4) tree.right.right.left = BST(1)
The Psuedo Code below is the solution to the problem.
- Assign the closest value to the root node.
- Check if |target - closest| > |target - tree's value|.
- If yes assign the tree's value as the closest value
- If no the continue using the closest value
- Check if the target's value > current tree's value
- If yes Go to the right sub tree.
- If no move on.
- Check if the target's value < current tree's value
- If yes Go to the left sub tree.
- If no move on.
- Check if there is are no sub trees left
- If yes return current closest value
- If no go back to step 2
The Pseudo Code above can be implemented recursively or iteratively
# Recursive solution closest = tree.value # Initial closest value is the root's value def findClosestValueInBstRecursive(tree, target, closest): if tree is None: return closest if abs(target - closest) > abs(target - tree.value): closest = tree.value if target < tree.value: return findClosestValueInBstRecursive(tree.left, target, closest) elif target > tree.value: return findClosestValueInBstRecursive(tree.right, target, closest) else: return closest # Iterative solution def findClosestValueInBstIterative(tree, target, closest): currentNode = tree while currentNode is not None: if abs(target - closest) > abs(target - currentNode.value): closest = currentNode.value if target < currentNode.value: currentNode = currentNode.left elif target > currentNode.value: currentNode = currentNode.right else: break return closest
Now time to test both solutions given the value of 14 find its closest value within the tree defined earlier.
tar = 14 findClosestValueInBstRecursive(tree, tar, closest) # Output: 15 tar = 14 findClosestValueInBstIterative(tree, tar, closest) #Output: 15
Both solutions arrived at the same answer 15 which just happens to be the closest value in the tree.
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