Find Distance Between Two Nodes in a Binary Tree using Python

Suppose, we are given a binary tree and are asked to find the distance between two nodes in the binary tree. We find out the edges between the two nodes like in a graph and return the number of edges or the distance between them. A node of a tree has the structure as below −

data : <integer value>
right : <pointer to another node of the tree>
left : <pointer to another node of the tree>

So, if the input is like

and the nodes between which we have to find the distance between are 2 and 8; then the output will be 4.

The edges between the two nodes 2 and 8 are: (2, 3), (3, 5), (5, 7), and (7, 8). There are 4 edges in the path between them, so the distance is 4.

To solve this, we will follow these steps −

• Define a function findLca() . This will take root, p, q
  • if root is same as null, then
    • return null
  • if data of root is any of (p,q), then
    • return root
  • left := findLca(left of root, p, q)
  • right := findLca(right of root, p, q)
  • if left and right is not null, then
    • return root
  • return left or right
• Define a function findDist() . This will take root, data
  • queue := a new deque
  • insert a new pair (root, 0) at the end of queue
  • while queue is not empty, do
    • current := first value of the leftmost pair in queue
    • dist := second value of the leftmost pair in queue
    • if data of current is same as data, then
      • return dist
    • if left of current is not null, then
      • add pair (left of current, dist+1) to queue
    • if right of current is not null, then
      • add pair (current.right, dist+1) to queue
• node := findLca(root, p, q)
• return findDist(node, p) + findDist(node, q)

Example

Let us see the following implementation to get better understanding −

import collections
class TreeNode:
   def __init__(self, data, left = None, right = None):
      self.data = data
      self.left = left
      self.right = right

def insert(temp,data):
   que = []
   que.append(temp)
   while (len(que)):
      temp = que[0]
      que.pop(0)
      if (not temp.left):
         if data is not None:
            temp.left = TreeNode(data)
         else:
            temp.left = TreeNode(0)
         break
      else:
         que.append(temp.left)

      if (not temp.right):
         if data is not None:
            temp.right = TreeNode(data)
         else:
            temp.right = TreeNode(0)
         break
      else:
         que.append(temp.right)

def make_tree(elements):
   Tree = TreeNode(elements[0])
   for element in elements[1:]:
      insert(Tree, element)
   return Tree

def search_node(root, element):
   if (root == None):
      return None

   if (root.data == element):
      return root

   res1 = search_node(root.left, element)
   if res1:
      return res1

   res2 = search_node(root.right, element)
   return res2

def print_tree(root):
   if root is not None:
      print_tree(root.left)
      print(root.data, end == ', ')
      print_tree(root.right)

def findLca(root, p, q):
   if root is None:
      return None
   if root.data in (p,q):
      return root
   left = findLca(root.left, p, q)
   right = findLca(root.right, p, q)
   if left and right:
      return root
   return left or right

def findDist(root, data):
   queue = collections.deque()
   queue.append((root, 0))
   while queue:
      current, dist = queue.popleft()
      if current.data == data:
         return dist
      if current.left: queue.append((current.left, dist+1))
      if current.right: queue.append((current.right, dist+1))

def solve(root, p, q):
   node = findLca(root, p, q)
   return findDist(node, p) + findDist(node, q)

root = make_tree([5, 3, 7, 2, 4, 6, 8])
print(solve(root, 2, 8))

Input

root = make_tree([5, 3, 7, 2, 4, 6, 8])
print(solve(root, 2, 8))

Output

4