 ### Python program to find distance between two nodes of a binary tree.

Description:

Distance between two nodes is the minimum number of edges to be traversed to reach one node from other. Dist(4,5)=2
Dist(4,6)=4
Dist(3,4)=3
Dist(2,4)=1
Dist(8,5)=5

Program:

class Node: def __init__(self, data): self.data = data self.right = None self.left = None def pathToNode(root, path, k): # base case handling if root is None: return False # append the node value in path path.append(root.data) # See if the k is same as root's data if root.data == k : return True # Check if k is found in left or right # sub-tree if ((root.left != None and pathToNode(root.left, path, k)) or (root.right!= None and pathToNode(root.right, path, k))): return True # If not present in subtree rooted with root, # remove root from path and return False path.pop() return False def distance(root, data1, data2): if root: # store path corresponding to node: data1 path1 = [] pathToNode(root, path1, data1) # store path corresponding to node: data2 path2 = [] pathToNode(root, path2, data2) # iterate through the paths to find the # common path length i=0 while i<len(path1) and i<len(path2): # get out as soon as the path differs # or any path's length get exhausted if path1[i] != path2[i]: break i = i+1 # get the path length by deducting the # intersecting path length (or till LCA) return (len(path1)+len(path2)-2*i) else: return 0 # Driver Code to test above functions root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.right.right= Node(7) root.right.left = Node(6) root.left.right = Node(5) root.right.left.right = Node(8) dist = distance(root, 4, 5) print ("Distance between node {} & {}: {}".format(4, 5, dist) ) dist = distance(root, 4, 6) print( "Distance between node {} & {}: {}".format(4, 6, dist) ) dist = distance(root, 3, 4) print ("Distance between node {} & {}: {}".format(3, 4, dist) ) dist = distance(root, 2, 4) print ("Distance between node {} & {}: {}".format(2, 4, dist) ) dist = distance(root, 8, 5) print ("Distance between node {} & {}: {}".format(8, 5, dist) )

Output:

Distance between node 4 & 5: 2
Distance between node 4 & 6: 4
Distance between node 3 & 4: 3
Distance between node 2 & 4: 1
Distance between node 8 & 5: 5
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