how to find the height of a node in binary tree recursively

问题

path = 0 # the lenght of the path
    while self.right != None or self.left != None:
        while self.right != None:
            self = self.right
            path = path +1 
        while self.left != None:
            self = self.left
            path = path +1
    return path

this is my sample code for find the Height, is defined as the length of the longest path by number of nodes from self to a leaf. The height of a leaf node is 1.

it doesn't work.

回答1:

What you're doing isn't recursive, it's iterative. Recursive would be something like:

def height(node):
    if node is None:
        return 0
    else:
        return max(height(node.left), height(node.right)) + 1

回答2:

You were given the solution by mata, but I suggest you also look at your code and understand what it is doing:

    while self.right != None:
        self = self.right
        path = path +1

What will this do? it will find the right child, then its right child, and so on. So this checks only one path of the "rightmost" leaf.

This does the same for the left:

   while self.left != None:
        self = self.left
        path = path +1

The idea in recursion is that for each subproblem, you solve it using the exact same recipe for all other subproblems. So if you would apply your algorithm only to a subtree or a leaf, it would still work.

Also, a recursive definition calls itself (although you can implement this with a loop, but that is beyond the scope here).

Remeber the definition:

Recursion: see definition of Recursion.

;)

回答3:

def height(node):
    if node is None:
        return 0
    else:
        if node.left==None and node.right==None:
            return max(height(node.left), height(node.right))+0
        else:
            return max(height(node.left), height(node.right))+1

If you consider each increasing edge to be the height. To pass hackerrank testcases

回答4:

Here is the complete program in Python ::

class Node :
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

def maxDepth(node):
    if node is None :
        return 0
    else :
        ldepth = maxDepth(node.left)
        rdepth = maxDepth(node.right)

        if (ldepth>rdepth):
            return ldepth +1
        else :
            return rdepth +1

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)


print "Height of tree is %d" %(maxDepth(root))

Source : here

回答5:

def height(self):
    if self.root !=None:
        return self._height(self.root,0)
    else:
        return 0

def _height(self,cur_node,cur_height):
    if cur_node==None : 
         return cur_height
    left_height = self._height(cur_node.left_child,cur_height+1)
    right_height = self._height(cur_node.right_child,cur_height+1)
    return max(left_height,right_height)

来源：https://stackoverflow.com/questions/13322616/how-to-find-the-height-of-a-node-in-binary-tree-recursively

标签

python

algorithm

binary-tree