A lot of people say loop and recursion is basically the same. The only difference between two is that some algorithms are easier to understand in recursion or iteration. Besides, loop is always preferred, because of overhead of function calls. However, here is a python code to get the height of a binary search tree . How can I write it using loop?
bst = [(1, 2), (3, None), (None, None), (None, None)]
def recursion_height(tree, v=0):
if v is None:
return -1
else:
return max(recursion_height(tree, tree[v][0]), recursion_height(tree, tree[v][1])) + 1
This can be implemented iteratively using queues.
# A binary tree node
class Node:
# Constructor to create new node
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Iterative method to find height of Binary Tree
def treeHeight(root):
# Base Case
if root is None:
return 0
# Create a empty queue for level order traversal
q = []
# Enqueue Root and Initialize Height
q.append(root)
height = 0
while(True):
# nodeCount(queue size) indicates number of nodes
# at current level
nodeCount = len(q)
if nodeCount == 0 :
return height
height += 1
# Dequeue all nodes of current level and Enqueue
# all nodes of next level
while(nodeCount > 0):
node = q[0]
q.pop(0)
if node.left is not None:
q.append(node.left)
if node.right is not None:
q.append(node.right)
nodeCount -= 1
# Driver program to test above function
# Let us create binary tree shown in above diagram
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", treeHeight(root)
Related
How to insert a node in a complete binary tree without using queue DS? I tried the following code:
class TreeNode:
def __init__(self, value=None) -> None:
self.left = None
self.value = value
self.right = None
class Tree:
def __init__(self, root=None) -> None:
self.__root = root if not root else TreeNode(root)
self.__len = 1 if root else 0
def append(self, data, root="_"):
if self.__root.value is None:
self.__root = TreeNode(data)
self.__len += 1
return
root = self.__root if root == "_" else root
if not root:
return False
if root.left is None and root.right is None:
root.left = TreeNode(data)
self.__len += 1
return True
elif root.left is not None and root.right is None:
root.right = TreeNode(data)
self.__len += 1
return True
elif root.left is not None and root.right is not None:
if self.append(data, root.left):
return
else:
self.append(data, root.right)
return
the recursive call of that function always add the new node on the left side of the tree, so what should I do to make it recursively checks the right side too?
First of all, the first line in your append code seems to give a special meaning to the value in the root node. When it is None it is not considered a real node, but to represent an empty tree. This is not a good approach. An empty tree is represented by a __root that is None -- nothing else. I would also suggest to remove the optional data argument from the constructor. Either the constructor should allow an arbitrary number of values or none at all. To allow one is odd and strengthens the idea that a tree could have a special None in its root node.
To the core of your question. There is nice attribute to complete binary trees. The paths from the root to a leaf can be represented by a bit pattern, where a 0 means "go left" and a 1 means "go right". And the path to the "slot" where a new node should be injected has a relationship with the size of the tree once that node has been added:
new size
binary representation
path to new node
1
1
[]
2
10
[left]
3
11
[right]
4
100
[left,left]
5
101
[left,right]
In general the path to the new node is defined by the bits in the binary representation of the new tree size, ignoring the leftmost 1.
This leads to the following code:
class Tree:
def __init__(self) -> None:
self.__root = None
self.__len = 0
def append(self, data):
self.__len += 1
if self.__len == 1: # First node
self.__root = TreeNode(data)
return
node = self.__root
# Iterate all the bits except the leftmost 1 and the final bit
for bit in bin(self.__len)[3:-1]:
node = [node.left, node.right][int(bit)] # Choose side
if self.__len & 1: # Use final bit to determine where child goes:
node.right = TreeNode(data)
else:
node.left = TreeNode(data)
I am trying this coding problem on leetcode and not able to debug the error!!
It's been 3 hours and I tried re-writing the logic again but I am still missing something. What else can I add to make it work against the test case:
>>>input - [1,2,3,4,null,null,5]
>>>expected output - [[4,5],[2,3],[1]]
Although this code is working for the given test case:
>>> input - [3,9,20,null,null,15,7]
>>> output - [[15,7],[9,20],[3]]
This is my effort:
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def levelOrderBottom(self, root: TreeNode) -> List[List[int]]:
queue = []
level = []
result = []
if root is None:
return None
result.append([root.val])
queue.append(root)
while len(queue) > 0:
a = queue[0]
ans = self.traverse_value(a.left, a.right, queue)
if ans is not None:
result.append(ans)
queue.pop(0)
return reversed(result)
def traverse_value(self, r_left, r_right, queue):
if r_left is None and r_right is None: # both l and r are none
return
elif r_left is None and r_right is not None: # right is not none
queue.append(r_right)
return [r_right.val]
elif r_left is not None and r_right is None: # left is not none
queue.append(r_left)
return [r_left.val]
elif r_left is not None and r_right is not None: # both are not none
queue.append(r_left)
queue.append(r_right)
return [r_left.val, r_right.val]
Your code can only create sublists of up to two elements, via the function traverse_value. This cannot be right, since obviously more wide trees will have more elements on the same level. Your algorithm has no provision to put "cousins" in the same list, only direct siblings.
Your BFS approach is certainly a good idea, but make sure to distinguish correctly between layers, so you know when to put values in the same list or in a new one:
result = []
if root is None:
return None
queue = [root]
while len(queue):
# get the values out of the current queue
result.append([a.val for a in queue])
# perform a separate loop for the this layer only
nextlayer = []
for a in queue:
# just extend this new list for the whole layer
if a.left:
nextlayer.append(a.left)
if a.right:
nextlayer.append(a.right)
# finally put that whole layer in the queue
queue = nextlayer
return reversed(result)
For your info, it can also be done with a DFS solution where you just keep track of the depth you are at, and use that as index in the solution list:
level = []
def recur(node, depth):
if not node:
return
if depth >= len(level):
level.append([])
level[depth].append(node.val)
recur(node.left, depth+1)
recur(node.right, depth+1)
recur(root, 0)
level.reverse()
return level
I'm just getting started with binary trees and I have this task where I have to do a preorder iterative traversal search for a given binary tree '[1,null,2,3]'.
I tried to use a new binarytree module that I found, but it didn't worked and I saw a youtube video where some guy did it recursively but I just can't figure out.
#Input = [1,null, 2,3]
# 1
# \
# 2
# /
# 3
#Expected output = [1,2,3]
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def preorderTraversal(self, root: TreeNode) -> List[int]:
I'm just clueless, I wrote an algorithm but I can't turn it into actual functional code. Also I don't understand how the root: TreeNode works. Does it turn every element of the list into a TreeNode object? So far my best try had been this and it's obviously wrong in many ways.
def preorderTraversal(self, root: TreeNode) -> List[int]:
result = []
for i in root:
if i =! root[0] and root.left =! None:
root.left = i
if root.left =! null:
root.left.left = i
elif root.left == null:
root.right.left = i
elif root.left
result.append(i)
elif root.right == None:
root.right = i
else:
continue
A few points:
Function preorderTraversal should have no self parameter; it is not a method of a class.
I have modified the TreeNode class to make it more convenient to specify its children TreeNode objects.
Function preorderTraversal takes as an argument a TreeNode object. As I mentioned in a comment, your statement, #Input = [1,null, 2,3], is difficult to make sense of.
You need to keep a last in/first out (LIFO) stack of unvisited TreeNode objects to implement an iterative (rather than recursive solution). In the code below, variable nodes serves that purpose.
The code:
from typing import List
class TreeNode:
def __init__(self, val, left=None, right=None):
self.x = val
self.left = left
self.right = right
n3 = TreeNode(3)
n2 = TreeNode(2, left=n3)
n1 = TreeNode(1, right=n2)
def preorderTraversal(root: TreeNode) -> List[int]:
result = []
nodes = []
nodes.append(root) # initial node to visit
while len(nodes): # any nodes left top visit?
node = nodes.pop() # get topmost element, which is the next node to visit
result.append(node.x) # "output" its value before children are visited
if node.right is not None:
# show this node must be visited
nodes.append(node.right) # push first so it is popped after node.left
if node.left is not None:
# show this node must be visited
nodes.append(node.left)
return result
print(preorderTraversal(n1))
Prints:
[1, 2, 3]
Or a more complicated tree:
10
/ \
8 2
/ \ /
3 5 2
n3 = TreeNode(3)
n5 = TreeNode(5)
n8 = TreeNode(8, left=n3, right=n5)
n2a = TreeNode(2)
n2b = TreeNode(2, left=n2a)
n10 = TreeNode(10, left=n8, right=n2b)
print(preorderTraversal(n10))
Prints:
[10, 8, 3, 5, 2, 2]
You can use the queue data structure for it.
queue = []
result = []
queue.append(root)
while queue:
node = queue.pop()
result.append(node.val)
if node.left is not None:
queue.insert(0, node.left)
if node.right is not None:
queue.insert(0, node.right)
return result
This is a problem from leetcode platform, here is my solution. Runtime: 28 ms, faster than 81.08% of Python3 online submissions for Binary Tree Preorder Traversal.
class Solution:
def preorderTraversal(self, root: TreeNode) -> List[int]:
if not root:
return []
return [root.val] + self.preorderTraversal(root.left) + self.preorderTraversal(root.right)
The end goal is to copy a node from one tree to another tree. I want to visit each node in a binary tree and return a node instance after a number of traverses. I cannot seem to figure out how to return a specific node. Every time the node returned matches the id of the root node since I pass the root node to the function.
class node():
def __init__(self):
self.parent = None
self.left = None
self.right = None
def randnode(self, target):
global count
if target == count:
# print 'At target', '.'*25, target
return self
else:
if self.left is not None:
count += 1
self.left.randnode(target)
if self.right is not None:
count += 1
self.right.randnode(target)
If you're doing a DFS and counting iterations, you don't even need recursion, just a stack of places to try, and popping/pushing data.
def dfs(self,target):
count = 0
stack = [start]
while stack:
node = stack.pop()
if count == target:
return node
if node is None: # since we push left/right even if None
continue # stop pushing after we hit None node
stack.extend([self.left,self.right])
return -1 # ran out of nodes before count
Bonus points : swapping stack to a queue for BFS
Apart from that, you might want to pass the count as a parameter, like all self-respecting recursive calls, you can make this stateless ;-)
class node():
def __init__(self):
self.parent = None
self.left = None
self.right = None
def randnode(self, target,count=0):
if target == count:
# print 'At target', '.'*25, target
return self
if self.left is not None:
return self.left.randnode(target,count + 1)
if self.right is not None:
return self.right.randnode(target,count + 1)
So far I have
def tree_iterate():
parent, current = None, self.root
lst = []
while current is not None:
if current.left not None:
lst.append(current.item)
parent, current = current, current.left
if current.right not None:
lst.append(current.item)
parent, current = current, current.right
(sorry about spacing I'm quite new at this)
I'm not quite sure how to iterate on both sides of the tree when current has left and right, without using recursion. My main goal is to have a list of all the nodes in this BSTenter code here
To get a list of all nodes in the BST iteratively, use Breadth-First Search (BFS). Note that this won't give you the nodes in sorted order:
queue = [root]
result = []
while queue:
l = queue.pop(0)
result.append(l)
if l.left != None:
queue.append(l.left)
if l.right!= None:
queue.append(l.right)
If you want the nodes in sorted order, you will need to simulate inorder traversal using a stack:
result = []
stack = [root]
while stack:
stack[-1].visited = True
if stack[-1].left != None and not stack[-1].left.visited:
stack.append(stack[-1].left)
else:
node = stack.pop()
result.append(node)
if stack[-1].right != None:
stack.append(stack[-1].right)