Binary Tree

Binary Tree

• definition: at most two children

class TreeNode:
  def __init__(self, x):
    self.val = x
    self.left = None
    self. right = None

Tree Traverse

• pre-order: 先序遍历 left and then right

def preorder_traversal(self, root):
  res = []
  self.helper(root, res)
  return res
def helper(self, root, res):
  if not root:
    return
  res.append(root.val)
  self.helper(root.left, res)
  self.helper(root.right, res)
#time O(n)
#space O(h), h is the height of the tree, worst O(n)

• in-order: 中序遍历 left, then self and then right

def helper(self, root, res):
  if not root:
    return
  self.helper(root.left, res)
  res.append(root.val)
  self.helper(root.right, res)

• post-order 略
• Trick: base case usually refers to the None, ChildNode below the leaf node. 叶子的下一层

Blanced binary tree:

• a binary tree in which the depth of the left and right subtrees of every node differ by 1 or less

  
  
  

  image.png

Complete binary tree (same structure as heap):

• a binary tree in which every level, except possibly the last, is competely filled, as far left as possible

  
  
  

  image.png

Binary Search Tree: for every single:

• for every single node in the tree, the values in its left subtree are all smaller than its value, and the values in its right subtree are all larger than its value.
• in-order traversal: form an ascending order

Get height

def get_height(root):
  if not root:
    return 0
  left = get_height(root.left)
  right = get_height(root.right)
  return 1 + max(left, right)

Print Level order

first level
second level
third level

def level(root):
  q = [root] 
  next = []
  line = []
  while q:
    head = q.pop(0)
    if head.left:
      next.append(head.left)
    if head.right:
      next.append(head.right)
  line.append(head.val)
  if not q:
    print (line)
    if next:
      q = next
      next = []
      line = []
#time O(n)
#space O(max(len(q)))

Flip Upside Down

• given a binary tree where all the right nodes are either leaf nodes with a sibiling or empty

  
  
  

  image.png

def upside_bst(root):
  if not root:
    return root
  if not root.left and not root.right:
    return root
  left_tree = upside_bst(root.left)
  root.left.left = root.right
  root.left.right = root
  root.left = None
  root.right = None
  return left_tree
#time O(n)
#space O(h) 用recursion就一定会有新的space
#最后返回的是新的树的root

Homework

leetcode 226 104 110 236 103 109
book： data intensive application