Establish an ordered tree and traverse it, provided that the data is orderly. There are four methods to traverse an ordered tree: pre order, middle order, post order and hierarchical traversal
D (root node) L (left subtree) R (right subtree)
The preorder traversal is DLR. First access the root node, and then from left to right. A left subtree accesses the left subtree, and no left subtree accesses the right subtree
The middle order traversal is LDR. First access the left subtree, then from left to right. After accessing the root node on the left, continue to access the right half subtree, from left to right
The subsequent traversal is LRD. First access the left subtree, then from left to right. After the left access, skip the root node, continue to access the right half subtree, from left to right, and finally access the root node
Layered traversal is obviously a layer by layer downward access. After accessing the first layer, you can continue to access the second layer
import numpy as np class Node(): #Define node classes def __init__(self,data=''): self.data=data #Node value self.left=None #Left child node self.right=None #Right child node def __str__(self): #Implicit read current node method return str(self.data) #Returns the current node value class BuildTree(): def __init__(self,firstData): self.rootNode=Node(firstData) #The root node of the tree. The default data value is empty def addNodes(self,NewDatas): #Add nodes to the ordered tree, and newdata is the list. The premise is that the data has been sorted Datalength=len(NewDatas)+1 #1 is the root node depth=np.floor(np.log2(Datalength))+1 #Find the depth of the tree, and np.floor() returns the maximum integer not greater than the input parameter. log2 is the value of the logarithm of Datalength based on 2 i=2 stock=[self.rootNode] #Record root node address while i<=depth: #Handle the nodes of each layer of the tree currNN=2**(i-1) #Maximum number of nodes in current layer j=0 while j<currNN: #Add nodes to the current hierarchy until it is full curr=stock #Get current node address j+=1 if NewDatas: #When the list is not empty, the elements on the left will pop up data=NewDatas.pop(0) #Delete the element entering the new node in the list else: break; #The last layer node must consider the case that the value provided by the list is not full Node1=Node(data) #Generate new node print('Number of nodes%d'%(data)) if j%2==0: #Add left node for j=1 and right node for j=2 curr.right=Node1 #Add right child node to current node stock.pop(0) #Remove the front node address stock.append(Node1) #Rightmost node address else: curr.left=Node1 #Add left child node to current node stock.append(Node1) #Rightmost left node address i+=1 #Tree layer plus 1 line1=[1,20,30,40,50,60,70,80] #Value of node B1=BuildTree(line1) #Establish a binary tree instance with root node B1.addNodes(line1[1:]) #Build the tree from node 2 #=================================== def preoder(root): #Recursive traversal p1= if root: #Non empty node p1.append(root.data) p1+= preoder(root.left) #Recursive call to left node p1+= preoder(root.right) #Recursive call to right node return p1 #Return to list L1=preoder(B1.rootNode) print(L1) #===================================== def middle(root): #Recursive traversal p1= if root: #Non empty node p1+= middle(root.left) #Recursive call to left node p1.append(root.data) p1+= middle(root.right) #Recursive call to right node return p1 #Return to list L1=middle(B1.rootNode) print(L1) #===================================== def post(root): #Postorder traversal p1= if root: #Non empty node p1+= post(root.left) #Recursive call to left node p1+= post(root.right) #Recursive call to right node p1.append(root.data) return p1 #Return to list L1=post(B1.rootNode) print(L1) #==================================== def level(root): q1=[root.data,root.left, root.right]#Store data, left and right node addresses p1= #Record the value of the node while q1: em= q1.pop(0) #Jump an element from the list if em: if isinstance(em,Node): #Determine whether the element is a node address q1.append(em.data) #Put the values in the node into the list q1.append(em.left) #Put the address of the left child node in the node into the list q1.append(em.right) #Put the address of the right child node in the node into the list else: p1.append(em) #Put node data into the list return p1 L1=level(B1.rootNode) print(L1)
Graph theory is a branch of mathematics, which takes graph as the research object.
- Graph in graph theory is a graph composed of several given points and lines connecting two points. This graph is usually used to describe a specific relationship between things. Points represent things, and lines connecting two points represent that there is this relationship between the corresponding two things.
- Graph can be divided into directed graph and undirected graph. Every edge of a graph defines a direction, which is called a directed graph; A graph whose edges have no direction is called an undirected graph.
- The number of edges in and out of a node in a graph is called the degree of the node. The degree of the node is represented by d(v), and v represents the node.
- If an edge of a node starts and ends with the node, it is called a self ring. The realization of graph structure is mainly divided into adjacency matrix and adjacency table.
Adjacency Matrix is a square matrix that uses rows and columns to represent nodes and intersecting element values to represent the connection relationship.
In the adjacency matrix of unordered graphs, 0 represents non contiguity and 1 represents contiguity
In the adjacency matrix of ordered graphs, 0 represents unreachable and 1 represents reachable
Note: A → B → C in the order diagram can reach C