import java.util.*;
class Btree{
Node root;
static class Node{
public Node left;
public Node right;
public int height;
public String value;
public Node(String value){
this.left = null;
this.right = null;
this.height = 0;
this.value = value;
}
}
public Btree(){
this.root = null;
}
public static void main(String[] args){
Btree bt = new Btree();
Node N1 = new Node("N1");
Node N2 = new Node("N2");
Node N3 = new Node("N3");
Node N4 = new Node("N4");
Node N5 = new Node("N5");
Node N6 = new Node("N6");
Node N7 = new Node("N7");
bt.root = N1;
N1.right =N5;
N1.left = N2;
N2.right= N4;
N2.left=N3;
N5.left=N6;
N5.right=N7;
bt.preorder(bt.root);
}
void preorder(Node node){
if(node == null){
return;
}
System.out.print(node.value+ " ");
preorder(node.left);
preorder(node.right);
}
}
Create a step-by-step, frame-by-frame animation illustrating the execution of the provided Java code for a binary tree traversal. The animation should clearly depict the traversal process, highlighting each node's value and its position in the tree structure. Include the following elements in the animation: 1. Initial tree setup: Show the creation of the binary tree with the specified nodes (N1 to N7) and their connections. 2. Preorder traversal: Visualize the preorder traversal process, highlighting each node as it is visited, and display the output in a clear and readable format. 3. Node values and positions: Ensure that each node's value and position in the tree are clearly visible throughout the animation. 4. High-quality format: Produce the animation in a high-quality format, suitable for presentation or educational purposes. Deliver the animation in a format that can be easily shared and viewed, such as a video or an interactive visualization. Ensure that the animation accurately represents the code's execution and is easy to follow.
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答案文本
视频字幕
Binary trees are fundamental hierarchical data structures in computer science. Each node in a binary tree has at most two children, called left and right children. This structure makes them ideal for efficient searching, sorting, and data organization. In our Java implementation, each node contains references to its left and right children, a height value, and the actual data value stored in the node.
Binary trees are fundamental data structures in computer science. Each node can have at most two children: left and right. Preorder traversal is a systematic way to visit all nodes in a specific order: first the root, then the left subtree, and finally the right subtree. Let's see how this works with Java code.
Now let's build the binary tree step by step. First, we create seven nodes with values N1 through N7. Then we establish the tree structure: N1 becomes the root, N2 and N5 are N1's left and right children, N3 and N4 are N2's children, and N6 and N7 are N5's children. This creates our complete binary tree ready for traversal.
Now let's execute the preorder traversal. We start at the root N1, print it, then recursively traverse the left subtree starting with N2, then N3, then N4. After completing the left subtree, we traverse the right subtree starting with N5, then N6, and finally N7. The final output will be: N1 N2 N3 N4 N5 N6 N7.
To summarize, preorder traversal follows a simple recursive pattern: visit the current node first, then traverse the left subtree, and finally traverse the right subtree. This gives us the output N1 N2 N3 N4 N5 N6 N7. The algorithm has O(n) time complexity since we visit each node exactly once, and O(h) space complexity due to the recursion stack, where h is the height of the tree.
The preorder traversal algorithm follows a simple recursive pattern. First, we visit the current node and process it. Then we recursively traverse the entire left subtree before moving to the right subtree. This creates a depth-first search pattern that visits nodes in the order: Root, Left, Right. The numbers above each node show the visitation order for our tree structure.
Now let's execute the preorder traversal step by step. We start at root N1, print it, then recursively visit the left subtree. We go to N2, print it, then to N3, print it, backtrack to N2, then visit N4. After completing the left subtree, we return to N1 and traverse the right subtree: N5, then N6, then N7. The final output is N1 N2 N3 N4 N5 N6 N7.
In summary, our preorder traversal successfully visited all nodes in the order N1, N2, N3, N4, N5, N6, N7. The algorithm follows the Root-Left-Right pattern, creating a depth-first search through the tree. With O(n) time complexity and O(h) space complexity, preorder traversal is efficient and widely used in applications like expression parsing, file system traversal, and syntax tree processing.