There are several types of binary trees, including:
Full Binary Tree: A binary tree in which every node has either two children or no children.
Complete Binary Tree: A binary tree in which all levels are completely filled except possibly the last level, which is filled from left to right.
Perfect Binary Tree: A binary tree in which all the internal nodes have two children and all the leaf nodes are at the same level.
Balanced Binary Tree: A binary tree in which the height of the left and right subtrees of any node differ by at most one. Examples of balanced binary trees include AVL trees and Red-Black trees.
Skewed Binary Tree: A binary tree in which all the nodes are either left-skewed or right-skewed. In a left-skewed binary tree, all nodes have a left child but no right child, while in a right-skewed binary tree, all nodes have a right child but no left child.
Threaded Binary Tree: A binary tree in which every null pointer is replaced with a thread pointing to either its inorder predecessor or inorder successor.
These are some of the common types of binary trees. Each type has its own advantages and disadvantages, and is used in different scenarios based on the requirements of the problem being solved.
Full Binary Tree:
scssstruct Node {
int val; struct Node* left; struct Node* right;
}; struct Node* newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val; node->left = NULL; node->right = NULL; return node;
} int main() {
struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5);
return 0;
}
Complete Binary Tree:
scssstruct Node {
int val; struct Node* left; struct Node* right;
}; struct Node*newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val;
node->left = NULL; node->right = NULL;
return node; }
int main() {
struct Node* root = newNode(1); root->left = newNode(2);
root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); root->right->left = newNode(6); return 0;
}
Perfect Binary Tree:
scssstruct Node {
int val; struct Node* left; struct Node* right;
}; struct Node* newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val;
node->left = NULL; node->right = NULL;
return node; }
int main() {
struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); root->right->left = newNode(6); root->right->right = newNode(7); return 0;
}
Balanced Binary Tree:
scssstruct Node {
int val; struct Node* left;
struct Node* right;
}; struct Node* newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val; node->left = NULL;
node->right = NULL; return node; }
int main() {
struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); root->right->left = newNode(6); root->right->right = newNode(7); root->left->left->left = newNode(8); return 0;
}
Skewed Binary Tree:
scssstruct Node {
int val; struct Node* left; struct Node* right; }; struct Node* newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val;
node->left = NULL; node->right = NULL;
return node; }
int main() {
struct Node* root = newNode(1); root->left = newNode(2); root->left->left = newNode(3); root->left->left->left = newNode(4); root->left->left->here's an example code in C that demonstrates the implementation of a skewed tree: arduino Copy code #include <stdio.h> #include <stdlib.h> struct Node { int val; struct Node* right; }; struct Node* newNode(int val) { struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val; node->right = NULL; return node; } struct Node* insert(struct Node* root, int val) { if (root == NULL) { return newNode(val); } root->right = insert(root->right, val); return root; } void printSkewedTree(struct Node* root) { if (root == NULL) { return; } printf("%d ", root->val); printSkewedTree(root->right); } int main() { struct Node* root = NULL; // Insert nodes into skewed tree root = insert(root, 1); insert(root, 2); insert(root, 3); insert(root, 4); insert(root, 5); // Print the skewed tree printf("Skewed Tree: "); printSkewedTree(root); printf("\n"); return 0; } This code creates a skewed tree with the values 1, 2, 3, 4, and 5 inserted in that order. The program then prints out the skewed tree in a left-skewed form. The output of the program will be: yaml Copy code Skewed Tree: 1 2 3 4 5 Note that this implementation assumes a left-skewed tree, but it can be easily modified to create a right-skewed tree by inserting new nodes to the left of the root node.
A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. The left child is always less than the parent node, while the right child is always greater than the parent node. Binary trees are commonly used in computer science and programming, particularly for searching and sorting algorithms.
A skewed tree, on the other hand, is a binary tree in which all the nodes are either left-skewed or right-skewed. In a left-skewed tree, all nodes have a left child but no right child, while in a right-skewed tree, all nodes have a right child but no left child. Skewed trees are unbalanced, which means that the height of one subtree is much greater than the other subtree. This can lead to inefficient performance in algorithms that rely on balanced trees, such as binary search tree algorithms.
Skewed trees are sometimes used in certain scenarios, such as when dealing with degenerate cases in search and sorting algorithms. However, in most cases, balanced binary trees, such as AVL trees and Red-Black trees, are preferred over skewed trees because they provide better performance guarantees and avoid worst-case scenarios.
here's an example code in C that demonstrates the implementation of a binary tree:
rust#include <stdio.h> #include <stdlib.h> struct Node {
int val; struct Node* left; struct Node* right;
};struct Node* newNode(int val) {
struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->val = val;
node->left = NULL; node->right = NULL; return node;
} int main() {
struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5);printf("Binary Tree: \n"); printf("%d -> %d \n", root->val, root->left->val);printf("%d -> %d \n", root->val, root->right->val); printf("%d -> %d \n", root->left->val, root->left->left->val);printf("%d -> %d \n", root->left->val, root->left->right->val);return 0;
}
This code creates a binary tree with a root node of 1 and two child nodes of 2 and 3. The node 2 has two child nodes of 4 and 5. The program then prints out the binary tree in the form of an adjacency list.
The output of the program will be:
rustBinary Tree: 1 -> 2
1 -> 3 2 -> 4 2 -> 5
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