Comparison between Heap and Tree in C++

In this article, you will learn about the comparison between the Heap and Tree with their types and examples.

What is Heap?

A specialized tree-based data structure that satisfies the heap property is called a heap. The relationship between parent and child nodes is determined by this property, which guarantees that in a Max-Heap, each node's value is more significant than or equal to that of its children. In a Min-Heap, it is less than or equal to that of its children. Heaps are essential to implementing priority queues because they enable the effective extraction of the maximum (or minimum) element. Heaps are often implemented as a complete binary tree. Their applications extend to various algorithms, including Dijkstra's shortest path and Huffman coding.

Max-Heap and Min-Heap are the two primary types of heaps, distinguished by the order defined by their heap property. It is usually implemented as complete binary trees. Both types are binary heaps, which means each node has a maximum of two children.

Max Heap

Every node in a Max-Heap has a value greater than or equal to the values of its children.
The maximum element is at the root of the heap.
Max-heaps are often used to efficiently find and remove the maximum element, making them suitable for priority queue implementations.

Code:

Let us take an example to illustrate the use of Max heap in C++.

#include <iostream>
#include <queue>
int main() 
{
    // Declaration of Max-Heap
    std::priority_queue<int> maxHeap;
    // Insert elements into the Max-Heap
    maxHeap.push(3);
    maxHeap.push(1);
    maxHeap.push(4);
    maxHeap.push(1);
    maxHeap.push(5);
    //Access the maximum element without removing it
    int maxValue = maxHeap.top();
    std::cout << "Maximum Element: " << maxValue << std::endl;
    // Extract the maximum element
    maxHeap.pop();
    // Display the Max-Heap
    std::cout << "Max-Heap elements: ";
    while (!maxHeap.empty())
    {
        std::cout << maxHeap.top() << " ";
        maxHeap.pop();
    }
    return 0;
}

Output:

Maximum Element: 5
Max-Heap elements: 4 3 1 1

Explanation:

In this example, a default Max-Heap behaviour is provided by the C++ 'priority_queue'class.
After that, elements are added to the Max-Heap using the 'push' method.
The top (maximum) element can be accessed without being removed using the 'top' function.
The top element in the Max-Heap is eliminated using the 'pop' function.
Utilize the 'empty' Function to determine if the heap is empty.

Min Heap

Every node in a Min-Heap has a value that is either less than or equal to the values of its children.
The minimum element is at the root of the heap.
Min-heaps are commonly used to efficiently find and remove the minimum element, making them suitable for priority queue implementations.

Code:

Let us take an example to illustrate the use of Min heap in C++.

#include <iostream>
#include <queue>
#include <vector>
int main() 
{
    // Declaration of Min-Heap
    std::priority_queue<int, std::vector<int>, std::greater<int>> minHeap;
    // Insert elements into the Min-Heap
    minHeap.push(3);
    minHeap.push(1);
    minHeap.push(4);
    minHeap.push(1);
    minHeap.push(5);
    //Access the minimum element without removing it
    int minValue = minHeap.top();
    std::cout << "Minimum Element: " << minValue << std::endl;
    // Extract the minimum element
    minHeap.pop();
    // Display the Min-Heap
    std::cout << "Min-Heap elements: ";
    while (!minHeap.empty()) 
    {
        std::cout << minHeap.top() << " ";
        minHeap.pop();
    }
    return 0;
}

Output:

Minimum Element: 1
Min-Heap elements: 1 3 4 5

Explanation:

In this example, a Min-Heap is created in C++ using the 'priority_queue'
After that, use the third template option, 'std::greater<int>' to define the comparison function for a Min-Heap.
Elements are inserted into the Min-Heap using the 'push'
Use the 'top' Function to access the top (minimum) element without removing it.
The top element in the Min-Heap can be eliminated using the 'pop'
Use the 'empty' Function to determine if the heap is empty.

Depending on whether you require instant access to the maximum or smallest element, these two heap types have different uses. The particular needs of the heap-using algorithm or data structure determine which heap types are best. Developers can select the heap type that best suits their needs in various applications due to the freedom to employ either a Max-Heap or a Min-Heap.

1. Operations

Insertion

The process of adding a new element to the heap.
Preserves the heap property after insertion, heapify-up, or moving the newly inserted element up the tree.

Extraction

The process of removing the heap's most significant (in the Max-Heap) or lowest (in the Min-Heap) element.
After extraction, the last element is moved to the root, and the element is then moved down the tree (heapify-down) to preserve the heap property.

2. Use Cases

Priority queue

Priority queues are frequently implemented using heaps.
In algorithms where certain items need to be processed before others based on their priority, priority queues are crucial.

Heap Sort

In the heap sort algorithm, heap data structures are used.
With a time complexity of O(n log n), heap sort is an effective in-place sorting algorithm.

3. Complexity of Time

Insertion

O(log n) - Due to the heap's height being logarithmic about the number of elements.

Extraction

O(log n) - Extraction of the maximum or minimum element requires logarithmic time to maintain the heap property, similar to insertion.

4. Advantages

There are several advantages of the heaps. Some main advantages of the heaps are as follows:

Efficiency

Efficient Access to the maximum or least element is possible using heaps.
Logarithmic time is used for priority queue operations like extraction and insertion.

Efficiency of Space

Heaps are space-efficient compared to other data structures because arrays can be implemented.

5. Applications for Common Heaps

Dijkstra's Shortest Path Algorithm

Heaps are employed in graph algorithms such as Dijkstra's shortest path algorithm to create priority queues efficiently.

Huffman Coding

Based on character frequencies, Huffman coding is a compression method that uses heaps to assign variable-length codes to input characters.
Heaps are versatile data structures with applications in various algorithms and data processing scenarios, offering efficient Access to extreme elements and supporting priority-based operations.

What is a Tree?

A tree is a hierarchical data structure representing parent-child connections by having nodes linked by edges. Trees are commonly used to organize and visualize data that is hierarchical. There are several kinds of trees, including balanced trees like AVL, binary, and search trees.

Trees are used in many different scenarios:

They can represent file systems and database indexing structures or even serve as the building block for search engines.

Tree operations encompass insertion, deletion, searching, and traversal.

Example:

Let us take an example to illustrate the use of Tree in C++.

#include <iostream>
// Define a basic structure for a tree node
struct TreeNode
{
    int data;
    TreeNode* left;
    TreeNode* right;

    TreeNode(int value) : data(value), left(nullptr), right(nullptr) {}
};
//Function to perform an inorder traversal of the tree
void inorderTraversal(TreeNode* node)
{
    if (node != nullptr)
    {
        inorderTraversal(node->left);
        std::cout << node->data << " ";
        inorderTraversal(node->right);
    }
}
int main()
{
    // Creating nodes for the binary tree
    TreeNode* root = new TreeNode(1);
    root->left = new TreeNode(2);
    root->right = new TreeNode(3);
    root->left->left = new TreeNode(4);
    root->left->right = new TreeNode(5);
    // Perform an inorder traversal and print the values
    std::cout << "Inorder Traversal: ";
    inorderTraversal(root);
    std::cout << std::endl;
    // Remember to free the memory to avoid memory leaks
    // In a real-world scenario, you might use smart pointers or a custom memory management strategy.
    delete root->left->left;
    delete root->left->right;
    delete root->left;
    delete root->right;
    delete root;
    return 0;
}

Output:

Inorder Traversal: 4 2 5 1 3

Explanation:

a. Include Header

In this example, the standard input/output stream header is included on this line, enabling you to print to the console using tools like cout and endl.

b. Tree Node Structure

This code defines the TreeNode structure to represent a node in a binary tree. Each node has pointers to its left and right children (left and right) and an integer data value (data). The left and right pointers are set to nullptr by the constructor, which initializes the node with the supplied value.

c. Inorder Traversal Function

A binary tree inorder traverse is carried out by this Function (inorderTraversal). The left, root, and right subtree are all visited by inorder traversal. Throughout traversal, the values are displayed on the console.

d. Inorder Traversal and Output

After that, the code calls the inorder traversal Function on the tree's root and prints the result to the console.

e. Memory Deallocation

Ultimately, the code manually releases each tree node's dynamically allocated memory. You may find it more convenient to use intelligent pointers or another memory management technique to manage memory automatically in a production environment.

1. Basic Operations of the Tree

Insertion

A new node is inserted into the tree.
An order is maintained in a binary search tree (BST) by inserting a new node based on its value.

Deletion

Removing a node from the tree.
In a binary search tree, the deletion process needs to preserve the tree's order.

Searching

Finding a specific node in the tree.
In a binary search tree, searching is performed based on the values of the nodes.

2. Applications

Some applications of the tree are as follows:

File Systems

Hierarchical file structures are represented using trees.

Database Indexing

Databases use trees for effective indexing, such as B-trees and B+ trees.

Expression Trees

Trees represent mathematical expressions.

Hierarchical Structures

Representing hierarchical relationships in organizational charts and family trees.

Search Algorithms

Binary search is one of the search algorithms that uses trees as its fundamental structure.

3. Advantages

Some advantages of the tree are as follows:

Organization and Hierarchy

Trees help to organize and represent relationships in various applications because they offer a natural approach to representing hierarchical structures.
File systems, organizational charts, and family trees are a few examples.

Efficient Searching

Searching can be done more effectively with the help of binary search trees (BST). Searching in a BST has a logarithmic time complexity because the values in the right subtree are more significant, and those in the left subtree are smaller than the root.

Efficient Sorting

Elements of logarithmic time complexity can be sorted using binary trees. An element's sequence is sorted upon in-order traversal of a binary search tree.

Efficient Insertion and Deletion

The order of elements is maintained throughout efficient insertion and deletion operations with binary search trees.
Self-balancing trees, including Red-Black and AVL trees, guarantee the tree maintains equilibrium, resulting in effective insertions and deletions.

Efficient Database Indexing

Databases frequently use tree architectures like B-trees and B+ trees for effective indexing.
Large dataset databases can benefit from B-trees because of their balanced structure, which facilitates effective insertion, deletion, and searching.

Effective Indexing in Databases

B-trees and B+ trees are two common tree structures used for effective indexing in database systems.
Large dataset databases can benefit from the balanced structure of B-trees, which allows efficient insertion, deletion, and searching.

Graph Representation

Trees can represent hierarchical relationships in graphs. Graphs without cycles are a specific instance of trees.

Natural Representation of Recursive Structures

Trees offer a natural representation of recursive structures in computer science and mathematics.
Trees are a common way for recursive algorithms, like tree traversals, to be naturally described.

4. Time Complexity

a) Binary Search Tree (BST)

Best Case

Search (for a specific element): O(1) if the tree is perfectly balanced, you find the desired element at the root.

Insertion and Deletion: O(1) if the tree is empty, the new node becomes the root.

Worst Case

Search: O(n) in the worst case for an unbalanced tree, where each tree level needs to be traversed.

Insertion and Deletion: O(n) is the worst case for an unbalanced tree; each level may need to be modified or traversed.

b) Balanced Trees (e.g., AVL Tree, Red-Black Tree)

Best Case

Search (for a specific element): O(log n) in the best case, where the tree is perfectly balanced.

Insertion and Deletion: O(log n) is the best case for a balanced tree.

Worst Case

Search: O(log n) in the worst case for a balanced tree, as each level is traversed.

Insertion and Deletion: O(log n) in the worst case for a balanced tree, as rebalancing may be required.

c) Traversal (Inorder, Preorder, Postorder)

Best Case: O(n) for any traversal operation where every node needs to be visited.

Worst Case: O(n) for any traversal operation, as each node must be visited once.

Comparison between Heap and Tree

There are several differences between the Heap and the Tree. Some main differences between them are as follows:

1. Purpose

Heap: For max- or min-heaps, heaps are generally utilized to efficiently retrieve the maximum (or minimum) element in constant time. They are frequently utilized in priority-based processing algorithms like heap sorting and Dijkstra's algorithm.

Tree: Trees can be used for several purposes, such as hierarchical data representation (expression trees), searching and retrieval (binary search trees), and showing hierarchical relationships (file systems, organization charts).

2. Structure

Heap: The heap is an entire binary tree possessing the heap property. The tree is usually implemented as an array on a binary heap.

Tree: There are many types of trees, such as multi-way trees (like B-trees), binary trees, and balanced trees (like AVL and red-black trees). A tree's structure is determined by its kind and the particular needs of its intended use.

3. Operations

Heap: Inserting and extracting the minimum (or maximum) element are among the actions that heaps generally facilitate. Maintaining the heap property also frequently involves heapify activities.

Tree: Trees may perform a wide range of operations, such as traversal (e.g., inorder, preorder, postorder), insertion, deletion, and searching.

4. Efficiency

Heap: Heaps offer quick Access to the minimum or maximum element, which is suitable for applications involving priority queues. However, some processes might not be as effective as others.

Tree: Activities can be more or less efficient depending on the kind of tree. For example, compared to unbalanced trees, balanced trees offer more effective search and retrieval operations.

Conclusion:

In conclusion, heaps and trees are two types of hierarchical data structures with different functions and features. Trees are more versatile and can take on different shapes based on the situation's needs, whereas Heaps are specifically designed for efficient Access to extremal elements.

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