Implementing the Heap Sort Algorithm in C++
Heap sort is an efficient sorting algorithm based on the heap data structure, with a time complexity of O(n log n) and a space complexity of O(1), making it suitable for large-scale data. A heap is a special complete binary tree, divided into max heaps (parent ≥ children) and min heaps, with max heaps commonly used in sorting. It is stored in an array where the parent of index i is (i-1)/2, and the left and right children are 2i+1 and 2i+2, respectively. The core steps are: 1. Constructing the initial max heap (adjusting from the last non-leaf node upwards); 2. Sorting (swapping the top element with the end of the unsorted part, adjusting the heap, and repeating until completion). The C++ implementation includes swap, max_heapify (iteratively adjusting the subtree to form a max heap), and heap_sort (constructing the heap and performing sorting) functions. The main function tests array sorting, and the output result is correct.
Read MoreImplementing Heap Sort Algorithm with Python
Heap Sort is an efficient sorting algorithm that leverages the heap data structure, with a stable time complexity of O(n log n) and a space complexity of O(1), making it suitable for sorting large-scale data. A heap is a complete binary tree where parent node values are either greater than or equal to (max heap) or less than or equal to (min heap) their child node values. In an array representation, the indices of a heap follow these relationships: the children of a parent node at index i are located at 2i+1 and 2i+2, while the parent of a child node at index j is at (j-1)//2. The core operations include: 1. **Heapify**: Adjust the subtree rooted at index i to be a max heap by recursively comparing child nodes and swapping values as needed. 2. **Build Max Heap**: Starting from the last non-leaf node (n//2 - 1) and moving upward, adjust all nodes to ensure the entire tree satisfies the max heap property. The sorting process involves: first building the max heap, then repeatedly swapping the root (maximum value) with the last element of the heap, followed by calling Heapify to re-adjust the remaining elements into a max heap. This results in a sorted array from smallest to largest. Heap Sort is an in-place sorting algorithm, making it well-suited for scenarios with large data volumes.
Read MoreWhat is a Heap? A Detailed Explanation of Basic Operations on Heaps in Data Structures
A heap is a special structure based on a complete binary tree, stored in an array, and satisfies the properties of a max heap (parent node value ≥ child node) or a min heap (parent node value ≤ child node). It can efficiently retrieve the maximum or minimum value and is widely used in algorithms. The array indices map parent-child relationships: left child is at 2i+1, right child at 2i+2, and parent is at (i-1)//2. A max heap has the largest root (e.g., [9,5,7,3,6,2,4]), while a min heap has the smallest root (e.g., [3,6,5,9,7,2,4]). Core operations include insertion (appending new element to the end and adjusting upward to satisfy heap property), deletion (swapping root with last element and adjusting downward), heap construction (adjusting from the last non-leaf node downward), and retrieving the root (directly accessing the root node). It is applied in priority queues, heap sort, and Top K problems. The efficient structure and operations of heaps are crucial for understanding algorithms, and beginners can start with array simulation to master them.
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