Introduction to algorithms-Chapter 2-heap sorting

1.In-situ sortingIt refers to the sorting by comparison and exchange in the original sorting data without applying for additional space. For example, fast sorting and heap sorting are all in-situ sorting, Merge Sorting, and count sorting.

Stable sortingThat is, if the two numbers are the same, the sorting results for them will not change their relative order. 2 Stack definition:
　

 N key word sequences Kl, K2 ,..., Kn is called a heap, and only when the sequence meets the following properties (referred to as heap properties ):

 (1) ki <= k (2i + 1) and ki <= k (2i + 2) (1 ≤ I ≤
N), of course, this is a small root heap, and the big root heap is replaced with the "> =" sign. // Ki is equivalent to a non-leaf node of a binary tree. K2i is the left child and k2i + 1 is the right child.

 If we regard the vector R [1. n] stored in this sequence as a storage structure of a Complete Binary Tree, the heap is essentially a Complete Binary Tree that meets the following requirements:

 The keywords of any non-leaf node in the tree are not greater than (or not less than) the keywords of its left and right children (if any) nodes.

Heap sorting:

Heap sorting is a kind of sorting. Is an unstable sorting method. The time complexity is O (nlogn ).

Heap sorting is characterized by the sequential storage structure of a Complete Binary Tree in the sorting process. The inherent relationship between parent and child nodes in the Complete Binary Tree is used, select the record with the maximum or minimum keyword in the unordered area.

Basic Idea of heap sorting:

1. Create an array to be sorted as a large root heap. The top element of the heap is the largest element in the heap.

2. Swap the top elements of a large root heap with the last element in the unordered zone, enter the last position of the unordered zone as an example, and then change the new unordered zone to a large root heap. Repeated operations: unordered areas are decreasing, and ordered areas are increasing.

Basic nature of a Complete Binary Tree:

The array contains n elements, I is a node, and 1 <= I <= n/2 means that the last half of the array is a leaf node.

 I parent node location: I/2

 I left subnode position: I * 2

 I right sub-node position: I * 2 + 1

Length [A] is the number of elements in the array, and heap-size [A] is the number of elements stored in heap.

Below I follow the algorithms provided in the introduction to algorithms, and use c ++ to implement heap sorting and debugging.

# Include <iostream> using namespace std; int data [10] = {151,138,160, 63,174,169, 79, 78}; void max_heapify (int data [], int I, int heapsize) // adjust the subtree with a node as the root node to a large top heap {int l = 2 * I + 1; int r = 2 * I + 2; int largest = I; if (l