Classic sorting algorithm-heap sort heap sorts

Classic sorting algorithm-heap sort heap sorts

The heap sort is a little complex, divided into three pieces.

The first block, what is the heap, what is the maximum heap

The second block, how to adjust the heap to the maximum heap, this part is the focus

Third piece, heap sort introduction

The first block, what is the heap, what is the maximum heap

What is a heap

Here the heap (binary heap), refers to not the stack of the heap, but a data structure.

The heap can be regarded as a complete two-fork tree, and an "excellent" property of a complete binary tree is that each layer is full except the bottommost, which allows the heap to be represented by an array, with each node corresponding to an element in the array.

The relationship between the array and the heap

Binary heaps are generally divided into two types: maximum heap and minimum heap.

What is the maximum heap

The element value of each parent node in the heap is greater than or equal to its child node (if present), so the heap is a maximum heap

Therefore, the largest element value in the maximum heap appears at the root node (heap top).

Relationship between node and array index

For a given node subscript I, it is easy to calculate the parent node of the node, the child node subscript, and the calculation formula is very beautiful and simple

The second block, how to adjust the heap to the maximum heap, this part is the focus

The whole process is as shown

In this small heap of 4,14,7, the parent node 4 is smaller than the left child 14, so the two exchange

In 4,2,8 this small heap inside, the parent node 4 small less right operand child 8, so the two exchange

Shows the process of adjustment, which is implemented recursively until the maximum heap is adjusted.

Third piece, heap sort introduction

The heap sort is to take the maximum number out of the top of the heap,

The remaining heap continues to be adjusted to the maximum heap, and the process is introduced in the second block, which is implemented recursively

After the remainder is adjusted to the maximum heap, the maximum number of heap tops is removed again, the remainder is adjusted to the maximum heap, and the process lasts until the remaining number is only one end

The bottom three graphs describe the whole process in detail

Reference articles

Http://blog.kingsamchen.com/archives/547#viewSource

Classic sorting algorithm-heap sort heap sorts