Jimy Ma's Zone
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堆的实现

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堆结构

  • 定义
    • 一种特殊形式的完全二叉树
    • 任何一个非终结节点的元素都不小（大）于其左右儿子节点的元素，则称此二叉树为最大（小）堆。

堆结构的基本操作

  1. MaxHeap() 申请一个空堆
  2. Insert() 向堆中插入元素
  3. HeapEmpty() 是否堆空
  4. DeletMax() 删除最大元素

插入操作

  • 插入到最后，然后和父节点比较，如果比父节点大，那么和父节点交换位置

删除操作

  • 将堆的末尾元素替换堆顶元素，然后将子节点，父节点中较大的元素作为父节点这样一直迭代下去。

堆结构的 golang 实现

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package max_heap

import "fmt"

type MaxHeap struct {
	Elements []int
	Cnt int
}

func NewMaxHeap() *MaxHeap {
	return &MaxHeap {Elements: []int{}, Cnt: -1}
}

func GenMaxHeap(elements []int) *MaxHeap {
	maxHeap := NewMaxHeap()
	for i:= 0; i < len(elements); i++ {
		maxHeap.Insert(elements[i])
	}
	return maxHeap
}

func (maxHeap MaxHeap) PrintElements() {
	for i := 0; i <= maxHeap.Cnt; i++ {
		fmt.Print(maxHeap.Elements[i], " ")
	}
}

func (maxHeap MaxHeap) HeapEmpty() bool {
	return maxHeap.Cnt == -1
}

func (maxHeap *MaxHeap) Insert(element int) {
	maxHeap.Cnt += 1
	maxHeap.Elements = append(maxHeap.Elements, element)
	var i = maxHeap.Cnt
	for i != 0 && maxHeap.Elements[i] > maxHeap.Elements[(i+1) / 2 - 1] {
		maxHeap.Elements[i], maxHeap.Elements[(i+1) / 2 - 1] =
			maxHeap.Elements[(i + 1) / 2 - 1], maxHeap.Elements[i]
		i = (i + 1) / 2 - 1
	}
}

func (maxHeap *MaxHeap) DeleteMax() int {
	tmp := maxHeap.Elements[0]
	maxHeap.Elements[0] = maxHeap.Elements[maxHeap.Cnt]
	maxHeap.Elements = maxHeap.Elements[0:maxHeap.Cnt]
	maxHeap.Cnt -= 1
	parentIdx := 0
	for parentIdx <= maxHeap.Cnt {
		leftchildIdx := (parentIdx + 1) * 2 - 1
		if leftchildIdx > maxHeap.Cnt {
			break
		}
		maxChildIdx := leftchildIdx
		rightChildIdx := leftchildIdx + 1
		if rightChildIdx <= maxHeap.Cnt && maxHeap.Elements[rightChildIdx] > maxHeap.Elements[leftchildIdx] {
			maxChildIdx = rightChildIdx
		}
		if maxHeap.Elements[parentIdx] < maxHeap.Elements[maxChildIdx] {
			maxHeap.Elements[parentIdx], maxHeap.Elements[maxChildIdx] =
				maxHeap.Elements[maxChildIdx], maxHeap.Elements[parentIdx]

			parentIdx = maxChildIdx
		} else {
			break
		}
	}
	return tmp
}

func main() {
	var num int
	fmt.Scanf("%d", &num)
	var heapArr []int
	for i:= 0; i < num; i++ {
		var tmp int
		fmt.Scanf("%d", &tmp)
		heapArr = append(heapArr, tmp)
	}
	maxHeap := GenMaxHeap(heapArr)
	maxHeap.DeleteMax()
	maxHeap.PrintElements()
}