Go语言数据结构（二）堆/优先队列

更多内容以及其他Go常用数据结构的实现在这里，感谢Star：https://github.com/acezsq/Data_Structure_Golang

1. container中定义的heap

在golang中的"container/heap"源码包中定义了堆的实现，我们在使用时需要实现heap接口中定义的方法，以此实现一个堆。
在container/heap.go中的heap接口的定义如下：

type Interface interface {sort.InterfacePush(x any) // add x as element Len()Pop() any   // remove and return element Len() - 1.
}

而sort包中的接口定义如下：

type Interface interface {// Len is the number of elements in the collection.Len() int// Less reports whether the element with index i// must sort before the element with index j.//// If both Less(i, j) and Less(j, i) are false,// then the elements at index i and j are considered equal.// Sort may place equal elements in any order in the final result,// while Stable preserves the original input order of equal elements.//// Less must describe a transitive ordering://  - if both Less(i, j) and Less(j, k) are true, then Less(i, k) must be true as well.//  - if both Less(i, j) and Less(j, k) are false, then Less(i, k) must be false as well.//// Note that floating-point comparison (the < operator on float32 or float64 values)// is not a transitive ordering when not-a-number (NaN) values are involved.// See Float64Slice.Less for a correct implementation for floating-point values.Less(i, j int) bool// Swap swaps the elements with indexes i and j.Swap(i, j int)
}

所以我们实现一个堆时需要实现这五个方法，然后相当于实现了这个接口，然后就可以调用container/heap.go中定义的Init方法、Push方法、Pop方法进行堆的基础入堆、出堆操作。
在使用这三个方法时，需要注意按照源码中定义的函数的入参和返回值的类型来使用。

// Init establishes the heap invariants required by the other routines in this package.
// Init is idempotent with respect to the heap invariants
// and may be called whenever the heap invariants may have been invalidated.
// The complexity is O(n) where n = h.Len().
func Init(h Interface) {// heapifyn := h.Len()for i := n/2 - 1; i >= 0; i-- {down(h, i, n)}
}

// Push pushes the element x onto the heap.
// The complexity is O(log n) where n = h.Len().
func Push(h Interface, x any) {h.Push(x)up(h, h.Len()-1)
}

// Pop removes and returns the minimum element (according to Less) from the heap.
// The complexity is O(log n) where n = h.Len().
// Pop is equivalent to Remove(h, 0).
func Pop(h Interface) any {n := h.Len() - 1h.Swap(0, n)down(h, 0, n)return h.Pop()
}

2. heap的使用示例

在golang的源码中也有堆的使用示例：
可以看到实现上我们用切片来作为heap的底层实现类型。
下面的代码是定义一个小根堆的示例，如果我们想定义一个存int类型数据的大根堆，只需要把Less函数中的小于号换成大于号即可。

// Copyright 2012 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.// This example demonstrates an integer heap built using the heap interface.
package heap_testimport ("container/heap""fmt"
)// An IntHeap is a min-heap of ints.
type IntHeap []intfunc (h IntHeap) Len() int           { return len(h) }
func (h IntHeap) Less(i, j int) bool { return h[i] < h[j] }
func (h IntHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }func (h *IntHeap) Push(x any) {// Push and Pop use pointer receivers because they modify the slice's length,// not just its contents.*h = append(*h, x.(int))
}func (h *IntHeap) Pop() any {old := *hn := len(old)x := old[n-1]*h = old[0 : n-1]return x
}// This example inserts several ints into an IntHeap, checks the minimum,
// and removes them in order of priority.
func Example_intHeap() {h := &IntHeap{2, 1, 5}heap.Init(h)heap.Push(h, 3)fmt.Printf("minimum: %d\n", (*h)[0])for h.Len() > 0 {fmt.Printf("%d ", heap.Pop(h))}// Output:// minimum: 1// 1 2 3 5
}

3. 刷lc应用堆的示例

我们看一下23. 合并 K 个升序链表

这个题需要定义一个小根堆来存链表节点指针。

/*** Definition for singly-linked list.* type ListNode struct {*     Val int*     Next *ListNode* }*/
func mergeKLists(lists []*ListNode) *ListNode {h := minHeap{}for _, head := range lists {if head != nil {h = append(h, head) }}     heap.Init(&h) dummyhead := &ListNode{}cur := dummyheadfor len(h)>0 {node := heap.Pop(&h).(*ListNode)if node.Next != nil {heap.Push(&h, node.Next)}cur.Next = nodecur = cur.Next}return dummyhead.Next
}type minHeap []*ListNode
func (h minHeap) Len() int {return len(h)}
func (h minHeap) Less(i,j int) bool {return h[i].Val<h[j].Val}
func (h minHeap) Swap(i,j int) { h[i], h[j] = h[j], h[i]}
func (h *minHeap) Push(x any) { *h = append(*h, x.(*ListNode))}
func (h *minHeap) Pop() any { old:=*h; n:=len(old); x:=old[n-1]; *h=old[:n-1]; return x}