package heap

import "container/heap"

heap包提供了对任意类型(实现了heap.Interface接口)的堆操作。(最小)堆是具有“每个节点都是以其为根的子树中最小值”属性的树。

树的最小元素为其根元素,索引0的位置。

heap是常用的实现优先队列的方法。要创建一个优先队列,实现一个具有使用(负的)优先级作为比较的依据的Less方法的Heap接口,如此一来可用Push添加项目而用Pop取出队列最高优先级的项目。

Example (IntHeap)
// This example demonstrates an integer heap built using the heap interface.
package heap_test
import (
 "container/heap"
 "fmt"
)
// An IntHeap is a min-heap of ints.
type IntHeap []int
func (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 interface{}) {
 // 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() interface{} {
 old := *h
 n := 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
}
Example (PriorityQueue)
// This example demonstrates a priority queue built using the heap interface.
package heap_test
import (
 "container/heap"
 "fmt"
)
// An Item is something we manage in a priority queue.
type Item struct {
 value string // The value of the item; arbitrary.
 priority int // The priority of the item in the queue.
 // The index is needed by update and is maintained by the heap.Interface methods.
 index int // The index of the item in the heap.
}
// A PriorityQueue implements heap.Interface and holds Items.
type PriorityQueue []*Item
func (pq PriorityQueue) Len() int { return len(pq) }
func (pq PriorityQueue) Less(i, j int) bool {
 // We want Pop to give us the highest, not lowest, priority so we use greater than here.
 return pq[i].priority > pq[j].priority
}
func (pq PriorityQueue) Swap(i, j int) {
 pq[i], pq[j] = pq[j], pq[i]
 pq[i].index = i
 pq[j].index = j
}
func (pq *PriorityQueue) Push(x interface{}) {
 n := len(*pq)
 item := x.(*Item)
 item.index = n
 *pq = append(*pq, item)
}
func (pq *PriorityQueue) Pop() interface{} {
 old := *pq
 n := len(old)
 item := old[n-1]
 item.index = -1 // for safety
 *pq = old[0 : n-1]
 return item
}
// update modifies the priority and value of an Item in the queue.
func (pq *PriorityQueue) update(item *Item, value string, priority int) {
 item.value = value
 item.priority = priority
 heap.Fix(pq, item.index)
}
// This example creates a PriorityQueue with some items, adds and manipulates an item,
// and then removes the items in priority order.
func Example_priorityQueue() {
 // Some items and their priorities.
 items := map[string]int{
 "banana": 3, "apple": 2, "pear": 4,
 }
 // Create a priority queue, put the items in it, and
 // establish the priority queue (heap) invariants.
 pq := make(PriorityQueue, len(items))
 i := 0
 for value, priority := range items {
 pq[i] = &Item{
 value: value,
 priority: priority,
 index: i,
 }
 i++
 }
 heap.Init(&pq)
 // Insert a new item and then modify its priority.
 item := &Item{
 value: "orange",
 priority: 1,
 }
 heap.Push(&pq, item)
 pq.update(item, item.value, 5)
 // Take the items out; they arrive in decreasing priority order.
 for pq.Len() > 0 {
 item := heap.Pop(&pq).(*Item)
 fmt.Printf("%.2d:%s ", item.priority, item.value)
 }
 // Output:
 // 05:orange 04:pear 03:banana 02:apple
}

Index

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  • type Interface
  • func Init(h Interface)
  • func Push(h Interface, x interface{})
  • func Pop(h Interface) interface{}
  • func Remove(h Interface, i int) interface{}
  • func Fix(h Interface, i int)
  • Examples

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  • package (IntHeap)
  • package (PriorityQueue)
  • type Interface

    type Interface interface {
     sort.Interface
     Push(x interface{}) // 向末尾添加元素
     Pop() interface{} // 从末尾删除元素
    }

    任何实现了本接口的类型都可以用于构建最小堆。最小堆可以通过heap.Init建立,数据是递增顺序或者空的话也是最小堆。最小堆的约束条件是:

    !h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()
    

    注意接口的Push和Pop方法是供heap包调用的,请使用heap.Push和heap.Pop来向一个堆添加或者删除元素。

    func Init

    func Init(h Interface)

    一个堆在使用任何堆操作之前应先初始化。Init函数对于堆的约束性是幂等的(多次执行无意义),并可能在任何时候堆的约束性被破坏时被调用。本函数复杂度为O(n),其中n等于h.Len()。

    func Push

    func Push(h Interface, x interface{})

    向堆h中插入元素x,并保持堆的约束性。复杂度O(log(n)),其中n等于h.Len()。

    func Pop

    func Pop(h Interface) interface{}

    删除并返回堆h中的最小元素(不影响约束性)。复杂度O(log(n)),其中n等于h.Len()。等价于Remove(h, 0)。

    func Remove

    func Remove(h Interface, i int) interface{}

    删除堆中的第i个元素,并保持堆的约束性。复杂度O(log(n)),其中n等于h.Len()。

    func Fix

    func Fix(h Interface, i int)

    在修改第i个元素后,调用本函数修复堆,比删除第i个元素后插入新元素更有效率。

    复杂度O(log(n)),其中n等于h.Len()。

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