golang中container/heap包源码分析
Posted Davygeek
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学习golang难免需要分析源码包中一些实现,下面就来说说container/heap包的源码
heap的实现使用到了小根堆,下面先对堆做个简单说明
1. 堆概念
2. heap
树的最小元素在根部,为index 0.
heap包对任意实现了heap接口的类型提供堆操作。
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。
// Any type that implements heap.Interface may be used as a // min-heap with the following invariants (established after // Init has been called or if the data is empty or sorted): // // !h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len() // // Note that Push and Pop in this interface are for package heap‘s // implementation to call. To add and remove things from the heap, // use heap.Push and heap.Pop. type Interface interface { sort.Interface Push(x interface{}) // add x as element Len() Pop() interface{} // remove and return element Len() - 1. }
// A type, typically a collection, that satisfies sort.Interface can be // sorted by the routines in this package. The methods require that the // elements of the collection be enumerated by an integer index. type Interface interface { // Len is the number of elements in the collection. Len() int // Less reports whether the element with // index i should sort before the element with index j. Less(i, j int) bool // Swap swaps the elements with indexes i and j. Swap(i, j int) }
根据上面interface的定义,可以看出这个堆结构继承自sort.Interface, 而sort.Interface,需要实现三个方法:Len(), Less() , Swap() 。
同事还需要实现堆接口定义的两个方法:Push(x interface{}) / Pop() interface{}, 所以我们要想使用heap定义一个堆, 只需要定义实现了这五个方法结构就可以了。
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。
以下是heap导出的方法:
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()。 func Init(h Interface) //初始化一个堆。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 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()。该函数等价于Remove(h, 0)。 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 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()。
实例:
1. 包含int的最小堆
// 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 }
2. 用heap创建一个优先级队列
// 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 }
说明:测试源码都是golang包里面提供的, 有兴趣可以直接去查阅下golang源码
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