// Copyright 2009 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. // Package heap provides heap operations for any type that implements // heap.Interface. A heap is a tree with the property that each node is the // minimum-valued node in its subtree. // // The minimum element in the tree is the root, at index 0. // // A heap is a common way to implement a priority queue. To build a priority // queue, implement the Heap interface with the (negative) priority as the // ordering for the Less method, so Push adds items while Pop removes the // highest-priority item from the queue. The Examples include such an // implementation; the file example_pq_test.go has the complete source. // package heap import "sort" // 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 heap must be initialized before any of the heap operations // can be used. Init is idempotent with respect to the heap invariants // and may be called whenever the heap invariants may have been invalidated. // Its complexity is O(n) where n = h.Len(). // func Init(h Interface) { // heapify n := 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 interface{}) { h.Push(x) up(h, h.Len()-1) } // Pop removes the minimum element (according to Less) from the heap // and returns it. The complexity is O(log(n)) where n = h.Len(). // It is equivalent to Remove(h, 0). // func Pop(h Interface) interface{} { n := h.Len() - 1 h.Swap(0, n) down(h, 0, n) return h.Pop() } // Remove removes the element at index i from the heap. // The complexity is O(log(n)) where n = h.Len(). // func Remove(h Interface, i int) interface{} { n := h.Len() - 1 if n != i { h.Swap(i, n) down(h, i, n) up(h, i) } return h.Pop() } // Fix re-establishes the heap ordering after the element at index i has changed its value. // Changing the value of the element at index i and then calling Fix is equivalent to, // but less expensive than, calling Remove(h, i) followed by a Push of the new value. // The complexity is O(log(n)) where n = h.Len(). func Fix(h Interface, i int) { down(h, i, h.Len()) up(h, i) } func up(h Interface, j int) { for { i := (j - 1) / 2 // parent if i == j || !h.Less(j, i) { break } h.Swap(i, j) j = i } } func down(h Interface, i, n int) { for { j1 := 2*i + 1 if j1 >= n || j1 < 0 { // j1 < 0 after int overflow break } j := j1 // left child if j2 := j1 + 1; j2 < n && !h.Less(j1, j2) { j = j2 // = 2*i + 2 // right child } if !h.Less(j, i) { break } h.Swap(i, j) i = j } }