libgo/go/container/heap/heap.go

   1 // Copyright 2009 The Go Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style
   3 // license that can be found in the LICENSE file.
   4
   5 // Package heap provides heap operations for any type that implements
   6 // heap.Interface. A heap is a tree with the property that each node is the
   7 // minimum-valued node in its subtree.
   8 //
   9 // The minimum element in the tree is the root, at index 0.
  10 //
  11 // A heap is a common way to implement a priority queue. To build a priority
  12 // queue, implement the Heap interface with the (negative) priority as the
  13 // ordering for the Less method, so Push adds items while Pop removes the
  14 // highest-priority item from the queue. The Examples include such an
  15 // implementation; the file example_pq_test.go has the complete source.
  16 //
  17 package heap
  18
  19 import "sort"
  20
  21 // Any type that implements heap.Interface may be used as a
  22 // min-heap with the following invariants (established after
  23 // Init has been called or if the data is empty or sorted):
  24 //
  25 //      !h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()
  26 //
  27 // Note that Push and Pop in this interface are for package heap's
  28 // implementation to call. To add and remove things from the heap,
  29 // use heap.Push and heap.Pop.
  30 type Interface interface {
  31         sort.Interface
  32         Push(x interface{}) // add x as element Len()
  33         Pop() interface{}   // remove and return element Len() - 1.
  34 }
  35
  36 // A heap must be initialized before any of the heap operations
  37 // can be used. Init is idempotent with respect to the heap invariants
  38 // and may be called whenever the heap invariants may have been invalidated.
  39 // Its complexity is O(n) where n = h.Len().
  40 //
  41 func Init(h Interface) {
  42         // heapify
  43         n := h.Len()
  44         for i := n/2 - 1; i >= 0; i-- {
  45                 down(h, i, n)
  46         }
  47 }
  48
  49 // Push pushes the element x onto the heap. The complexity is
  50 // O(log(n)) where n = h.Len().
  51 //
  52 func Push(h Interface, x interface{}) {
  53         h.Push(x)
  54         up(h, h.Len()-1)
  55 }
  56
  57 // Pop removes the minimum element (according to Less) from the heap
  58 // and returns it. The complexity is O(log(n)) where n = h.Len().
  59 // It is equivalent to Remove(h, 0).
  60 //
  61 func Pop(h Interface) interface{} {
  62         n := h.Len() - 1
  63         h.Swap(0, n)
  64         down(h, 0, n)
  65         return h.Pop()
  66 }
  67
  68 // Remove removes the element at index i from the heap.
  69 // The complexity is O(log(n)) where n = h.Len().
  70 //
  71 func Remove(h Interface, i int) interface{} {
  72         n := h.Len() - 1
  73         if n != i {
  74                 h.Swap(i, n)
  75                 if !down(h, i, n) {
  76                         up(h, i)
  77                 }
  78         }
  79         return h.Pop()
  80 }
  81
  82 // Fix re-establishes the heap ordering after the element at index i has changed its value.
  83 // Changing the value of the element at index i and then calling Fix is equivalent to,
  84 // but less expensive than, calling Remove(h, i) followed by a Push of the new value.
  85 // The complexity is O(log(n)) where n = h.Len().
  86 func Fix(h Interface, i int) {
  87         if !down(h, i, h.Len()) {
  88                 up(h, i)
  89         }
  90 }
  91
  92 func up(h Interface, j int) {
  93         for {
  94                 i := (j - 1) / 2 // parent
  95                 if i == j || !h.Less(j, i) {
  96                         break
  97                 }
  98                 h.Swap(i, j)
  99                 j = i
 100         }
 101 }
 102
 103 func down(h Interface, i0, n int) bool {
 104         i := i0
 105         for {
 106                 j1 := 2*i + 1
 107                 if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
 108                         break
 109                 }
 110                 j := j1 // left child
 111                 if j2 := j1 + 1; j2 < n && h.Less(j2, j1) {
 112                         j = j2 // = 2*i + 2  // right child
 113                 }
 114                 if !h.Less(j, i) {
 115                         break
 116                 }
 117                 h.Swap(i, j)
 118                 i = j
 119         }
 120         return i > i0
 121 }