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  package heap
    17  
    18  import "sort"
    19  
    20  // The Interface type describes the requirements
    21  // for a type using the routines in this package.
    22  // Any type that implements it may be used as a
    23  // min-heap with the following invariants (established after
    24  // [Init] has been called or if the data is empty or sorted):
    25  //
    26  //	!h.Less(j, i) for 0 <= i < h.Len() and 2*i+1 <= j <= 2*i+2 and j < h.Len()
    27  //
    28  // Note that [Push] and [Pop] in this interface are for package heap's
    29  // implementation to call. To add and remove things from the heap,
    30  // use [heap.Push] and [heap.Pop].
    31  type Interface interface {
    32  	sort.Interface
    33  	Push(x any) // add x as element Len()
    34  	Pop() any   // remove and return element Len() - 1.
    35  }
    36  
    37  // Init establishes the heap invariants required by the other routines in this package.
    38  // Init is idempotent with respect to the heap invariants
    39  // and may be called whenever the heap invariants may have been invalidated.
    40  // The complexity is O(n) where n = h.Len().
    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.
    50  // The complexity is O(log n) where n = h.Len().
    51  func Push(h Interface, x any) {
    52  	h.Push(x)
    53  	up(h, h.Len()-1)
    54  }
    55  
    56  // Pop removes and returns the minimum element (according to Less) from the heap.
    57  // The complexity is O(log n) where n = h.Len().
    58  // Pop is equivalent to [Remove](h, 0).
    59  func Pop(h Interface) any {
    60  	n := h.Len() - 1
    61  	h.Swap(0, n)
    62  	down(h, 0, n)
    63  	return h.Pop()
    64  }
    65  
    66  // Remove removes and returns the element at index i from the heap.
    67  // The complexity is O(log n) where n = h.Len().
    68  func Remove(h Interface, i int) any {
    69  	n := h.Len() - 1
    70  	if n != i {
    71  		h.Swap(i, n)
    72  		if !down(h, i, n) {
    73  			up(h, i)
    74  		}
    75  	}
    76  	return h.Pop()
    77  }
    78  
    79  // Fix re-establishes the heap ordering after the element at index i has changed its value.
    80  // Changing the value of the element at index i and then calling Fix is equivalent to,
    81  // but less expensive than, calling [Remove](h, i) followed by a Push of the new value.
    82  // The complexity is O(log n) where n = h.Len().
    83  func Fix(h Interface, i int) {
    84  	if !down(h, i, h.Len()) {
    85  		up(h, i)
    86  	}
    87  }
    88  
    89  func up(h Interface, j int) {
    90  	for {
    91  		i := (j - 1) / 2 // parent
    92  		if i == j || !h.Less(j, i) {
    93  			break
    94  		}
    95  		h.Swap(i, j)
    96  		j = i
    97  	}
    98  }
    99  
   100  func down(h Interface, i0, n int) bool {
   101  	i := i0
   102  	for {
   103  		j1 := 2*i + 1
   104  		if j1 >= n || j1 < 0 { // j1 < 0 after int overflow
   105  			break
   106  		}
   107  		j := j1 // left child
   108  		if j2 := j1 + 1; j2 < n && h.Less(j2, j1) {
   109  			j = j2 // = 2*i + 2  // right child
   110  		}
   111  		if !h.Less(j, i) {
   112  			break
   113  		}
   114  		h.Swap(i, j)
   115  		i = j
   116  	}
   117  	return i > i0
   118  }
   119
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