Source file src/pkg/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.
     7	//
     8	package heap
     9	
    10	import "sort"
    11	
    12	// Any type that implements heap.Interface may be used as a
    13	// min-heap with the following invariants (established after
    14	// Init has been called):
    15	//
    16	//	!h.Less(j, i) for 0 <= i < h.Len() and j = 2*i+1 or 2*i+2 and j < h.Len()
    17	//
    18	type Interface interface {
    19		sort.Interface
    20		Push(x interface{})
    21		Pop() interface{}
    22	}
    23	
    24	// A heap must be initialized before any of the heap operations
    25	// can be used. Init is idempotent with respect to the heap invariants
    26	// and may be called whenever the heap invariants may have been invalidated.
    27	// Its complexity is O(n) where n = h.Len().
    28	//
    29	func Init(h Interface) {
    30		// heapify
    31		n := h.Len()
    32		for i := n/2 - 1; i >= 0; i-- {
    33			down(h, i, n)
    34		}
    35	}
    36	
    37	// Push pushes the element x onto the heap. The complexity is
    38	// O(log(n)) where n = h.Len().
    39	//
    40	func Push(h Interface, x interface{}) {
    41		h.Push(x)
    42		up(h, h.Len()-1)
    43	}
    44	
    45	// Pop removes the minimum element (according to Less) from the heap
    46	// and returns it. The complexity is O(log(n)) where n = h.Len().
    47	// Same as Remove(h, 0).
    48	//
    49	func Pop(h Interface) interface{} {
    50		n := h.Len() - 1
    51		h.Swap(0, n)
    52		down(h, 0, n)
    53		return h.Pop()
    54	}
    55	
    56	// Remove removes the element at index i from the heap.
    57	// The complexity is O(log(n)) where n = h.Len().
    58	//
    59	func Remove(h Interface, i int) interface{} {
    60		n := h.Len() - 1
    61		if n != i {
    62			h.Swap(i, n)
    63			down(h, i, n)
    64			up(h, i)
    65		}
    66		return h.Pop()
    67	}
    68	
    69	func up(h Interface, j int) {
    70		for {
    71			i := (j - 1) / 2 // parent
    72			if i == j || h.Less(i, j) {
    73				break
    74			}
    75			h.Swap(i, j)
    76			j = i
    77		}
    78	}
    79	
    80	func down(h Interface, i, n int) {
    81		for {
    82			j1 := 2*i + 1
    83			if j1 >= n {
    84				break
    85			}
    86			j := j1 // left child
    87			if j2 := j1 + 1; j2 < n && !h.Less(j1, j2) {
    88				j = j2 // = 2*i + 2  // right child
    89			}
    90			if h.Less(i, j) {
    91				break
    92			}
    93			h.Swap(i, j)
    94			i = j
    95		}
    96	}
The Go Programming Language

Source file src/pkg/container/heap/heap.go
