Fibonacci heap: Difference between revisions

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=={{header|C++}}==
<langsyntaxhighlight lang="cpp">template <class V> class FibonacciHeap;
 
template <class V> struct node {
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}
 
</syntaxhighlight>
</lang>
 
=={{header|Go}}==
A package. Implementation follows Fredman and Tarjan's 1987 paper.
<langsyntaxhighlight lang="go">package fib
 
import "fmt"
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}
f(h.Node, "")
}</langsyntaxhighlight>
A demonstration:
<langsyntaxhighlight lang="go">package main
 
import (
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h.Delete(x)
h.Vis()
}</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Julia}}==
{{trans|Python}}
<langsyntaxhighlight lang="julia">module FibonacciHeaps
 
export FNode, FibonacciHeap, insert, extractmin, findmin, decreasekey, delete!
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print(h3)
println("The minimum of h3 is now: ", Minimum(h3).value
</langsyntaxhighlight>{{out}}
<pre>
Made heap 1:
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=={{header|Kotlin}}==
{{trans|Go}}
<langsyntaxhighlight lang="scala">// version 1.2.21
 
class Node<V : Comparable<V>>(var value: V) {
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h.delete(x)
h.visualize()
}</langsyntaxhighlight>
 
{{out}}
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</pre>
 
=={{header|PhixNim}}==
{{trans|Go & Kotlin}}
<syntaxhighlight lang="nim">import strutils, tables
<lang Phix>enum VALUE, PARENT, CHILD, PREV, NEXT, RANK, MARK, NODELEN=$
 
type
function new_node()
return repeat(NULL,NODELEN)
end function
 
Node*[T] = ref object
sequence nodes = {}
value: T
integer freelist = NULL
parent: Node[T]
child: Node[T]
prev, next: Node[T]
rank: int
mark: bool
 
Heap*[T] = object
function new_slot()
integernode: resNode[T]
if freelist!=NULL then
res = freelist
freelist = nodes[freelist]
nodes[freelist] = NULL
else
nodes = append(nodes,NULL)
res = length(nodes)
end if
return res
end function
 
procedure release_slot(integer n)
nodes[n] = freelist
freelist = n
end procedure
 
func meld1[T](list, single: Node[T]) =
-- task requirement
list.prev.next = single
function MakeHeap()
single.prev = list.prev
return new_slot()
single.next = list
end function
list.prev = single
procedure meld1(integer list, single)
nodes[nodes[list][PREV]][NEXT] = single
nodes[single][PREV] = nodes[list][PREV]
nodes[single][NEXT] = list
nodes[list][PREV] = single
end procedure
 
-- task requirement
function Insert(integer h, object v)
integer n = 0
sequence x = new_node()
x[VALUE] = v
if nodes[h] == NULL then
x[NEXT] = h
x[PREV] = h
nodes[h] = x
else
n = new_slot()
nodes[n] = x
meld1(h, n)
if nodes[n][VALUE]<nodes[h][VALUE] then
h = n
end if
end if
return {h,n}
end function
procedure meld2(integer a, b)
nodes[nodes[a][PREV]][NEXT] = b
nodes[nodes[b][PREV]][NEXT] = a
{nodes[a][PREV], nodes[b][PREV]} = {nodes[b][PREV], nodes[a][PREV]}
end procedure
 
func meld2[T](a, b: Node[T]) =
-- task requirement
a.prev.next = b
function Union(integer h, h2)
b.prev.next = a
if nodes[h] == NULL then
swap a.prev, b.prev
h = h2
elsif nodes[h2] != NULL then
meld2(h, h2)
if nodes[h2][VALUE]<nodes[h][VALUE] then
h = h2
end if
else
release_slot(h2)
end if
return {h,NULL} -- (h2:=NULL implied)
end function
-- task requirement
function Minimum(integer h)
if nodes[h] == NULL then
return {"<none>",false}
end if
return {nodes[h][VALUE], true}
end function
 
procedure add_roots(integer r, integer roots)
nodes[r][PREV] = r
nodes[r][NEXT] = r
while true do
integer node = getd_index(nodes[r][RANK],roots)
if node=NULL then exit end if
integer x = getd_by_index(node,roots)
deld(nodes[r][RANK],roots)
if nodes[x][VALUE]<nodes[r][VALUE] then
{r, x} = {x, r}
end if
nodes[x][PARENT] = r
nodes[x][MARK] = false
if nodes[r][CHILD] == NULL then
nodes[x][NEXT] = x
nodes[x][PREV] = x
nodes[r][CHILD] = x
else
meld1(nodes[r][CHILD], x)
end if
nodes[r][RANK] += 1
end while
setd(nodes[r][RANK],r,roots)
end procedure
-- task requirement
function ExtractMin(integer h)
if nodes[h] == NULL then
return {h,"<none>",false}
end if
object minimum = nodes[h][VALUE]
integer roots = new_dict()
integer r = nodes[h][NEXT], n
while r != h do
n := nodes[r][NEXT]
add_roots(r,roots)
r = n
end while
integer c = nodes[h][CHILD]
if c != NULL then
nodes[c][PARENT] = NULL
r := nodes[c][NEXT]
add_roots(c,roots)
while r != c do
n := nodes[r][NEXT]
nodes[r][PARENT] = NULL
add_roots(r,roots)
r = n
end while
end if
if dict_size(roots) == 0 then
destroy_dict(roots)
return {NULL, minimum, true}
end if
integer d = getd_partial_key(0,roots)
integer mv = getd(d,roots)
deld(d,roots)
nodes[mv][NEXT] = mv
nodes[mv][PREV] = mv
sequence rs = getd_all_keys(roots)
for i=1 to length(rs) do
r = getd(rs[i],roots)
nodes[r][PREV] = mv
nodes[r][NEXT] = nodes[mv][NEXT]
nodes[nodes[mv][NEXT]][PREV] = r
nodes[mv][NEXT] = r
if nodes[r][VALUE]<nodes[mv][VALUE] then
mv = r
end if
end for
h = mv
destroy_dict(roots)
return {h, minimum, true}
end function
 
# Task requirement.
procedure cut_and_meld(integer h, x, bool meld)
func initHeap*[T]: Heap[T] = discard
integer p := nodes[x][PARENT]
nodes[p][RANK] -= 1
if nodes[p][RANK] == 0 then
nodes[p][CHILD] = NULL
else
nodes[p][CHILD] = nodes[x][NEXT]
nodes[nodes[x][PREV]][NEXT] = nodes[x][NEXT]
nodes[nodes[x][NEXT]][PREV] = nodes[x][PREV]
end if
if nodes[p][PARENT] == NULL then
return
end if
if not nodes[p][MARK] then
nodes[p][MARK] = true
return
end if
cut_and_meld(h,p,true)
if meld then
nodes[x][PARENT] = NULL
meld1(h, x)
end if
end procedure
 
-- task requirement
function DecreaseKey(integer h, n, object v)
if nodes[n][VALUE]<v then
crash("DecreaseKey new value greater than existing value")
end if
nodes[n][VALUE] = v
if n!=h then
integer p := nodes[n][PARENT]
if p == NULL then
if v<nodes[h][VALUE] then
h = n
end if
else
cut_and_meld(h,n,true)
end if
end if
return h
end function
 
--# taskTask requirement.
func insert*[T](heap: var Heap[T]; value: T): Node[T] =
function Delete(integer h, n)
result = Node[T](value: value)
integer p := nodes[n][PARENT]
if p == NULL thenheap.node.isNil:
if nresult.next == h thenresult
{h}result.prev = ExtractMin(h)result
heap.node = result
return h
else:
end if
heap.node.meld1(result)
nodes[nodes[n][PREV]][NEXT] = nodes[n][NEXT]
if result.value < heap.node.value:
nodes[nodes[n][NEXT]][PREV] = nodes[n][PREV]
heap.node = result
else
cut_and_meld(h,n,false)
end if
integer c := nodes[n][CHILD]
if c != NULL then
while true do
nodes[c][PARENT] = NULL
c = nodes[c][NEXT]
if c == nodes[n][CHILD] then
exit
end if
end while
meld2(h, c)
end if
return h
end function
constant W=platform()=WINDOWS,
Horizontal = iff(W?#C4:'-'),
Vertical = iff(W?#B3:'|'),
sBtmLeft = iff(W?#C0:'+'),
sLeftTee = iff(W?#C3:'+'),
sTopRight = iff(W?#BF:'+')
 
procedure vis(integer n, string pre)
string pc = Vertical&" "
sequence x = nodes[n]
while true do
integer next = x[NEXT]
if next!=n then
printf(1,pre&sLeftTee&Horizontal)
else
printf(1,pre&sBtmLeft&Horizontal)
pc = " "
end if
if x[CHILD] == NULL then
printf(1,"%c %s\n",{Horizontal,sprint(x[VALUE])})
else
printf(1,"%c %s\n",{sTopRight,sprint(x[VALUE])})
vis(x[CHILD], pre&pc)
end if
if next=n then exit end if
x = nodes[next]
end while
end procedure
 
# Task requirement.
procedure Vis(integer h)
func union*[T](heap1: var Heap[T]; heap2: var Heap[T]) =
if nodes[h] == NULL then
if heap1.node.isNil:
printf(1,"<empty>\n")
heap1 = returnheap2
elif not heap2.node.isNil:
end if
vismeld2(hheap1.node,"" heap2.node)
if heap2.node.value < heap1.node.value:
end procedure
heap1 = heap2
heap2.node = nil
 
printf(1,"MakeHeap:\n")
integer h := MakeHeap()
Vis(h)
printf(1,"\nInsert:\n")
{h} = Insert(h,"cat")
Vis(h)
printf(1,"\nUnion:\n")
integer h2 := MakeHeap()
{h2} = Insert(h2,"rat")
{h,h2} = Union(h,h2) -- (h2:=NULL)
Vis(h)
printf(1,"\nMinimum:\n")
{object m, {}} = Minimum(h)
?m
printf(1,"\nExtractMin:\n")
-- add a couple more items to demonstrate parent-child linking that
-- happens on delete min.
{h} = Insert(h,"bat")
{h,integer x} = Insert(h,"meerkat") -- save x for decrease key and delete demos
{h,m,{}} = ExtractMin(h)
printf(1,"(extracted %s)\n", {sprint(m)})
Vis(h)
 
# Task requirement.
printf(1,"\nDecreaseKey:\n")
func min*[T](heap: Heap[T]): T =
h = DecreaseKey(h, x, "gnat")
if heap.node.isNil:
Vis(h)
raise newException(ValueError, "cannot find minimum value in an empty heap.")
result = heap.node.value
 
 
printf(1,"\nDelete:\n")
func add[T](roots: var Table[int, Node[T]]; root: Node[T]) =
-- add yet a couple more items to show how F&T's original delete was
root.prev = root
-- lazier than CLRS's delete.
root.next = root
{h} = Insert(h,"bobcat")
var root = root
{h} = Insert(h,"bat")
while true:
printf(1,"(deleting %s)\n", {sprint(nodes[x][VALUE])})
if root.rank notin roots: break
h = Delete(h,x)
var node = roots.getOrDefault(root.rank, nil)
Vis(h)</lang>
if node.isNil: break
roots.del(root.rank)
if node.value < root.value: swap node, root
node.parent = root
node.mark = false
if root.child.isNil:
node.next = node
node.prev = node
root.child = node
else:
meld1(root.child, node)
inc root.rank
roots[root.rank] = root
 
 
proc firstKey[T1, T2](t: Table[T1, T2]): T1 =
for key in t.keys: return key
 
 
# Task requirement.
func extractMin*[T](heap: var Heap[T]): T =
let m = min(heap)
var roots: Table[int, Node[T]]
 
var root = heap.node.next
while root != heap.node:
let node = root.next
roots.add root
root = node
 
var child = heap.node.child
if not child.isNil:
child.parent = nil
var root = child.next
roots.add child
while root != child:
let node = root.next
root.parent = nil
roots.add root
root = node
 
if roots.len == 0:
heap.node = nil
return m
 
let key = roots.firstKey()
var node = roots[key]
roots.del(key)
node.next = node
node.prev = node
for root in roots.values:
root.prev = node
root.next = node.next
node.next.prev = root
node.next = root
if root.value < node.value: node = root
heap.node = node
result = m
 
 
# Forward reference.
func cutAndMeld[T](heap: Heap[T]; node: Node[T])
 
 
func cut[T](heap: Heap[T]; node: Node[T]) =
let parent = node.parent
dec parent.rank
if parent.rank == 0:
parent.child = nil
else:
parent.child = node.next
node.prev.next = node.next
node.next.prev = node.prev
if parent.parent.isNil: return
if parent.mark:
heap.cutAndMeld(parent)
else:
parent.mark = true
 
 
func cutAndMeld[T](heap: Heap[T]; node: Node[T]) =
heap.cut(node)
node.parent = nil
meld1(heap.node, node)
 
 
# Task requirement.
func decreaseKey*[T](heap: var Heap[T]; node: Node[T]; val: T) =
if node.value < val:
raise newException(ValueError, "“decreaseKey” new value greater than existing value.")
 
node.value = val
if node == heap.node: return
 
if node.parent.isNil:
if val < heap.node.value:
heap.node = node
else:
heap.cutAndMeld(node)
 
 
# Task requirement.
func delete*[T](heap: var Heap[T]; node: Node[T]) =
 
let parent = node.parent
if parent.isNil:
if node == heap.node:
discard heap.extractMin()
return
node.prev.next = node.next
node.next.prev = node.prev
else:
heap.cut(node)
 
var child = node.child
if child.isNil: return
 
while true:
child.parent = nil
child = child.next
if child == node.child: break
 
meld2(heap.node, child)
 
 
iterator nodes[T](head: Node[T]): Node[T] =
if not head.isNil:
yield head
var node = head.next
while node != head:
yield node
node = node.next
 
 
proc visualize[T](heap: Heap[T]) =
 
if heap.node.isNil:
echo "<empty>"
return
 
proc print[T](node: Node[T]; pre: string) =
var pc = "│ "
for curr in node.nodes():
if curr.next != node:
stdout.write pre, "├─"
else:
stdout.write pre, "└─"
pc = " "
if curr.child.isNil:
echo "╴", curr.value
else:
echo "┐", curr.value
print(curr.child, pre & pc)
 
print(heap.node, "")
 
 
when isMainModule:
 
echo "MakeHeap:"
var heap = initHeap[string]()
heap.visualize()
 
echo "\nInsert:"
discard heap.insert("cat")
heap.visualize()
 
echo "\nUnion:"
var heap2 = initHeap[string]()
discard heap2.insert("rat")
heap.union(heap2)
heap.visualize()
 
echo "\nMinimum:"
var m = min(heap)
echo m
 
echo "\nExtractMin:"
# Add a couple more items to demonstrate parent-child linking that happens on delete min.
discard heap.insert("bat")
let node = heap.insert("meerkat") # Save node for decrease key and delete demos.
m = heap.extractMin()
echo "(extracted $#)" % m
heap.visualize()
 
echo "\nDecreaseKey:"
heap.decreaseKey(node, "gnat")
heap.visualize()
 
echo "\nDelete:"
# Add a couple more items.
discard heap.insert("bobcat")
discard heap.insert("bat")
echo "(deleting $#)" % node.value
heap.delete(node)
heap.visualize()</syntaxhighlight>
 
{{out}}
<pre>MakeHeap:
<empty>
 
Insert:
└─╴cat
 
Union:
├─╴cat
└─╴rat
 
Minimum:
cat
 
ExtractMin:
(extracted bat)
├─┐cat
│ └─╴rat
└─╴meerkat
 
DecreaseKey:
├─┐cat
│ └─╴rat
└─╴gnat
 
Delete:
(deleting gnat)
├─╴bat
├─╴bobcat
└─┐cat
└─╴rat</pre>
 
=={{header|Phix}}==
{{trans|Go}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">VALUE</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">PARENT</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">CHILD</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">PREV</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NEXT</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">RANK</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MARK</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">NODELEN</span><span style="color: #0000FF;">=$</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">new_node</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">NODELEN</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nodes</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">new_slot</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">freelist</span><span style="color: #0000FF;">!=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">freelist</span>
<span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">freelist</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">res</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">nodes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">release_slot</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">freelist</span>
<span style="color: #000000;">freelist</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">MakeHeap</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">new_slot</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">meld1</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">single</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">list</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">single</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">single</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">list</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">single</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">list</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">list</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">single</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- (helps with refcounts for pwa/p2js)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">new_node</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h</span>
<span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">new_slot</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">meld1</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">meld2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">Union</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h2</span>
<span style="color: #008080;">elsif</span> <span style="color: #008080;">not</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">meld2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">h2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">release_slot</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- (h2:=NULL implied)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">Minimum</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"&lt;none&gt;"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">],</span> <span style="color: #004600;">true</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">add_roots</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">node</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">],</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">node</span><span style="color: #0000FF;">=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_by_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">node</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">deld</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">],</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">MARK</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">meld1</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #7060A8;">setd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">],</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">ExtractMin</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"&lt;none&gt;"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">minimum</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">roots</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">!=</span> <span style="color: #000000;">h</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">add_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">!=</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">add_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">!=</span> <span style="color: #000000;">c</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #000000;">add_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">dict_size</span><span style="color: #0000FF;">(</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">destroy_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">minimum</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">true</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_partial_key</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">mv</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">deld</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mv</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mv</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd_all_keys</span><span style="color: #0000FF;">(</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">getd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mv</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">mv</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">mv</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mv</span>
<span style="color: #7060A8;">destroy_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">roots</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">minimum</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">true</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">cut_and_meld</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">meld</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">RANK</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">MARK</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">p</span><span style="color: #0000FF;">][</span><span style="color: #000000;">MARK</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">return</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">cut_and_meld</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">meld</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #000000;">meld1</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">DecreaseKey</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]<</span><span style="color: #000000;">v</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"DecreaseKey new value greater than existing value"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">v</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">h</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">v</span><span style="color: #0000FF;"><</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">cut_and_meld</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">h</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- task requirement</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">Delete</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">h</span> <span style="color: #008080;">then</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ExtractMin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">h</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PREV</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">cut_and_meld</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">!=</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">PARENT</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">][</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">][</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000000;">meld2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">h</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">W</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">WINDOWS</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">Horizontal</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">?</span><span style="color: #000000;">#C4</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">Vertical</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">?</span><span style="color: #000000;">#B3</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'|'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">sBtmLeft</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">?</span><span style="color: #000000;">#C0</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'+'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">sLeftTee</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">?</span><span style="color: #000000;">#C3</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'+'</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">sTopRight</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">W</span><span style="color: #0000FF;">?</span><span style="color: #000000;">#BF</span><span style="color: #0000FF;">:</span><span style="color: #008000;">'+'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">vis</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">pre</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">pc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Vertical</span><span style="color: #0000FF;">&</span><span style="color: #008000;">" "</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">next</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">NEXT</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pre</span><span style="color: #0000FF;">&</span><span style="color: #000000;">sLeftTee</span><span style="color: #0000FF;">&</span><span style="color: #000000;">Horizontal</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pre</span><span style="color: #0000FF;">&</span><span style="color: #000000;">sBtmLeft</span><span style="color: #0000FF;">&</span><span style="color: #000000;">Horizontal</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">pc</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">" "</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%c %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">Horizontal</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])})</span>
<span style="color: #008080;">else</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%c %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">sTopRight</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])})</span>
<span style="color: #000000;">vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">CHILD</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">pre</span><span style="color: #0000FF;">&</span><span style="color: #000000;">pc</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">next</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">next</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">is_null</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"&lt;empty&gt;\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"MakeHeap:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">MakeHeap</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nInsert:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"cat"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nUnion:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">h2</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">MakeHeap</span><span style="color: #0000FF;">()</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"rat"</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Union</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h2</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (h2:=NULL)</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Minimum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nMinimum:\n%v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">m</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nExtractMin:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- add a couple more items to demonstrate parent-child linking that
-- happens on delete min.</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bat"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">x</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"meerkat"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- save x for decrease key and delete demos</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ExtractMin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"(extracted %s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nDecreaseKey:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">DecreaseKey</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"gnat"</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nDelete:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- add yet a couple more items to show how F&T's original delete was
-- lazier than CLRS's delete.</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bobcat"</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Insert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bat"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"(deleting %s)\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nodes</span><span style="color: #0000FF;">[</span><span style="color: #000000;">x</span><span style="color: #0000FF;">][</span><span style="color: #000000;">VALUE</span><span style="color: #0000FF;">])})</span>
<span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Delete</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">Vis</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
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<pre>
Line 1,665 ⟶ 1,975:
 
=={{header|Python}}==
<langsyntaxhighlight lang="python">class FibonacciHeap:
# internal node class
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node.right.parent = parent
node.left.right = node.right
node.right.left = node.left</langsyntaxhighlight>
 
=={{header|Raku}}==
{{trans|Go & Kotlin}}
<syntaxhighlight lang="raku" perl6line># 20200609 Raku programming solution
 
subset vEle of Any;
Line 2,090 ⟶ 2,400:
say "deleting: ", $x.value;
$h.Delete($x);
$h.Vis;</langsyntaxhighlight>
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<pre>MakeHeap:
Line 2,127 ⟶ 2,437:
{{libheader|Wren-str}}
This just deals with nodes whose values are strings.
<langsyntaxhighlight ecmascriptlang="wren">import "./str" for Str
 
class Node {
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System.print("(deleting '%(x.value)')")
h.delete(x)
h.visualize()</langsyntaxhighlight>
 
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edits