1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
|
{ binary heap priority queue
code contributed by Rassim Eminli }
{$INCLUDE Switches.inc}
unit IPQ;
interface
type
TIntegerArray = array [0 .. $40000000 div sizeof(integer)] of integer;
PIntegerArray = ^TIntegerArray;
TheapItem = record
Item: integer;
Value: integer;
end;
TItemArray = array [0 .. $40000000 div sizeof(TheapItem)] of TheapItem;
PItemArray = ^TItemArray;
TIPQ = class
constructor Create(max: integer);
destructor Destroy; override;
procedure Empty;
function Put(Item, Value: integer): boolean;
function TestPut(Item, Value: integer): boolean;
function Get(var Item, Value: integer): boolean;
private
// n - is the size of the heap.
// fmax - is the max size of the heap.
n, fmax: integer;
// bh - stores (Value, Item) pairs of the heap.
// Ix - stores the positions of pairs in the heap bh.
bh: PItemArray;
Ix: PIntegerArray;
end;
implementation
constructor TIPQ.Create(max: integer);
begin
inherited Create;
fmax := max;
GetMem(bh, fmax * sizeof(TheapItem));
GetMem(Ix, fmax * sizeof(integer));
n := -1;
Empty
end;
destructor TIPQ.Destroy;
begin
FreeMem(bh);
FreeMem(Ix);
inherited Destroy;
end;
procedure TIPQ.Empty;
begin
if n <> 0 then
begin
FillChar(Ix^, fmax * sizeof(integer), 255);
n := 0;
end;
end;
// Parent(i) = (i-1)/2.
function TIPQ.Put(Item, Value: integer): boolean; // O(lg(n))
var
i, j: integer;
lbh: PItemArray;
lIx: PIntegerArray;
begin
lIx := Ix;
lbh := bh;
i := lIx[Item];
if i >= 0 then
begin
if lbh[i].Value <= Value then
begin
result := False;
exit;
end;
end
else
begin
i := n;
Inc(n);
end;
while i > 0 do
begin
j := (i - 1) shr 1; // Parent(i) = (i-1)/2
if Value >= lbh[j].Value then
break;
lbh[i] := lbh[j];
lIx[lbh[i].Item] := i;
i := j;
end;
// Insert the new Item at the insertion point found.
lbh[i].Value := Value;
lbh[i].Item := Item;
lIx[lbh[i].Item] := i;
result := True;
end;
function TIPQ.TestPut(Item, Value: integer): boolean;
var
i: integer;
begin
i := Ix[Item];
result := (i < 0) or (bh[i].Value > Value);
end;
// Left(i) = 2*i+1.
// Right(i) = 2*i+2 => Left(i)+1
function TIPQ.Get(var Item, Value: integer): boolean; // O(lg(n))
var
i, j: integer;
last: TheapItem;
lbh: PItemArray;
begin
if n = 0 then
begin
result := False;
exit;
end;
lbh := bh;
Item := lbh[0].Item;
Value := lbh[0].Value;
Ix[Item] := -1;
dec(n);
if n > 0 then
begin
last := lbh[n];
i := 0;
j := 1;
while j < n do
begin
// Right(i) = Left(i)+1
if (j < n - 1) and (lbh[j].Value > lbh[j + 1].Value) then
Inc(j);
if last.Value <= lbh[j].Value then
break;
lbh[i] := lbh[j];
Ix[lbh[i].Item] := i;
i := j;
j := j shl 1 + 1; // Left(j) = 2*j+1
end;
// Insert the root in the correct place in the heap.
lbh[i] := last;
Ix[last.Item] := i;
end;
result := True
end;
end.
|