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
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
|
using System.Numerics;
using System.Collections.Generic;
namespace Dafny
{
public class Set<T>
{
Dictionary<T, bool> dict;
public Set() { }
Set(Dictionary<T, bool> d) {
dict = d;
}
public static Set<T> Empty {
get {
return new Set<T>(new Dictionary<T, bool>(0));
}
}
public static Set<T> FromElements(params T[] values) {
Dictionary<T, bool> d = new Dictionary<T, bool>(values.Length);
foreach (T t in values)
d.Add(t, true);
return new Set<T>(d);
}
public IEnumerable<T> Elements {
get {
return dict.Keys;
}
}
public bool Equals(Set<T> other) {
return dict.Count == other.dict.Count && IsSubsetOf(other);
}
public override bool Equals(object other) {
return other is Set<T> && Equals((Set<T>)other);
}
public override int GetHashCode() {
return dict.GetHashCode();
}
public bool IsProperSubsetOf(Set<T> other) {
return dict.Count < other.dict.Count && IsSubsetOf(other);
}
public bool IsSubsetOf(Set<T> other) {
if (other.dict.Count < dict.Count)
return false;
foreach (T t in dict.Keys) {
if (!other.dict.ContainsKey(t))
return false;
}
return true;
}
public bool IsSupersetOf(Set<T> other) {
return other.IsSubsetOf(this);
}
public bool IsProperSupersetOf(Set<T> other) {
return other.IsProperSubsetOf(this);
}
public bool IsDisjointFrom(Set<T> other) {
Dictionary<T, bool> a, b;
if (dict.Count < other.dict.Count) {
a = dict; b = other.dict;
} else {
a = other.dict; b = dict;
}
foreach (T t in a.Keys) {
if (b.ContainsKey(t))
return false;
}
return true;
}
public bool Contains(T t) {
return dict.ContainsKey(t);
}
public Set<T> Union(Set<T> other) {
if (dict.Count == 0)
return other;
else if (other.dict.Count == 0)
return this;
Dictionary<T, bool> a, b;
if (dict.Count < other.dict.Count) {
a = dict; b = other.dict;
} else {
a = other.dict; b = dict;
}
Dictionary<T, bool> r = new Dictionary<T, bool>();
foreach (T t in b.Keys)
r[t] = true;
foreach (T t in a.Keys)
r[t] = true;
return new Set<T>(r);
}
public Set<T> Intersect(Set<T> other) {
if (dict.Count == 0)
return this;
else if (other.dict.Count == 0)
return other;
Dictionary<T, bool> a, b;
if (dict.Count < other.dict.Count) {
a = dict; b = other.dict;
} else {
a = other.dict; b = dict;
}
Dictionary<T, bool> r = new Dictionary<T, bool>();
foreach (T t in a.Keys) {
if (b.ContainsKey(t))
r.Add(t, true);
}
return new Set<T>(r);
}
public Set<T> Difference(Set<T> other) {
if (dict.Count == 0)
return this;
else if (other.dict.Count == 0)
return this;
Dictionary<T, bool> r = new Dictionary<T, bool>();
foreach (T t in dict.Keys) {
if (!other.dict.ContainsKey(t))
r.Add(t, true);
}
return new Set<T>(r);
}
}
public class Sequence<T>
{
T[] elmts;
public Sequence() { }
Sequence(T[] ee) {
elmts = ee;
}
public static Sequence<T> Empty {
get {
return new Sequence<T>(new T[0]);
}
}
public static Sequence<T> FromElements(params T[] values) {
return new Sequence<T>(values);
}
public BigInteger Length {
get { return new BigInteger(elmts.Length); }
}
public T[] Elements {
get {
return elmts;
}
}
public T Select(BigInteger index) {
return elmts[(int)index];
}
public Sequence<T> Update(BigInteger index, T t) {
T[] a = (T[])elmts.Clone();
a[(int)index] = t;
return new Sequence<T>(a);
}
public bool Equals(Sequence<T> other) {
int n = elmts.Length;
return n == other.elmts.Length && EqualUntil(other, n);
}
public override bool Equals(object other) {
return other is Sequence<T> && Equals((Sequence<T>)other);
}
public override int GetHashCode() {
return elmts.GetHashCode();
}
bool EqualUntil(Sequence<T> other, int n) {
for (int i = 0; i < n; i++) {
if (!elmts[i].Equals(other.elmts[i]))
return false;
}
return true;
}
public bool IsProperPrefixOf(Sequence<T> other) {
int n = elmts.Length;
return n < other.elmts.Length && EqualUntil(other, n);
}
public bool IsPrefixOf(Sequence<T> other) {
int n = elmts.Length;
return n <= other.elmts.Length && EqualUntil(other, n);
}
public Sequence<T> Concat(Sequence<T> other) {
if (elmts.Length == 0)
return other;
else if (other.elmts.Length == 0)
return this;
T[] a = new T[elmts.Length + other.elmts.Length];
System.Array.Copy(elmts, 0, a, 0, elmts.Length);
System.Array.Copy(other.elmts, 0, a, elmts.Length, other.elmts.Length);
return new Sequence<T>(a);
}
public bool Contains(T t) {
int n = elmts.Length;
for (int i = 0; i < n; i++) {
if (t.Equals(elmts[i]))
return true;
}
return false;
}
public Sequence<T> Take(BigInteger n) {
int m = (int)n;
if (elmts.Length == m)
return this;
T[] a = new T[m];
System.Array.Copy(elmts, a, m);
return new Sequence<T>(a);
}
public Sequence<T> Drop(BigInteger n) {
if (n.IsZero)
return this;
int m = (int)n;
T[] a = new T[elmts.Length - m];
System.Array.Copy(elmts, m, a, 0, elmts.Length - m);
return new Sequence<T>(a);
}
}
public struct Pair<A, B>
{
public readonly A Car;
public readonly B Cdr;
public Pair(A a, B b) {
this.Car = a;
this.Cdr = b;
}
}
public class Helpers
{
public static T[] InitNewArray<T>(BigInteger size) {
int sz = (int)size;
T[] a = new T[sz];
BigInteger[] b = a as BigInteger[];
if (b != null) {
BigInteger z = new BigInteger(0);
for (int i = 0; i < sz; i++) {
b[i] = z;
}
}
return a;
}
}
}
|
