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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;
}
}
}
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