Related
I want to understand the A* algorithm. I wrote by examples, but often it gets into an infinite loop.
What is the problem?
Please forgive me for the English language.
Path Search Code:
public Node GetPath(Vector2 goal,Vector2 start) {
List<Node> OpenNodes = new List<Node>(); //список с не просмотренными узлами
List<Node> ClosedNodes = new List<Node>(); //список с не просмотренными узлами
OpenNodes.Add(new Node
{
pos = start,
parent = null,
DistStart = 0,
DistOnGoal = GetDistOnGoal(Vector2.zero, goal)
});
while (OpenNodes.Count > 0) {
var FirstNode = OpenNodes.OrderBy(node => node.FullDist).First();
ClosedNodes.Add(FirstNode);
OpenNodes.Remove(FirstNode);
if (FirstNode.pos == goal) {
Debug.Log("путь есть");
return FirstNode;
}
foreach (Node n in NighBours(FirstNode, goal)) {
var chanel = false;
foreach (Node d in ClosedNodes) {
if (n == d) {
chanel = true;
continue;
}
}
if (chanel)
{
chanel = false;
continue;
}
var opennod = OpenNodes.FirstOrDefault(node => node.pos == n.pos);
if (opennod == null)
{
OpenNodes.Add(n);
}
else {
if (opennod.DistStart >n.DistStart) {
opennod.DistStart = n.DistStart;
opennod.parent = FirstNode;
}
}
}
}
return null;
}
public float GetDistOnGoal(Vector2 n, Vector2 goal) {//дистанция до цели
return Mathf.Abs((goal - n).magnitude);
}
public List<Node> NighBours(Node n,Vector2 goal)//соседи
{
var Point = new Vector2[4];
var Nodes = new List<Node>();
Point[0] = new Vector2(n.pos.x - 1, n.pos.y);
Point[1] = new Vector2(n.pos.x + 1, n.pos.y);
Point[2] = new Vector2(n.pos.x, n.pos.y + 1);
Point[3] = new Vector2(n.pos.x, n.pos.y - 1);
for (var i = 0; i < Point.Length; i++)
{
if (Point[i].x > 1 && Point[i].x < map.GetLength(0) - 2 && Point[i].y > 1 && Point[i].y < map.GetLength(1) - 2)
{
if (map[(int)Point[i].x, (int)Point[i].y] == 0)
{
Nodes.Add(
new Node
{
pos = Point[i],
parent = n,
DistStart = n.DistStart + 1,
DistOnGoal = GetDistOnGoal(Point[i],goal),
});
}
}
}
return Nodes;
}
public class Node {
public Vector2 pos;
public Node parent;
public float DistStart;
public float DistOnGoal;
public float FullDist
{
get
{
return DistStart + DistOnGoal;
}
}
}
This is the node code.
The function never returned null, although an example of this implies.
Debug also can't because Unity hangs tight
I am implementing an N-1ry tree in C#. I am wondering how can I calculate the complexity of below methods. Here is my code:
Structure:
public class Node
{
public int Value { get; set; }
public Node Children { get; set; }
public Node Sibilings { get; set; }
}
This method for searching:
public Node search(Node root, int data)
{
if (root == null)
return null;
if (data == root.Value)
return root;
Node t = search(root.Children, data);
if (t == null)
t = search(root.Sibilings, data);
return t;
}
This method for insertion:
public void Add(int[] data)
{
Node temp = null;
temp = search(ROOT, data[0]);
if (temp == null)
temp = new Node(data[0]);
if (this.ROOT == null)
ROOT = temp;
Node parent = temp;
for (int j = 1; j <= this.NoOfChildrens; j++)
{
// for first child
if (j == 1)
{
parent.Children = new Node(data[j]);
parent = parent.Children;
}
//for all other childs
else
{
parent.Sibilings = new Node(data[j]);
parent = parent.Sibilings;
}
}
}
Program entry point:
static void Main(string[] args)
{
NAryTree naryTree = new NAryTree(3);
// 1st element in each row is node Value,>=2nd....=>value of child
int[][] data = { new int[] { 1, 2, 3, 4 }, new int[] { 2, 1, 6,0 }, new int[] { 3, 8, 9, 10 }, new int[] { 4, 0, 0, 0 } };
naryTree.Add(data[0]);
naryTree.Add(data[1]);
naryTree.Add(data[2]);
naryTree.Add(data[3]);
naryTree.Add(new int[] {10,3,6,4});
naryTree.preorder(naryTree.ROOT);
Console.ReadLine();
}
What is the bigO complexity of these methods?
Let's see what we have in Search method. It is not a binary tree and we have recursion. So the Search method will call N times till we find a necessary value. So we can conclude that we have O(N) where N is the maximum(worst) number of iteration to find a value at the last iteration:
public Node search(Node root, int data)
{
if (root == null)
return null;
if (data == root.Value)
return root;
Node t = search(root.Children, data);
if (t == null)
t = search(root.Sibilings, data);
return t;
}
For Addition method is simpler as we have for statement and no nested loops. So we have O(N) for Addition method.
As Wisconsin university says:
So for loops for (i = 0; i < N; i++) {
sequence of statements } The loop executes N times, so the sequence of statements also executes N times. Since we assume the
statements are O(1), the total time for the for loop is N * O(1),
which is O(N) overall.
Where can I find a simple (as much as possible, but no simpler!) implementation of an LR(1) parser generator?
I'm not looking for performance, just the ability to generate the LR(1) states (item sets).
C++, C#, Java, and Python would all work for me.
I've written a very simple one in C# and wanted to share it here.
It basically populates the action lookup table, which tells you which state to shift to or which rule to use for reduction.
If the number is nonnegative, then it denotes a new state; if it's negative, then its one's complement (i.e. ~x) denotes the rule index.
All you need now is to make a lexer and to do the actual parsing with the action table.
Note 1: It might be quite slow at generating the states for a real-world grammar, so you might want to think twice before using it in production code!
Note 2: You might want to double-check its correctness, since I've only checked it a bit.
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using size_t = System.UInt32;
public class LRParser
{
private string[] symbols; // index => symbol
private IDictionary<string, size_t> interned = new SortedDictionary<string, size_t>(); // symbol => index
private int[/*state*/, /*lookahead*/] actions; // If >= 0, represents new state after shift. If < 0, represents one's complement (i.e. ~x) of reduction rule.
public LRParser(params KeyValuePair<string, string[]>[] grammar)
{
this.interned.Add(string.Empty, new size_t());
foreach (var rule in grammar)
{
if (!this.interned.ContainsKey(rule.Key))
{ this.interned.Add(rule.Key, (size_t)this.interned.Count); }
foreach (var symbol in rule.Value)
{
if (!this.interned.ContainsKey(symbol))
{ this.interned.Add(symbol, (size_t)this.interned.Count); }
}
}
this.symbols = this.interned.ToArray().OrderBy(p => p.Value).Select(p => p.Key).ToArray();
var syntax = Array.ConvertAll(grammar, r => new KeyValuePair<size_t, size_t[]>(this.interned[r.Key], Array.ConvertAll(r.Value, s => this.interned[s])));
var nonterminals = Array.ConvertAll(this.symbols, s => new List<size_t>());
for (size_t i = 0; i < syntax.Length; i++) { nonterminals[syntax[i].Key].Add(i); }
var firsts = Array.ConvertAll(Enumerable.Range(0, this.symbols.Length).ToArray(), s => nonterminals[s].Count > 0 ? new HashSet<size_t>() : new HashSet<size_t>() { (size_t)s });
int old;
do
{
old = firsts.Select(l => l.Count).Sum();
foreach (var rule in syntax)
{
foreach (var i in First(rule.Value, firsts))
{ firsts[rule.Key].Add(i); }
}
} while (old < firsts.Select(l => l.Count).Sum());
var actions = new Dictionary<int, IDictionary<size_t, IList<int>>>();
var states = new Dictionary<HashSet<Item>, int>(HashSet<Item>.CreateSetComparer());
var todo = new Stack<HashSet<Item>>();
var root = new Item(0, 0, new size_t());
todo.Push(new HashSet<Item>());
Closure(root, todo.Peek(), firsts, syntax, nonterminals);
states.Add(new HashSet<Item>(todo.Peek()), states.Count);
while (todo.Count > 0)
{
var set = todo.Pop();
var closure = new HashSet<Item>();
foreach (var item in set)
{ Closure(item, closure, firsts, syntax, nonterminals); }
var grouped = Array.ConvertAll(this.symbols, _ => new HashSet<Item>());
foreach (var item in closure)
{
if (item.Symbol >= syntax[item.Rule].Value.Length)
{
IDictionary<size_t, IList<int>> map;
if (!actions.TryGetValue(states[set], out map))
{ actions[states[set]] = map = new Dictionary<size_t, IList<int>>(); }
IList<int> list;
if (!map.TryGetValue(item.Lookahead, out list))
{ map[item.Lookahead] = list = new List<int>(); }
list.Add(~(int)item.Rule);
continue;
}
var next = item;
next.Symbol++;
grouped[syntax[item.Rule].Value[item.Symbol]].Add(next);
}
for (size_t symbol = 0; symbol < grouped.Length; symbol++)
{
var g = new HashSet<Item>();
foreach (var item in grouped[symbol])
{ Closure(item, g, firsts, syntax, nonterminals); }
if (g.Count > 0)
{
int state;
if (!states.TryGetValue(g, out state))
{
state = states.Count;
states.Add(g, state);
todo.Push(g);
}
IDictionary<size_t, IList<int>> map;
if (!actions.TryGetValue(states[set], out map))
{ actions[states[set]] = map = new Dictionary<size_t, IList<int>>(); }
IList<int> list;
if (!map.TryGetValue(symbol, out list))
{ map[symbol] = list = new List<int>(); }
list.Add(state);
}
}
}
this.actions = new int[states.Count, this.symbols.Length];
for (int i = 0; i < this.actions.GetLength(0); i++)
{
for (int j = 0; j < this.actions.GetLength(1); j++)
{ this.actions[i, j] = int.MinValue; }
}
foreach (var p in actions)
{
foreach (var q in p.Value)
{ this.actions[p.Key, q.Key] = q.Value.Single(); }
}
foreach (var state in states.OrderBy(p => p.Value))
{
Console.WriteLine("State {0}:", state.Value);
foreach (var item in state.Key.OrderBy(i => i.Rule).ThenBy(i => i.Symbol).ThenBy(i => i.Lookahead))
{
Console.WriteLine(
"\t{0}: {1} \xB7 {2} | {3} → {0}",
this.symbols[syntax[item.Rule].Key],
string.Join(" ", syntax[item.Rule].Value.Take((int)item.Symbol).Select(s => this.symbols[s]).ToArray()),
string.Join(" ", syntax[item.Rule].Value.Skip((int)item.Symbol).Select(s => this.symbols[s]).ToArray()),
this.symbols[item.Lookahead] == string.Empty ? "\x04" : this.symbols[item.Lookahead],
string.Join(
", ",
Array.ConvertAll(
actions[state.Value][item.Symbol < syntax[item.Rule].Value.Length ? syntax[item.Rule].Value[item.Symbol] : item.Lookahead].ToArray(),
a => a >= 0 ? string.Format("state {0}", a) : string.Format("{0} (rule {1})", this.symbols[syntax[~a].Key], ~a))));
}
Console.WriteLine();
}
}
private static void Closure(Item item, HashSet<Item> closure /*output*/, HashSet<size_t>[] firsts, KeyValuePair<size_t, size_t[]>[] syntax, IList<size_t>[] nonterminals)
{
if (closure.Add(item) && item.Symbol >= syntax[item.Rule].Value.Length)
{
foreach (var r in nonterminals[syntax[item.Rule].Value[item.Symbol]])
{
foreach (var i in First(syntax[item.Rule].Value.Skip((int)(item.Symbol + 1)), firsts))
{ Closure(new Item(r, 0, i == new size_t() ? item.Lookahead : i), closure, firsts, syntax, nonterminals); }
}
}
}
private struct Item : IEquatable<Item>
{
public size_t Rule;
public size_t Symbol;
public size_t Lookahead;
public Item(size_t rule, size_t symbol, size_t lookahead)
{
this.Rule = rule;
this.Symbol = symbol;
this.Lookahead = lookahead;
}
public override bool Equals(object obj) { return obj is Item && this.Equals((Item)obj); }
public bool Equals(Item other)
{ return this.Rule == other.Rule && this.Symbol == other.Symbol && this.Lookahead == other.Lookahead; }
public override int GetHashCode()
{ return this.Rule.GetHashCode() ^ this.Symbol.GetHashCode() ^ this.Lookahead.GetHashCode(); }
}
private static IEnumerable<size_t> First(IEnumerable<size_t> symbols, IEnumerable<size_t>[] map)
{
foreach (var symbol in symbols)
{
bool epsilon = false;
foreach (var s in map[symbol])
{
if (s == new size_t()) { epsilon = true; }
else { yield return s; }
}
if (!epsilon) { yield break; }
}
yield return new size_t();
}
private static KeyValuePair<K, V> MakePair<K, V>(K k, V v) { return new KeyValuePair<K, V>(k, v); }
private static void Main(string[] args)
{
var sw = Stopwatch.StartNew();
var parser = new LRParser(
MakePair("start", new string[] { "exps" }),
MakePair("exps", new string[] { "exps", "exp" }),
MakePair("exps", new string[] { }),
MakePair("exp", new string[] { "INTEGER" })
);
Console.WriteLine(sw.ElapsedMilliseconds);
}
}
LRSTAR 9.1 is a minimal LR(1) and LR(*) parser generator. You can use it to verify that your parser generator is giving the correct states, by using option '/s'. LRSTAR has been tested against HYACC and found to be giving the correct LR(1) states. 20 grammars are provided with LRSTAR and 6 Microsoft Visual Studio projects.
What C# template engine
that uses 'pure' HTML having only text and markers
sans any control flow like if, while, loop or expressions,
separating html from control code ?
Below is the example phone book list code,
expressing how this should be done:
string html=#"
<html><head><title>#title</title></head>
<body>
<table>
<tr>
<td> id</td> <td> name</td> <td> sex</td> <td>phones</td>
</tr><!--#contacts:-->
<tr>
<td>#id</td> <td>#name</td> <td>#sex</td>
<td>
<!--#phones:-->#phone <br/>
<!--:#phones-->
</td>
</tr><!--:#contacts-->
</table>
</body>
</html>";
var contacts = from c in db.contacts select c;
Marker m = new Marker(html);
Filler t = m.Mark("title");
t.Set("Phone book");
Filler c = m.Mark("contacts", "id,name,sex");
// **foreach** expressed in code, not in html
foreach(var contact in contacts) {
int id = contact.id;
c.Add(id, contact.name, contact.sex);
Filler p = c.Mark("phones", "phone");
var phones = from ph in db.phones
where ph.id == id
select new {ph.phone};
if (phones.Any()) {
foreach(var ph in phones) {
p.Add(ph);
}
} else {
fp.Clear();
}
}
Console.Out.WriteLine(m.Get());
Use this code:
Templet.cs
using System;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
namespace templaten.com.Templaten
{
public class tRange
{
public int head, toe;
public tRange(int _head, int _toe)
{
head = _head;
toe = _toe;
}
}
public enum AType
{
VALUE = 0,
NAME = 1,
OPEN = 2,
CLOSE = 3,
GROUP = 4
}
public class Atom
{
private AType kin;
private string tag;
private object data;
private List<Atom> bag;
public Atom(string _tag = "",
AType _kin = AType.VALUE,
object _data = null)
{
tag = _tag;
if (String.IsNullOrEmpty(_tag))
_kin = AType.GROUP;
kin = _kin;
if (_kin == AType.GROUP)
bag = new List<Atom>();
else
bag = null;
data = _data;
}
public AType Kin
{
get { return kin; }
}
public string Tag
{
get { return tag; }
set { tag = value; }
}
public List<Atom> Bag
{
get { return bag; }
}
public object Data
{
get { return data; }
set { data = value; }
}
public int Add(string _tag = "",
AType _kin = AType.VALUE,
object _data = null)
{
if (bag != null)
{
bag.Add(new Atom(_tag, _kin, _data));
return bag.Count - 1;
}
else
{
return -1;
}
}
}
public class Templet
{
private string content;
string namepat = "\\w+";
string justName = "(\\w+)";
string namePre = "#";
string namePost = "";
string comment0 = "\\<!--\\s*";
string comment1 = "\\s*--\\>";
private Atom tokens; // parsed contents
private Dictionary<string, int> iNames; // name index
private Dictionary<string, tRange> iGroups; // groups index
private Atom buffer; // output buffer
private Dictionary<string, int> _iname; // output name index
private Dictionary<string, tRange> _igroup; // output index
public Templet(string Content = null)
{
Init(Content);
}
private int[] mark(string[] names, string group)
{
if (names == null || names.Length < 1) return null;
tRange t = new tRange(0, buffer.Bag.Count - 1);
if (group != null)
{
if (!_igroup.ContainsKey(group)) return null;
t = _igroup[group];
}
int[] marks = new int[names.Length];
for (int i = 0; i < marks.Length; i++)
marks[i] = -1;
for (int i = t.head; i <= t.toe; i++)
{
if (buffer.Bag[i].Kin == AType.NAME)
{
for (int j = 0; j < names.Length; j++)
{
if (String.Compare(
names[j],
buffer.Bag[i].Tag,
true) == 0)
{
marks[j] = i;
break;
}
}
}
}
return marks;
}
public Filler Mark(string group, string names)
{
Filler f = new Filler(this, names);
f.di = mark(f.names, group);
f.Group = group;
tRange t = null;
if (_igroup.ContainsKey(group)) t = _igroup[group];
f.Range = t;
return f;
}
public Filler Mark(string names)
{
Filler f = new Filler(this, names);
f.di = mark(f.names, null);
f.Group = "";
f.Range = null;
return f;
}
public void Set(int[] locations, object[] x)
{
int j = Math.Min(x.Length, locations.Length);
for (int i = 0; i < j; i++)
{
int l = locations[i];
if ((l >= 0) && (buffer.Bag[l] != null))
buffer.Bag[l].Data = x[i];
}
}
public void New(string group, int seq = 0)
{
// place new group copied from old group just below it
if (!( iGroups.ContainsKey(group)
&& _igroup.ContainsKey(group)
&& seq > 0)) return;
tRange newT = null;
tRange t = iGroups[group];
int beginRange = _igroup[group].toe + 1;
for (int i = t.head; i <= t.toe; i++)
{
buffer.Bag.Insert(beginRange,
new Atom(tokens.Bag[i].Tag,
tokens.Bag[i].Kin,
tokens.Bag[i].Data));
beginRange++;
}
newT = new tRange(t.toe + 1, t.toe + (t.toe - t.head + 1));
// rename past group
string pastGroup = group + "_" + seq;
t = _igroup[group];
buffer.Bag[t.head].Tag = pastGroup;
buffer.Bag[t.toe].Tag = pastGroup;
_igroup[pastGroup] = t;
// change group indexes
_igroup[group] = newT;
}
public void ReMark(Filler f, string group)
{
if (!_igroup.ContainsKey(group)) return;
Map(buffer, _iname, _igroup);
f.di = mark(f.names, group);
f.Range = _igroup[group];
}
private static void Indexing(string aname,
AType kin,
int i,
Dictionary<string, int> dd,
Dictionary<string, tRange> gg)
{
switch (kin)
{
case AType.NAME: // index all names
dd[aname] = i;
break;
case AType.OPEN: // index all groups
if (!gg.ContainsKey(aname))
gg[aname] = new tRange(i, -1);
else
gg[aname].head = i;
break;
case AType.CLOSE:
if (!gg.ContainsKey(aname))
gg[aname] = new tRange(-1, i);
else
gg[aname].toe = i;
break;
default:
break;
}
}
private static void Map(Atom oo,
Dictionary<string, int> dd,
Dictionary<string, tRange> gg)
{
for (int i = 0; i < oo.Bag.Count; i++)
{
string aname = oo.Bag[i].Tag;
Indexing(oo.Bag[i].Tag, oo.Bag[i].Kin, i, dd, gg);
}
}
public void Init(string Content = null)
{
content = Content;
tokens = new Atom("", AType.GROUP);
iNames = new Dictionary<string, int>();
iGroups = new Dictionary<string, tRange>();
// parse content into tokens
string namePattern = namePre + namepat + namePost;
string patterns =
"(?<var>" + namePattern + ")|" +
"(?<head>" + comment0 + namePattern + ":" + comment1 + ")|" +
"(?<toe>" + comment0 + ":" + namePattern + comment1 + ")";
Regex jn = new Regex(justName, RegexOptions.Compiled);
Regex r = new Regex(patterns, RegexOptions.Compiled);
MatchCollection ms = r.Matches(content);
int pre = 0;
foreach (Match m in ms)
{
tokens.Add(content.Substring(pre, m.Index - pre));
int idx = -1;
if (m.Groups.Count >= 3)
{
string aname = "";
MatchCollection x = jn.Matches(m.Value);
if (x.Count > 0 && x[0].Groups.Count > 1)
aname = x[0].Groups[1].ToString();
AType t = AType.VALUE;
if (m.Groups[1].Length > 0) t = AType.NAME;
if (m.Groups[2].Length > 0) t = AType.OPEN;
if (m.Groups[3].Length > 0) t = AType.CLOSE;
if (aname.Length > 0)
{
tokens.Add(aname, t);
idx = tokens.Bag.Count - 1;
}
Indexing(aname, t, idx, iNames, iGroups);
}
pre = m.Index + m.Length;
}
if (pre < content.Length)
tokens.Add(content.Substring(pre, content.Length - pre));
// copy tokens into buffer
buffer = new Atom("", AType.GROUP);
for (int i = 0; i < tokens.Bag.Count; i++)
buffer.Add(tokens.Bag[i].Tag, tokens.Bag[i].Kin);
// initialize index of output names
_iname = new Dictionary<string, int>();
foreach (string k in iNames.Keys)
_iname[k] = iNames[k];
// initialize index of output groups
_igroup = new Dictionary<string, tRange>();
foreach (string k in iGroups.Keys)
{
tRange t = iGroups[k];
_igroup[k] = new tRange(t.head, t.toe);
}
}
public string Get()
{
StringBuilder sb = new StringBuilder("");
for (int i = 0; i < buffer.Bag.Count; i++)
{
switch (buffer.Bag[i].Kin)
{
case AType.VALUE:
sb.Append(buffer.Bag[i].Tag);
break;
case AType.NAME:
sb.Append(buffer.Bag[i].Data);
break;
case AType.OPEN:
case AType.CLOSE:
break;
default: break;
}
}
return sb.ToString();
}
}
public class Filler
{
private Templet t = null;
public int[] di;
public string[] names;
public string Group { get; set; }
public tRange Range { get; set; }
private int seq = 0;
public Filler(Templet tl, string markers = null)
{
t = tl;
if (markers != null)
names = markers.Split(new char[] { ',' },
StringSplitOptions.RemoveEmptyEntries);
else
names = null;
}
public void init(int length)
{
di = new int[length];
for (int i = 0; i < length; i++)
di[i] = -1;
seq = 0;
Group = "";
Range = null;
}
// clear contents inside marked object or group
public void Clear()
{
object[] x = new object[di.Length];
for (int i = 0; i < di.Length; i++)
x[i] = null;
t.Set(di, x);
}
// set value for marked object,
// or add row to group and set value to columns
public void Set(params object[] x)
{
t.Set(di, x);
}
public void Add(params object[] x)
{
if (Group.Length > 0)
{
t.New(Group, seq);
++seq;
t.ReMark(this, Group);
}
t.Set(di, x);
}
}
}
Testing program
Program.cs
Templet m = new Templet(html);
Filler f= m.Mark("title");
f.Set("Phone book");
Filler fcontacts = m.Mark("contacts", "id,name,sex,phone");
fcontacts.Add(1, "Akhmad", "M", "123456");
fcontacts.Add(2, "Barry", "M", "234567");
fcontacts.Add(1, "Charles", "M", "345678");
Console.Out.WriteLine(m.Get());
Still can't do nested loop- yet.
Just use ASP.NET. Whether you use webforms or MVC, it's super easy to have C# in your .cs files, and HTML in your .aspx files.
As with anything in programming, it's 99% up to you to do things right. Flexible UI engines aren't going to enforce that you follow good coding practices.
In principle most any template engine you choose can separate HTML from control logic with the proper architecture. using an MVC (Or MVVM) pattern, if you construct your model in such a way that the controller contains the if/then logic instead of the view you can eliminate it from the view.
That said, the syntax you use is very close to Razor syntax which is easily available for ASP.NET MVC through NuGet packages.
I totally hear you. I built SharpFusion, which has some other stuff in it but if you look for the template.cs file you will see the handler that parses a HTML file and simply replaces out tokens with values that you've made in c#.
Because no XML parsing is done like ASP.NET the framework loads much faster than even an MVC site.
Another alternative is ServiceStack.
How can I compute the minimum bipartite vertex cover in C#? Is there a code snippet to do so?
EDIT: while the problem is NP-complete for general graphs, it is solvable in polynomial time for bipartite graphs. I know that it's somehow related to maximum matching in bipartite graphs (by Konig's theorem) but I can't understand the theorem correctly to be able to convert the result of maximum bipartite matching to vertex cover.
I could figure it out:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class VertexCover
{
static void Main(string[] args)
{
var v = new VertexCover();
v.ParseInput();
v.FindVertexCover();
v.PrintResults();
}
private void PrintResults()
{
Console.WriteLine(String.Join(" ", VertexCoverResult.Select(x => x.ToString()).ToArray()));
}
private void FindVertexCover()
{
FindBipartiteMatching();
var TreeSet = new HashSet<int>();
foreach (var v in LeftVertices)
if (Matching[v] < 0)
DepthFirstSearch(TreeSet, v, false);
VertexCoverResult = new HashSet<int>(LeftVertices.Except(TreeSet).Union(RightVertices.Intersect(TreeSet)));
}
private void DepthFirstSearch(HashSet<int> TreeSet, int v, bool left)
{
if (TreeSet.Contains(v))
return;
TreeSet.Add(v);
if (left) {
foreach (var u in Edges[v])
if (u != Matching[v])
DepthFirstSearch(TreeSet, u, true);
} else if (Matching[v] >= 0)
DepthFirstSearch(TreeSet, Matching[v], false);
}
private void FindBipartiteMatching()
{
Bicolorate();
Matching = Enumerable.Repeat(-1, VertexCount).ToArray();
var cnt = 0;
foreach (var i in LeftVertices) {
var seen = new bool[VertexCount];
if (BipartiteMatchingInternal(seen, i)) cnt++;
}
}
private bool BipartiteMatchingInternal(bool[] seen, int u)
{
foreach (var v in Edges[u]) {
if (seen[v]) continue;
seen[v] = true;
if (Matching[v] < 0 || BipartiteMatchingInternal(seen, Matching[v])) {
Matching[u] = v;
Matching[v] = u;
return true;
}
}
return false;
}
private void Bicolorate()
{
LeftVertices = new HashSet<int>();
RightVertices = new HashSet<int>();
var colors = new int[VertexCount];
for (int i = 0; i < VertexCount; ++i)
if (colors[i] == 0 && !BicolorateInternal(colors, i, 1))
throw new InvalidOperationException("Graph is NOT bipartite.");
}
private bool BicolorateInternal(int[] colors, int i, int color)
{
if (colors[i] == 0) {
if (color == 1) LeftVertices.Add(i);
else RightVertices.Add(i);
colors[i] = color;
} else if (colors[i] != color)
return false;
else
return true;
foreach (var j in Edges[i])
if (!BicolorateInternal(colors, j, 3 - color))
return false;
return true;
}
private int VertexCount;
private HashSet<int>[] Edges;
private HashSet<int> LeftVertices;
private HashSet<int> RightVertices;
private HashSet<int> VertexCoverResult;
private int[] Matching;
private void ReadIntegerPair(out int x, out int y)
{
var input = Console.ReadLine();
var splitted = input.Split(new char[] { ' ' }, 2);
x = int.Parse(splitted[0]);
y = int.Parse(splitted[1]);
}
private void ParseInput()
{
int EdgeCount;
ReadIntegerPair(out VertexCount, out EdgeCount);
Edges = new HashSet<int>[VertexCount];
for (int i = 0; i < Edges.Length; ++i)
Edges[i] = new HashSet<int>();
for (int i = 0; i < EdgeCount; i++) {
int x, y;
ReadIntegerPair(out x, out y);
Edges[x].Add(y);
Edges[y].Add(x);
}
}
}
As you can see, this code solves the problem in polynomial time.
Its probably best to just go ahead and pick a node at random. For each node, either it goes in the vertex cover, or all of its neighbors do (since you need to include that edge). The end-result of the whole thing will be a set of vertex covers, and you pick the smallest one. I"m not going to sit here and code it out, though, since if I remember correctly, its NP complete.
private void DepthFirstSearch(HashSet TreeSet, int v, bool left)
{
if (TreeSet.Contains(v))
return;
TreeSet.Add(v);
if (left) {
foreach (var u in Edges[v])
if (u != Matching[v])
DepthFirstSearch(TreeSet, u, true);
} else if (Matching[v] >= 0)
DepthFirstSearch(TreeSet, Matching[v], false);
}
when the if(left) will execute i am figuring that it's value is always will be false.