// numbes, constants, variables and brakets
private ExpressionTreeNode ExprLevel6()
{
ExpressionTreeNode temp = null;
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Number:
case Lexeme.Pi:
case Lexeme.E:
case Lexeme.Var:
temp = new ExpressionTreeNode(CurrentLexeme, null, null);
NextLexeme();
break;
case Lexeme.LeftBracket:
NextLexeme();
temp = ExprLevel1();
if (CurrentLexeme.Lexeme != Lexeme.RightBracket)
{
throw new ExpressionSyntaxException(") excepted", _expression, _parsedExpression);
}
NextLexeme();
break;
}
return(temp);
}
private SortedList FindVariables(ExpressionTreeNode node)
{
SortedList list = new SortedList();
if (node.ExpressionLexeme.Lexeme == Lexeme.Var)
{
list.Add(node.ExpressionLexeme.LexemeName.ToLower(), "");
}
if (node.Left != null)
{
foreach (DictionaryEntry e in FindVariables(node.Left))
{
if (!list.ContainsKey(e.Key))
{
list.Add(e.Key, e.Value);
}
}
}
if (node.Right != null)
{
foreach (DictionaryEntry e in FindVariables(node.Right))
{
if (!list.ContainsKey(e.Key))
{
list.Add(e.Key, e.Value);
}
}
}
return(list);
}
// ^ operator
private ExpressionTreeNode ExprLevel3()
{
ExpressionTreeNode temp = ExprLevel4();
ExpressionLexeme lex;
while (true)
{
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Power:
if (temp == null)
{
throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
}
lex = CurrentLexeme;
NextLexeme();
ExpressionTreeNode right = ExprLevel3();
if (right == null)
{
throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
}
temp = new ExpressionTreeNode(lex, temp, right);
break;
default:
return(temp);
}
}
}
// unary + - operators
private ExpressionTreeNode ExprLevel4()
{
ExpressionTreeNode temp = null;
ExpressionLexeme lex;
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Plus:
NextLexeme();
temp = ExprLevel5();
break;
case Lexeme.Minus:
lex = new ExpressionLexeme("", Lexeme.UMinus);
NextLexeme();
ExpressionTreeNode right = ExprLevel5();
if (right == null)
{
throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
}
temp = new ExpressionTreeNode(lex, right);
break;
default:
temp = ExprLevel5();
break;
}
return(temp);
}
// math functions
private ExpressionTreeNode ExprLevel5()
{
ExpressionTreeNode temp = null;
switch (CurrentLexeme.LexemeType)
{
case LexemeType.ltFunction:
temp = new ExpressionTreeNode(CurrentLexeme, null, null);
NextLexeme();
if (CurrentLexeme.Lexeme != Lexeme.LeftBracket)
{
throw new ExpressionSyntaxException("( excepted", _expression, _parsedExpression);
}
NextLexeme();
ExpressionTreeNode left = ExprLevel1();
if (left == null)
{
throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
}
temp.Left = left;
if (CurrentLexeme.Lexeme != Lexeme.RightBracket)
{
throw new ExpressionSyntaxException(") excepted", _expression, _parsedExpression);
}
NextLexeme();
break;
default:
temp = ExprLevel6();
break;
}
return(temp);
}
private void CreateTree(ExpressionLexeme[] lexemes)
{
_root = null;
_lexemesQueue = new Queue (lexemes);
NextLexeme();
_root = ExprLevel1();
if (CurrentLexeme.Lexeme != ExpressionLexeme.EndLexeme.Lexeme)
throw new ExpressionSyntaxException("operator expected", _expression, _parsedExpression);
}
private void CreateTree(ExpressionLexeme[] lexemes)
{
_root = null;
_lexemesQueue = new Queue(lexemes);
NextLexeme();
_root = ExprLevel1();
if (CurrentLexeme.Lexeme != ExpressionLexeme.EndLexeme.Lexeme)
{
throw new ExpressionSyntaxException("operator expected", _expression, _parsedExpression);
}
}
// * / operators
private ExpressionTreeNode ExprLevel2()
{
ExpressionTreeNode temp = ExprLevel3();
ExpressionLexeme lex;
while (true)
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Multiply:
case Lexeme.Divide:
if (temp == null) throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
lex = CurrentLexeme;
NextLexeme();
ExpressionTreeNode right = ExprLevel2();
if (right == null) throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
temp = new ExpressionTreeNode(lex,temp,right);
break;
default:
return temp;
}
}
private static string df(ExpressionTreeNode node, string diffVar)
{
if (!node.HasVariable(diffVar))
{
return("0");
}
bool leftDiffVar = (node.Left != null) && (node.Left.HasVariable(diffVar));
bool rightDiffVar = (node.Right != null) && (node.Right.HasVariable(diffVar));
switch (node.ExpressionLexeme.LexemeType)
{
case LexemeType.ltConstant:
switch (node.ExpressionLexeme.Lexeme)
{
case Lexeme.Var: return("1");
default: return("0");
}
case LexemeType.ltOperator:
switch (node.ExpressionLexeme.Lexeme)
{
case Lexeme.Plus:
case Lexeme.Minus:
return(String.Format("({0}{1}{2})",
df(node.Left, diffVar),
node.ExpressionLexeme.LexemeName,
df(node.Right, diffVar)));
case Lexeme.UMinus:
return(String.Format("(-({0}))", df(node.Left, diffVar)));
case Lexeme.Multiply:
return(String.Format("(({0})*({1})+({2})*({3}))",
df(node.Left, diffVar),
node.Right,
df(node.Right, diffVar),
node.Left));
case Lexeme.Divide:
return(String.Format("(({0})*({1})-({2})*({3}))/({4})^2",
df(node.Left, diffVar),
node.Right,
df(node.Right, diffVar),
node.Left,
node.Right));
case Lexeme.Power:
// diff f(x)^g(y)
if (leftDiffVar && !rightDiffVar)
{
return(String.Format("((({0})^({1})*({1})*({2}))/({0}))",
node.Left, node.Right, df(node.Left, diffVar)));
}
// diff f(y)^g(x)
if (!leftDiffVar && rightDiffVar)
{
return(String.Format("((({0})^({1}))*({2})*log({0})))",
node.Left, node.Right, df(node.Right, diffVar)));
}
// diff f(x)^g(x)
return(String.Format("((({0})^({1}))*(({3})*log({0})+({1})*({2})/({0})))",
node.Left, node.Right,
df(node.Left, diffVar), df(node.Right, diffVar)));
default: throw new Exception();
}
case LexemeType.ltFunction:
return(String.Format("((" + node.ExpressionLexeme.LexemeDiffMask + ")*({1}))",
node.Left, df(node.Left, diffVar)));
default:
throw new Exception();
}
}
public ExpressionTreeNode(ExpressionLexeme lexeme, ExpressionTreeNode leftNode, ExpressionTreeNode rightNode)
{
ExpressionLexeme = lexeme;
Left = leftNode;
Right = rightNode;
}
public ExpressionTreeNode(ExpressionLexeme lexeme, ExpressionTreeNode leftNode) :
this(lexeme, leftNode, null)
{
}
// math functions
private ExpressionTreeNode ExprLevel5()
{
ExpressionTreeNode temp = null;
switch (CurrentLexeme.LexemeType)
{
case LexemeType.ltFunction:
temp = new ExpressionTreeNode(CurrentLexeme,null,null);
NextLexeme();
if (CurrentLexeme.Lexeme != Lexeme.LeftBracket)
throw new ExpressionSyntaxException("( excepted", _expression, _parsedExpression);
NextLexeme();
ExpressionTreeNode left = ExprLevel1();
if (left == null) throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
temp.Left = left;
if (CurrentLexeme.Lexeme != Lexeme.RightBracket)
throw new ExpressionSyntaxException(") excepted", _expression, _parsedExpression);
NextLexeme();
break;
default:
temp = ExprLevel6();
break;
}
return temp;
}
private ExpressionTreeNode SimplifyNode(ExpressionTreeNode node)
{
if (node.Left != null)
{
node.Left = SimplifyNode(node.Left);
}
if (node.Right != null)
{
node.Right = SimplifyNode(node.Right);
}
bool l_null = node.Left == null;
bool r_null = node.Right == null;
bool l_number = !l_null && (node.Left.ExpressionLexeme.Lexeme == Lexeme.Number);
bool r_number = !r_null && (node.Right.ExpressionLexeme.Lexeme == Lexeme.Number);
double l_value = l_number ? double.Parse(node.Left.ExpressionLexeme.LexemeName) : 0;
double r_value = r_number ? double.Parse(node.Right.ExpressionLexeme.LexemeName) : 0;
bool l_zero = l_number && (l_value == 0);
bool r_zero = r_number && (r_value == 0);
bool l_one = l_number && (l_value == 1);
bool r_one = r_number && (r_value == 1);
switch (node.ExpressionLexeme.LexemeType)
{
case LexemeType.ltOperator:
bool equal = (!l_null && !r_null) &&
(0 == String.Compare(node.Left.ToString(), node.Right.ToString()));
switch (node.ExpressionLexeme.Lexeme)
{
case Lexeme.Multiply:
if (l_zero || r_zero)
{
return(new ExpressionTreeNode(
new ExpressionLexeme("0", Lexeme.Number)));
}
if (l_one)
{
return(node.Right);
}
if (r_one)
{
return(node.Left);
}
if (l_number && r_number)
{
return(new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value * r_value), Lexeme.Number)));
}
break;
case Lexeme.Divide:
if (l_zero && !r_zero)
{
return(new ExpressionTreeNode(new ExpressionLexeme("0", Lexeme.Number)));
}
if (equal)
{
return(new ExpressionTreeNode(new ExpressionLexeme("1", Lexeme.Number)));
}
if (r_one)
{
return(node.Left);
}
if (l_number && r_number)
{
return(new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value / r_value), Lexeme.Number)));
}
break;
case Lexeme.Plus:
if (l_zero)
{
return(node.Right);
}
if (r_zero)
{
return(node.Left);
}
if (l_number && r_number)
{
return(new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value + r_value), Lexeme.Number)));
}
if (node.Right.ExpressionLexeme.Lexeme == Lexeme.UMinus)
{
return(new ExpressionTreeNode(
new ExpressionLexeme("-", Lexeme.Minus), node.Left, node.Right.Left));
}
break;
case Lexeme.Minus:
if (r_zero)
{
return(node.Left);
}
if (l_zero)
{
return(new ExpressionTreeNode(
new ExpressionLexeme("-", Lexeme.UMinus), node.Right));
}
if (equal)
{
return(new ExpressionTreeNode(new ExpressionLexeme("0", Lexeme.Number)));
}
if (l_number && r_number)
{
return(new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value - r_value), Lexeme.Number)));
}
break;
case Lexeme.UMinus:
if (node.Left.ExpressionLexeme.Lexeme == Lexeme.UMinus)
{
return(node.Left.Left);
}
break;
}
break;
}
return(node);
}
/// <summary>Simplifies binary tree of expression.</summary>
/// <remarks>
/// <para><strong>Simplify</strong> method removes all unneccessary nodes that can be
/// simplifided. For example, expression "1+(x*0)" will be simplifided to "1" because (x*0)
/// will always return zero.</para>
/// <para>Other samples of simplification</para>
/// <para>"0/x + x" -> "x"</para>
/// <para>"x/x" -> "1"</para>
/// </remarks>
public void Simplify()
{
_root = SimplifyNode(_root);
}
// numbes, constants, variables and brakets
private ExpressionTreeNode ExprLevel6()
{
ExpressionTreeNode temp = null;
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Number:
case Lexeme.Pi:
case Lexeme.E:
case Lexeme.Var:
temp = new ExpressionTreeNode(CurrentLexeme,null,null);
NextLexeme();
break;
case Lexeme.LeftBracket:
NextLexeme();
temp = ExprLevel1();
if (CurrentLexeme.Lexeme != Lexeme.RightBracket)
throw new ExpressionSyntaxException(") excepted", _expression, _parsedExpression);
NextLexeme();
break;
}
return temp;
}
private SortedList FindVariables(ExpressionTreeNode node)
{
SortedList list = new SortedList();
if (node.ExpressionLexeme.Lexeme == Lexeme.Var)
{
list.Add(node.ExpressionLexeme.LexemeName.ToLower(),"");
}
if (node.Left != null)
foreach(DictionaryEntry e in FindVariables(node.Left))
{
if (!list.ContainsKey(e.Key))
list.Add(e.Key,e.Value);
}
if (node.Right != null)
foreach(DictionaryEntry e in FindVariables(node.Right))
{
if (!list.ContainsKey(e.Key))
list.Add(e.Key,e.Value);
}
return list;
}
// unary + - operators
private ExpressionTreeNode ExprLevel4()
{
ExpressionTreeNode temp = null;
ExpressionLexeme lex;
switch (CurrentLexeme.Lexeme)
{
case Lexeme.Plus:
NextLexeme();
temp = ExprLevel5();
break;
case Lexeme.Minus:
lex = new ExpressionLexeme("",Lexeme.UMinus);
NextLexeme();
ExpressionTreeNode right = ExprLevel5();
if (right == null) throw new ExpressionSyntaxException("expression expected", _expression, _parsedExpression);
temp = new ExpressionTreeNode(lex,right);
break;
default:
temp = ExprLevel5();
break;
}
return temp;
}
public ExpressionTreeNode(ExpressionLexeme lexeme,ExpressionTreeNode leftNode) :
this (lexeme, leftNode,null)
{
}
/// <summary>Simplifies binary tree of expression.</summary>
/// <remarks>
/// <para><strong>Simplify</strong> method removes all unneccessary nodes that can be
/// simplifided. For example, expression "1+(x*0)" will be simplifided to "1" because (x*0)
/// will always return zero.</para>
/// <para>Other samples of simplification</para>
/// <para>"0/x + x" -> "x"</para>
/// <para>"x/x" -> "1"</para>
/// </remarks>
public void Simplify()
{
_root = SimplifyNode(_root);
}
private ExpressionTreeNode SimplifyNode(ExpressionTreeNode node)
{
if (node.Left != null) node.Left = SimplifyNode(node.Left);
if (node.Right != null) node.Right = SimplifyNode(node.Right);
bool l_null = node.Left == null;
bool r_null = node.Right == null;
bool l_number = !l_null && (node.Left.ExpressionLexeme.Lexeme == Lexeme.Number);
bool r_number = !r_null && (node.Right.ExpressionLexeme.Lexeme == Lexeme.Number);
double l_value = l_number ? double.Parse(node.Left.ExpressionLexeme.LexemeName) : 0;
double r_value = r_number ? double.Parse(node.Right.ExpressionLexeme.LexemeName) : 0;
bool l_zero = l_number && (l_value == 0);
bool r_zero = r_number && (r_value == 0);
bool l_one = l_number && (l_value == 1);
bool r_one = r_number && (r_value == 1);
switch (node.ExpressionLexeme.LexemeType)
{
case LexemeType.ltOperator:
bool equal = (!l_null && !r_null)
&& (0==String.Compare(node.Left.ToString(),node.Right.ToString()));
switch(node.ExpressionLexeme.Lexeme)
{
case Lexeme.Multiply:
if (l_zero || r_zero) return new ExpressionTreeNode(
new ExpressionLexeme("0",Lexeme.Number));
if (l_one) return node.Right;
if (r_one) return node.Left;
if (l_number && r_number) return new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value*r_value),Lexeme.Number));
break;
case Lexeme.Divide:
if (l_zero && !r_zero) return new ExpressionTreeNode(new ExpressionLexeme("0",Lexeme.Number));
if (equal) return new ExpressionTreeNode(new ExpressionLexeme("1",Lexeme.Number));
if (r_one) return node.Left;
if (l_number && r_number)
return new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value/r_value),Lexeme.Number));
break;
case Lexeme.Plus:
if (l_zero) return node.Right;
if (r_zero) return node.Left;
if (l_number && r_number)
return new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value+r_value),Lexeme.Number));
if (node.Right.ExpressionLexeme.Lexeme == Lexeme.UMinus)
return new ExpressionTreeNode(
new ExpressionLexeme("-",Lexeme.Minus),node.Left,node.Right.Left);
break;
case Lexeme.Minus:
if (r_zero) return node.Left;
if (l_zero) return new ExpressionTreeNode(
new ExpressionLexeme("-",Lexeme.UMinus),node.Right);
if (equal) return new ExpressionTreeNode(new ExpressionLexeme("0",Lexeme.Number));
if (l_number && r_number)
return new ExpressionTreeNode(
new ExpressionLexeme(Convert.ToString(l_value-r_value),Lexeme.Number));
break;
case Lexeme.UMinus:
if (node.Left.ExpressionLexeme.Lexeme == Lexeme.UMinus)
return node.Left.Left;
break;
}
break;
}
return node;
}
public ExpressionTreeNode(ExpressionLexeme lexeme,ExpressionTreeNode leftNode,ExpressionTreeNode rightNode )
{
ExpressionLexeme = lexeme;
Left = leftNode;
Right = rightNode;
}
private static string df(ExpressionTreeNode node, string diffVar)
{
if (!node.HasVariable(diffVar)) return "0";
bool leftDiffVar = (node.Left != null) && (node.Left.HasVariable(diffVar));
bool rightDiffVar = (node.Right != null) && (node.Right.HasVariable(diffVar));
switch (node.ExpressionLexeme.LexemeType)
{
case LexemeType.ltConstant:
switch (node.ExpressionLexeme.Lexeme)
{
case Lexeme.Var: return "1";
default: return "0";
}
case LexemeType.ltOperator:
switch (node.ExpressionLexeme.Lexeme)
{
case Lexeme.Plus:
case Lexeme.Minus:
return String.Format("({0}{1}{2})",
df(node.Left,diffVar),
node.ExpressionLexeme.LexemeName,
df(node.Right,diffVar));
case Lexeme.UMinus:
return String.Format("(-({0}))",df(node.Left,diffVar));
case Lexeme.Multiply:
return String.Format("(({0})*({1})+({2})*({3}))",
df(node.Left, diffVar),
node.Right,
df(node.Right, diffVar),
node.Left);
case Lexeme.Divide:
return String.Format("(({0})*({1})-({2})*({3}))/({4})^2",
df(node.Left, diffVar),
node.Right,
df(node.Right, diffVar),
node.Left,
node.Right);
case Lexeme.Power:
// diff f(x)^g(y)
if (leftDiffVar && !rightDiffVar)
{
return String.Format("((({0})^({1})*({1})*({2}))/({0}))",
node.Left, node.Right, df(node.Left, diffVar));
}
// diff f(y)^g(x)
if (!leftDiffVar && rightDiffVar)
{
return String.Format("((({0})^({1}))*({2})*log({0})))",
node.Left, node.Right, df(node.Right, diffVar));
}
// diff f(x)^g(x)
return String.Format("((({0})^({1}))*(({3})*log({0})+({1})*({2})/({0})))",
node.Left, node.Right,
df(node.Left, diffVar), df(node.Right, diffVar));
default: throw new Exception();
}
case LexemeType.ltFunction:
return String.Format("(("+node.ExpressionLexeme.LexemeDiffMask+")*({1}))",
node.Left, df(node.Left, diffVar));
default:
throw new Exception();
}
}
