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/*
 * @(#)RecursiveArgument.java        4.4.3    2022-05-28
 *
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package org.mariuszgromada.math.mxparser;

import java.util.ArrayList;
import java.util.List;
import org.mariuszgromada.math.mxparser.parsertokens.ParserSymbol;
/**
 * RecursiveArgument class enables to declare the argument
 * (variable) which is defined in a recursive way. Such an argument
 * can be used in further processing in expressions, functions and dependent
 * or recursive arguments.

 *
 * For example:
 * 

 * 
'fib(n) = fin(n-1)+fib(n-2), fib(0) = 0, fib(1) = 1'
 * 
'factorial(n) = n*factorial(n-1), factorial(0) = 1'
 * 
 * 

 * When creating an argument you should avoid:
 * 

 * 
names reserved as parser keywords, in general words known in mathematical language
 * as function names, operators (for example:
 * sin, cos, +, -, etc...). Please be informed that after associating
 * the argument with the expression, function or dependent/recursive argument
 * its name will be recognized by the parser as reserved key word.
 * It means that it could not be the same as any other key word known
 * by the parser for this particular expression.
 * 
defining statements with increasing index: 'a(n) = a(n+1) + ... ', otherwise
 * you will get Double.NaN
 * 
if recursion is not properly defined you will get Double.NaN in the result.
 * This is due to the recursion counter inside of the recursive argument. Calculating
 * n-th element requires no more than n recursion steps (usually less than n).
 * 
For negative 'n' you will get Double.NaN.
 *
 * 
 *
 * @author         Mariusz Gromada

 *                 [email protected]

 *                 MathSpace.pl

 *                 MathParser.org - mXparser project page

 *                 mXparser on GitHub

 *                 mXparser on SourceForge

 *                 mXparser on Bitbucket

 *                 mXparser on CodePlex

 *                 Janet Sudoku - project web page

 *                 Janet Sudoku on GitHub

 *                 Janet Sudoku on CodePlex

 *                 Janet Sudoku on SourceForge

 *                 Janet Sudoku on BitBucket

 *                 Scalar Free

 *                 Scalar Pro

 *                 ScalarMath.org

 *
 * @version        3.0.0
 *
 * @see Argument
 * @see Expression
 * @see Function
 * @see Constant
 */
public class RecursiveArgument extends Argument {
	/**
	 * Type identifier for recursive arguments.
	 */
	public static final int TYPE_ID_RECURSIVE		= 102;
	public static final String TYPE_DESC_RECURSIVE			= "User defined recursive argument";
	/**
	 * Base values
	 */
	private List baseValues;
	/**
	 * To avoid never ending loops
	 */
	private int recursiveCounter;
	private int startingIndex;
	/**
	 * Constructor - creates recursive argument.
	 *
	 * @param      argumentName                  the argument name
	 * @param      recursiveExpressionString     the recursive expression string
	 * @param      indexName                     index argument name
	 */
	public RecursiveArgument(String argumentName, String recursiveExpressionString, String indexName) {
		super(argumentName, recursiveExpressionString);
		if (argumentName.equals(this.getArgumentName())) {
			this.argumentType = RECURSIVE_ARGUMENT;
			baseValues = new ArrayList();
			this.n = new Argument(indexName);
			super.argumentExpression.addArguments(n);
			super.argumentExpression.addArguments(this);
			super.argumentExpression.setDescription(argumentName);
			recursiveCounter = -1;
		}
	}
	/**
	 * Constructor - creates recursive argument.
	 *
	 * @param      argumentName                  the argument name
	 * @param      recursiveExpressionString     the recursive expression string
	 * @param      n                             the index argument
	 * @param      elements                      Optional elements list (variadic - comma
	 *                                           separated) of types: Argument, Constant, Function
	 *
	 * @see        PrimitiveElement
	 * @see        Argument
	 */
	public RecursiveArgument(String argumentName, String recursiveExpressionString, Argument n, PrimitiveElement... elements) {
		super(argumentName, recursiveExpressionString);
		if (argumentName.equals(this.getArgumentName())) {
			this.argumentType = RECURSIVE_ARGUMENT;
			baseValues = new ArrayList();
			this.n = n;
			super.argumentExpression.addArguments(n);
			super.argumentExpression.addArguments(this);
			super.argumentExpression.addDefinitions(elements);
			super.argumentExpression.setDescription(argumentName);
			recursiveCounter = -1;
		}
	}
	/**
	 * Constructor - creates argument based on the argument definition string.
	 *
	 * @param      argumentDefinitionString        Argument definition string, i.e.:
	 *                                             

	 *                                                
'x' - only argument name
	 *                                                
'x=5' - argument name and argument value
	 *                                                
'x=2*5' - argument name and argument value given as simple expression
	 *                                                
'x=2*y' - argument name and argument expression (dependent argument 'x' on argument 'y')
	 *                                                
'x(n)=x(n-1)+x(n-2)' - for recursive arguments)
	 *                                             
	 *
	 * @param      elements                       Optional elements list
	 *                                            (variadic - comma separated) of types: Argument,
	 *                                            Constant, Function
	 *
	 * @see    PrimitiveElement
	 * @see    Argument
	 */
	public RecursiveArgument(String argumentDefinitionString, PrimitiveElement... elements) {
		super(argumentDefinitionString);
		if ( mXparser.regexMatch(argumentDefinitionString, ParserSymbol.function1ArgDefStrRegExp) ) {
			this.argumentType = RECURSIVE_ARGUMENT;
			baseValues = new ArrayList();
			recursiveCounter = -1;
			super.argumentExpression.addArguments(super.n);
			super.argumentExpression.addArguments(this);
			super.argumentExpression.addDefinitions(elements);
			super.argumentExpression.setDescription(argumentDefinitionString);
		} else {
			super.argumentExpression = new Expression();
			super.argumentExpression.setSyntaxStatus(SYNTAX_ERROR_OR_STATUS_UNKNOWN, "[" + argumentDefinitionString + "] " + "Invalid argument definition (patterns: f(n) = f(n-1) ...  ).");
		}
	}
	/**
	 * Adds base case
	 *
	 * @param      index               the base case index
	 * @param      value               the base case value
	 */
	public void addBaseCase(int index, double value) {
		int recSize = baseValues.size();
		if (index > recSize-1) {
			/*
			 * Expand base values array if necessary
			 */
			for (int i = recSize; i < index; i++)
				baseValues.add(Double.NaN);
			baseValues.add(value);
		} else
			baseValues.set(index, value);
	}
	/**
	 * Clears all based cases and stored calculated values
	 */
	public void resetAllCases() {
		baseValues.clear();
		recursiveCounter = -1;
	}
	/**
	 * Gets recursive argument value
	 *
	 * @param      index               the index
	 *
	 * @return     value as double
	 */
	public double getArgumentValue(double index) {
		/*
		 * Remember starting index
		 */
		if (recursiveCounter == -1)
			startingIndex = (int)Math.round(index);
		int recSize = baseValues.size();
		int idx = (int)Math.round(index);
		/*
		 * Count recursive calls
		 */
		recursiveCounter++;
		if ((recursiveCounter <= startingIndex) && (idx <= startingIndex)) {
			/*
			 * if recursive counter is still lower than starting index
			 * and current index is not increasing
			 */
			if ((idx >= 0) && (idx < recSize) && (!Double.isNaN(baseValues.get(idx).doubleValue())) ) {
				/*
				 * decrease recursive counter and return value
				 * if recursive value for the current index was already
				 * calculated and remembered in the base values table
				 */
				recursiveCounter--;
				return baseValues.get(idx).doubleValue();
			}
			else if (idx >= 0) {
				/*
				 * value is to be calculated by the recursive calls
				 */
				/*
				 * Set n to the current index
				 */
				n.setArgumentValue(idx);
				/*
				 * create new expression
				 */
				Expression newExp = new Expression(
						super.argumentExpression.expressionString
						,super.argumentExpression.argumentsList
						,super.argumentExpression.functionsList
						,super.argumentExpression.constantsList
						,Expression.INTERNAL
						,super.argumentExpression.UDFExpression
						,super.argumentExpression.UDFVariadicParamsAtRunTime);
				newExp.setDescription(super.getArgumentName());
				if (super.getVerboseMode() == true)
					newExp.setVerboseMode();
				/*
				 * perform recursive call
				 */
				double value = newExp.calculate();
				/*
				 * remember calculated in the base values array
				 */
				addBaseCase(idx, value);
				/*
				 * decrease recursive counter and return value
				 */
				recursiveCounter--;
				return value;
			} else {
				/*
				 * decrease recursive counter and
				 * return Double.NaN for negative index call
				 */
				recursiveCounter--;
				return Double.NaN;
			}
		} else {
			/* stop never ending loop
			 * decrease recursive counter and
			 * return Double.NaN
			 */
			recursiveCounter--;
			return Double.NaN;
		}
	}
}