| '''This module is supposed to contain all the combinatorics related stuff which can be performed by VisualMath (VisMa) | |
| Note: Please try to maintain proper documentation | |
| ''' | |
| from visma.io.tokenize import tokenizer | |
| from visma.simplify.simplify import simplify | |
| from visma.io.parser import tokensToString | |
| from visma.functions.constant import Constant | |
| def factorial(tokens): | |
| '''Used to get factorial of tokens provided | |
| Argument: | |
| tokens {list} -- list of tokens | |
| Returns: | |
| result {list} -- list of result tokens | |
| {empty list} | |
| token_string {string} -- final result stored in a string | |
| animation {list} -- list of equation solving process | |
| comments {list} -- list of comments in equation solving process | |
| ''' | |
| tokens, _, _, _, _ = simplify(tokens) | |
| animation = [] | |
| comments = [] | |
| if (isinstance(tokens[0], Constant) & len(tokens) == 1): | |
| value = int(tokens[0].calculate()) | |
| if value == 0: | |
| result = [Constant(1)] | |
| comments += [['Factorial of ZERO is defined to be 1']] | |
| animation += [tokenizer('f = ' + str(1))] | |
| else: | |
| resultString = '' | |
| for i in range(1, value + 1): | |
| resultString += (str(i) + '*') | |
| resultString = resultString[:-1] | |
| resultTokens = tokenizer(resultString) | |
| comments += [['Expanding the factorial as']] | |
| animation += [resultTokens] | |
| result, _, _, _, _ = simplify(resultTokens) | |
| token_string = tokensToString(result) | |
| comments += [['Hence result: ']] | |
| animation += [tokenizer('f = ' + token_string)] | |
| return result, [], token_string, animation, comments | |
| def permutation(nTokens, rTokens): | |
| '''Used to get Permutation (nPr) | |
| Argument: | |
| nTokens {list} -- list of tokens of "n" in nPr | |
| rTokens {list} -- list of tokens of "r" in nPr | |
| Returns: | |
| result {list} -- list of result tokens | |
| {empty list} | |
| token_string {string} -- final result stored in a string | |
| animation {list} -- list of equation solving process | |
| comments {list} -- list of comments in equation solving process | |
| ''' | |
| nTokens, _, _, _, _ = simplify(nTokens) | |
| rTokens, _, _, _, _ = simplify(rTokens) | |
| animation = [] | |
| comments = [] | |
| if (isinstance(nTokens[0], Constant) & len(nTokens) == 1) & (isinstance(rTokens[0], Constant) & len(rTokens) == 1): | |
| comments += [['nCr is defined as (n!)/(r!)*(n-r)!']] | |
| animation += [[]] | |
| comments += [['Solving for n!']] | |
| animation += [[]] | |
| numerator, _, _, animNew1, commentNew1 = factorial(nTokens) | |
| commentNew1[1] = ['(n)! is thus solved as: '] | |
| animation.extend(animNew1) | |
| comments.extend(commentNew1) | |
| denominator = nTokens[0] - rTokens[0] | |
| comments += [['Solving for (n - r)!']] | |
| animation += [[]] | |
| denominator, _, _, animNew2, commentNew2 = factorial([denominator]) | |
| commentNew2[1] = ['(n - r)! is thus solved as: '] | |
| comments.extend(commentNew2) | |
| animation.extend(animNew2) | |
| result = [numerator[0] / denominator[0]] | |
| comments += [['On placing values in (n!)/(n-r)!']] | |
| animation += [tokenizer('r = ' + tokensToString(result))] | |
| token_string = tokensToString(result) | |
| return result, [], token_string, animation, comments | |
| def combination(nTokens, rTokens): | |
| '''Used to get Combination (nCr) | |
| Argument: | |
| nTokens {list} -- list of tokens of "n" in nCr | |
| rTokens {list} -- list of tokens of "r" in nCr | |
| Returns: | |
| result {list} -- list of result tokens | |
| {empty list} | |
| token_string {string} -- final result stored in a string | |
| animation {list} -- list of equation solving process | |
| comments {list} -- list of comments in equation solving process | |
| ''' | |
| nTokens, _, _, _, _ = simplify(nTokens) | |
| rTokens, _, _, _, _ = simplify(rTokens) | |
| animation = [] | |
| comments = [] | |
| if (isinstance(nTokens[0], Constant) & len(nTokens) == 1) & (isinstance(rTokens[0], Constant) & len(rTokens) == 1): | |
| comments += [['nCr is defined as (n!)/(r!)*(n-r)!']] | |
| animation += [[]] | |
| comments += [['Solving for n!']] | |
| animation += [[]] | |
| numerator, _, _, animNew1, commentNew1 = factorial(nTokens) | |
| commentNew1[1] = ['(n)! is thus solved as: '] | |
| animation.extend(animNew1) | |
| comments.extend(commentNew1) | |
| denominator1 = nTokens[0] - rTokens[0] | |
| comments += [['Solving for (n - r)!']] | |
| animation += [[]] | |
| denominator1, _, _, animNew2, commentNew2 = factorial([denominator1]) | |
| commentNew2[1] = ['(n - r)! is thus solved as: '] | |
| comments.extend(commentNew2) | |
| animation.extend(animNew2) | |
| comments += [['Solving for r!']] | |
| animation += [[]] | |
| denominator2, _, _, animNew3, commentNew3 = factorial([rTokens[0]]) | |
| commentNew3[1] = ['r! is thus solved as: '] | |
| comments.extend(commentNew3) | |
| animation.extend(animNew3) | |
| denominator = denominator1[0] * denominator2[0] | |
| result = [numerator[0] / denominator] | |
| comments += [['On placing values in (n!)/(r!)*(n-r)!']] | |
| animation += [tokenizer('r = ' + tokensToString(result))] | |
| token_string = tokensToString(result) | |
| return result, [], token_string, animation, comments | |