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'''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
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