Pascal's Triangle Generator in Python

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4












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So I've been working on a generator for Pascal's triangle in Python. Now, I wouldn't call myself a Python god, so my program is a lot longer than the very confusing ones on the internet. It's more of a logical approach to creating the triangle.



Here's the program:



def double_chunker(lst):
leng = len(lst)
for i in range(leng):
if i == 0:
yield [lst[0]]
elif i == 1:
yield [lst[0], lst[1]]
elif i == leng:
yield [lst[-1]]
else:
yield [lst[i-1], lst[i]]
yield [lst[-1]]

def chunk_adder(lst):
for i in lst:
if len(i) == 1:
yield i[0]
else:
yield sum(i)

def pascal_next(lst):
return list(chunk_adder(double_chunker(lst)))

def pascal_triangle(rows):
end = [[1]]
for i in range(rows):
end.append(pascal_next(end[-1]))
return end


A simple go-through of how it works:



  1. double_chunker() splits up a row of Pascal's triangle into the pairs of numbers you would use when adding up to determine the numbers in the next row. This algorithm is little jerry-rigged - I had to add some special exceptions for some numbers on the end of the row to make it work properly.


  2. chunk_adder() adds together a list of chunks generated by double_chunker to determine the next row in the Pascal sequence.


  3. pascal_next()combines both double_chunker() and chunk_adder() to, when given one row in Pascal's triangle, determine the next row in the triangle.


  4. pascal_triangle() iteratively creates rows of Pascal's triangle using pascal_next().


So, here are some of my questions:



  1. Is there anything in my program that seems redundant, repetitive, or can be shortened?


  2. Is there any better code practices I should be employing and am not?


And obviously, as always, feel free to provide any other feedback you may have. Thanks in advance!










share|improve this question









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    4












    $begingroup$


    So I've been working on a generator for Pascal's triangle in Python. Now, I wouldn't call myself a Python god, so my program is a lot longer than the very confusing ones on the internet. It's more of a logical approach to creating the triangle.



    Here's the program:



    def double_chunker(lst):
    leng = len(lst)
    for i in range(leng):
    if i == 0:
    yield [lst[0]]
    elif i == 1:
    yield [lst[0], lst[1]]
    elif i == leng:
    yield [lst[-1]]
    else:
    yield [lst[i-1], lst[i]]
    yield [lst[-1]]

    def chunk_adder(lst):
    for i in lst:
    if len(i) == 1:
    yield i[0]
    else:
    yield sum(i)

    def pascal_next(lst):
    return list(chunk_adder(double_chunker(lst)))

    def pascal_triangle(rows):
    end = [[1]]
    for i in range(rows):
    end.append(pascal_next(end[-1]))
    return end


    A simple go-through of how it works:



    1. double_chunker() splits up a row of Pascal's triangle into the pairs of numbers you would use when adding up to determine the numbers in the next row. This algorithm is little jerry-rigged - I had to add some special exceptions for some numbers on the end of the row to make it work properly.


    2. chunk_adder() adds together a list of chunks generated by double_chunker to determine the next row in the Pascal sequence.


    3. pascal_next()combines both double_chunker() and chunk_adder() to, when given one row in Pascal's triangle, determine the next row in the triangle.


    4. pascal_triangle() iteratively creates rows of Pascal's triangle using pascal_next().


    So, here are some of my questions:



    1. Is there anything in my program that seems redundant, repetitive, or can be shortened?


    2. Is there any better code practices I should be employing and am not?


    And obviously, as always, feel free to provide any other feedback you may have. Thanks in advance!










    share|improve this question









    $endgroup$














      4












      4








      4


      1



      $begingroup$


      So I've been working on a generator for Pascal's triangle in Python. Now, I wouldn't call myself a Python god, so my program is a lot longer than the very confusing ones on the internet. It's more of a logical approach to creating the triangle.



      Here's the program:



      def double_chunker(lst):
      leng = len(lst)
      for i in range(leng):
      if i == 0:
      yield [lst[0]]
      elif i == 1:
      yield [lst[0], lst[1]]
      elif i == leng:
      yield [lst[-1]]
      else:
      yield [lst[i-1], lst[i]]
      yield [lst[-1]]

      def chunk_adder(lst):
      for i in lst:
      if len(i) == 1:
      yield i[0]
      else:
      yield sum(i)

      def pascal_next(lst):
      return list(chunk_adder(double_chunker(lst)))

      def pascal_triangle(rows):
      end = [[1]]
      for i in range(rows):
      end.append(pascal_next(end[-1]))
      return end


      A simple go-through of how it works:



      1. double_chunker() splits up a row of Pascal's triangle into the pairs of numbers you would use when adding up to determine the numbers in the next row. This algorithm is little jerry-rigged - I had to add some special exceptions for some numbers on the end of the row to make it work properly.


      2. chunk_adder() adds together a list of chunks generated by double_chunker to determine the next row in the Pascal sequence.


      3. pascal_next()combines both double_chunker() and chunk_adder() to, when given one row in Pascal's triangle, determine the next row in the triangle.


      4. pascal_triangle() iteratively creates rows of Pascal's triangle using pascal_next().


      So, here are some of my questions:



      1. Is there anything in my program that seems redundant, repetitive, or can be shortened?


      2. Is there any better code practices I should be employing and am not?


      And obviously, as always, feel free to provide any other feedback you may have. Thanks in advance!










      share|improve this question









      $endgroup$




      So I've been working on a generator for Pascal's triangle in Python. Now, I wouldn't call myself a Python god, so my program is a lot longer than the very confusing ones on the internet. It's more of a logical approach to creating the triangle.



      Here's the program:



      def double_chunker(lst):
      leng = len(lst)
      for i in range(leng):
      if i == 0:
      yield [lst[0]]
      elif i == 1:
      yield [lst[0], lst[1]]
      elif i == leng:
      yield [lst[-1]]
      else:
      yield [lst[i-1], lst[i]]
      yield [lst[-1]]

      def chunk_adder(lst):
      for i in lst:
      if len(i) == 1:
      yield i[0]
      else:
      yield sum(i)

      def pascal_next(lst):
      return list(chunk_adder(double_chunker(lst)))

      def pascal_triangle(rows):
      end = [[1]]
      for i in range(rows):
      end.append(pascal_next(end[-1]))
      return end


      A simple go-through of how it works:



      1. double_chunker() splits up a row of Pascal's triangle into the pairs of numbers you would use when adding up to determine the numbers in the next row. This algorithm is little jerry-rigged - I had to add some special exceptions for some numbers on the end of the row to make it work properly.


      2. chunk_adder() adds together a list of chunks generated by double_chunker to determine the next row in the Pascal sequence.


      3. pascal_next()combines both double_chunker() and chunk_adder() to, when given one row in Pascal's triangle, determine the next row in the triangle.


      4. pascal_triangle() iteratively creates rows of Pascal's triangle using pascal_next().


      So, here are some of my questions:



      1. Is there anything in my program that seems redundant, repetitive, or can be shortened?


      2. Is there any better code practices I should be employing and am not?


      And obviously, as always, feel free to provide any other feedback you may have. Thanks in advance!







      python






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      share|improve this question











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      asked Jan 17 at 11:24









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          4 Answers
          4






          active

          oldest

          votes


















          10












          $begingroup$


          def chunk_adder(lst):
          for i in lst:
          if len(i) == 1:
          yield i[0]
          else:
          yield sum(i)



          sum can happilly consume iterable of size 1, it can even consume iterable of size 0:



          >>> sum([1])
          1
          >>> sum()
          0


          So you can simplify it to:



          def chunck_adder(iterable):
          for element in iterable:
          yield sum(element)


          Which is simply



          def chunck_adder(iterable):
          yield from map(sum, iterable)


          So you could simplify pascal_next instead:



          def pascal_next(lst):
          return list(map(sum, double_chunker(lst)))




          def double_chunker(lst):
          leng = len(lst)
          for i in range(leng):
          if i == 0:
          yield [lst[0]]
          elif i == 1:
          yield [lst[0], lst[1]]
          elif i == leng:
          yield [lst[-1]]
          else:
          yield [lst[i-1], lst[i]]
          yield [lst[-1]]



          The intent is pretty much the same than the pairwise recipe from itertools. Except you want to yield the first and last element as well.



          Here you have two possibilities:




          • either yield them manually:



            import itertools

            def double_chunker(lst):
            if not lst:
            return
            a, b = itertools.tee(lst)
            next(b, None)

            yield [lst[0]]
            yield from zip(a, b)
            yield [lst[-1]]


            But this forces the argument to be a list, or at least to know if its empty and to implement __getitem__.




          • or add boundary values to your input so pairwise can work properly:



            import itertools


            def pairwise(iterable):
            a, b = itertools.tee(iterable)
            next(b, None)
            return zip(a, b)


            def double_chuncker(iterable):
            extended = itertools.chain([0], iterable, [0])
            return pairwise(extended)


            Which I recommend because it happily consume any iterable.





          def pascal_triangle(rows):
          end = [[1]]
          for i in range(rows):
          end.append(pascal_next(end[-1]))
          return end



          Instead of relying on the list being constructed, I would explicitly store the current row. I would also turn this into an infinite generator because it really is and maybe provide an helper function for convenience:



          def pascal_triangle():
          row = [1]
          while True:
          yield row
          row = pascal_next(row)


          def pascal_triangle_up_to(n):
          return list(itertools.islice(pascal_triangle(), n))



          Full code:



          import itertools


          def pairwise(iterable):
          a, b = itertools.tee(iterable)
          next(b, None)
          return zip(a, b)


          def double_chuncker(iterable):
          extended = itertools.chain([0], iterable, [0])
          return pairwise(extended)


          def pascal_next(iterable):
          return list(map(sum, double_chuncker(iterable)))


          def pascal_triangle():
          row = [1]
          while True:
          yield row
          row = pascal_next(row)


          def pascal_triangle_up_to(n):
          return list(itertools.islice(pascal_triangle(), n))


          if __name__ == '__main__':
          # Testing
          for row in pascal_triangle():
          print(row, end='')
          if (input()):
          break





          share|improve this answer











          $endgroup$




















            5












            $begingroup$

            Names



            I am not fully convinced by the different function names but I have nothing better to suggest for the time being.



            Style



            Python has a Style Guide called PEP 8. It is an interesting read. The most significant impact for your code would be to use 4 spaces for each indentation level instead of 2.



            Simplify double_chunker



            In double_chunker, the following condition is never true:



            elif i == leng:
            yield [lst[-1]]


            Also, you don't need to handle explicitly the case:



            elif i == 1:
            yield [lst[0], lst[1]]


            as it is just a particular case for [lst[i-1], lst[i]] with i == 1.



            Simplify chunk_adder



            In chunk_adder, instead of:



            if len(i) == 1:
            yield i[0]
            else:
            yield sum(i)


            We can write:



            yield sum(i)


            Then, we could rewrite the function using generator expressions:



            def chunk_adder(lst):
            return (sum(i) for i in lst)


            Then, it looks like the function is not really needed. We could write:



            def pascal_next(lst):
            return [sum(i) for i in double_chunker(lst)]



            At this stage, we have:



            def double_chunker(lst):
            for i in range(len(lst)):
            if i == 0:
            yield [lst[0]]
            else:
            yield [lst[i-1], lst[i]]
            yield [lst[-1]]


            def pascal_next(lst):
            return [sum(i) for i in double_chunker(lst)]

            def pascal_triangle(rows):
            end = [[1]]
            for i in range(rows):
            end.append(pascal_next(end[-1]))
            return end


            print(pascal_triangle(8))


            More simplification in double_chunker



            We could handle the case i == 0 before the loop rather than inside the loop. That could lead to a slightly different behavior when the input is an empty list but that case is not handled properly anyway (exception thrown).



            def double_chunker(lst):
            yield [lst[0]]
            for i in range(1, len(lst)):
            yield [lst[i-1], lst[i]]
            yield [lst[-1]]


            Then, it becomes obvious what we want to do: we want to iterate over all pairs of consecutive items in a list which is a problem common enough to find various solutions to it.






            share|improve this answer









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              3












              $begingroup$


              Is there any better code practices I should be employing and am not?




              • The first thing that caught my attention is the missing tests

              You should implement a few test cases to ensure that after changes the program does still work as intended



              Both the unittest module or doctest are good Python modules for testing, I have used the unittest as an example



              class PascalTriangleTest(unittest.TestCase):
              def test_triangle_0(self):
              self.assertEqual(
              pascal_triangle(0),
              [[1]]
              )

              def test_triangle_1(self):
              self.assertEqual(
              pascal_triangle(1),
              [[1], [1, 1]]
              )

              def test_triangle_2(self):
              self.assertEqual(
              pascal_triangle(2),
              [[1], [1, 1], [1, 2, 1]]
              )

              def test_triangle_3(self):
              self.assertEqual(
              pascal_triangle(3),
              [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
              )

              if __name__ == '__main__':
              unittest.main()


              • The second one would be the missing docstrings

              The comments below your code would be a good start to make the docstring for each function.



              See PEP257, for docstring conventions






              share|improve this answer









              $endgroup$




















                2












                $begingroup$


                Is there anything in my program that seems redundant, repetitive, or can be shortened?




                The 22 lines of double_chunker, chunk_adder, and pascal_next can be shortened to



                def pascal_next(lst):
                return [left + right for (left, right) in zip(lst + [0], [0] + lst)]





                share|improve this answer









                $endgroup$








                • 1




                  $begingroup$
                  Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                  $endgroup$
                  – Ludisposed
                  Jan 17 at 14:47











                • $begingroup$
                  @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                  $endgroup$
                  – Peter Taylor
                  Jan 17 at 15:28










                • $begingroup$
                  You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                  $endgroup$
                  – Graipher
                  Jan 17 at 15:30










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                4 Answers
                4






                active

                oldest

                votes








                4 Answers
                4






                active

                oldest

                votes









                active

                oldest

                votes






                active

                oldest

                votes









                10












                $begingroup$


                def chunk_adder(lst):
                for i in lst:
                if len(i) == 1:
                yield i[0]
                else:
                yield sum(i)



                sum can happilly consume iterable of size 1, it can even consume iterable of size 0:



                >>> sum([1])
                1
                >>> sum()
                0


                So you can simplify it to:



                def chunck_adder(iterable):
                for element in iterable:
                yield sum(element)


                Which is simply



                def chunck_adder(iterable):
                yield from map(sum, iterable)


                So you could simplify pascal_next instead:



                def pascal_next(lst):
                return list(map(sum, double_chunker(lst)))




                def double_chunker(lst):
                leng = len(lst)
                for i in range(leng):
                if i == 0:
                yield [lst[0]]
                elif i == 1:
                yield [lst[0], lst[1]]
                elif i == leng:
                yield [lst[-1]]
                else:
                yield [lst[i-1], lst[i]]
                yield [lst[-1]]



                The intent is pretty much the same than the pairwise recipe from itertools. Except you want to yield the first and last element as well.



                Here you have two possibilities:




                • either yield them manually:



                  import itertools

                  def double_chunker(lst):
                  if not lst:
                  return
                  a, b = itertools.tee(lst)
                  next(b, None)

                  yield [lst[0]]
                  yield from zip(a, b)
                  yield [lst[-1]]


                  But this forces the argument to be a list, or at least to know if its empty and to implement __getitem__.




                • or add boundary values to your input so pairwise can work properly:



                  import itertools


                  def pairwise(iterable):
                  a, b = itertools.tee(iterable)
                  next(b, None)
                  return zip(a, b)


                  def double_chuncker(iterable):
                  extended = itertools.chain([0], iterable, [0])
                  return pairwise(extended)


                  Which I recommend because it happily consume any iterable.





                def pascal_triangle(rows):
                end = [[1]]
                for i in range(rows):
                end.append(pascal_next(end[-1]))
                return end



                Instead of relying on the list being constructed, I would explicitly store the current row. I would also turn this into an infinite generator because it really is and maybe provide an helper function for convenience:



                def pascal_triangle():
                row = [1]
                while True:
                yield row
                row = pascal_next(row)


                def pascal_triangle_up_to(n):
                return list(itertools.islice(pascal_triangle(), n))



                Full code:



                import itertools


                def pairwise(iterable):
                a, b = itertools.tee(iterable)
                next(b, None)
                return zip(a, b)


                def double_chuncker(iterable):
                extended = itertools.chain([0], iterable, [0])
                return pairwise(extended)


                def pascal_next(iterable):
                return list(map(sum, double_chuncker(iterable)))


                def pascal_triangle():
                row = [1]
                while True:
                yield row
                row = pascal_next(row)


                def pascal_triangle_up_to(n):
                return list(itertools.islice(pascal_triangle(), n))


                if __name__ == '__main__':
                # Testing
                for row in pascal_triangle():
                print(row, end='')
                if (input()):
                break





                share|improve this answer











                $endgroup$

















                  10












                  $begingroup$


                  def chunk_adder(lst):
                  for i in lst:
                  if len(i) == 1:
                  yield i[0]
                  else:
                  yield sum(i)



                  sum can happilly consume iterable of size 1, it can even consume iterable of size 0:



                  >>> sum([1])
                  1
                  >>> sum()
                  0


                  So you can simplify it to:



                  def chunck_adder(iterable):
                  for element in iterable:
                  yield sum(element)


                  Which is simply



                  def chunck_adder(iterable):
                  yield from map(sum, iterable)


                  So you could simplify pascal_next instead:



                  def pascal_next(lst):
                  return list(map(sum, double_chunker(lst)))




                  def double_chunker(lst):
                  leng = len(lst)
                  for i in range(leng):
                  if i == 0:
                  yield [lst[0]]
                  elif i == 1:
                  yield [lst[0], lst[1]]
                  elif i == leng:
                  yield [lst[-1]]
                  else:
                  yield [lst[i-1], lst[i]]
                  yield [lst[-1]]



                  The intent is pretty much the same than the pairwise recipe from itertools. Except you want to yield the first and last element as well.



                  Here you have two possibilities:




                  • either yield them manually:



                    import itertools

                    def double_chunker(lst):
                    if not lst:
                    return
                    a, b = itertools.tee(lst)
                    next(b, None)

                    yield [lst[0]]
                    yield from zip(a, b)
                    yield [lst[-1]]


                    But this forces the argument to be a list, or at least to know if its empty and to implement __getitem__.




                  • or add boundary values to your input so pairwise can work properly:



                    import itertools


                    def pairwise(iterable):
                    a, b = itertools.tee(iterable)
                    next(b, None)
                    return zip(a, b)


                    def double_chuncker(iterable):
                    extended = itertools.chain([0], iterable, [0])
                    return pairwise(extended)


                    Which I recommend because it happily consume any iterable.





                  def pascal_triangle(rows):
                  end = [[1]]
                  for i in range(rows):
                  end.append(pascal_next(end[-1]))
                  return end



                  Instead of relying on the list being constructed, I would explicitly store the current row. I would also turn this into an infinite generator because it really is and maybe provide an helper function for convenience:



                  def pascal_triangle():
                  row = [1]
                  while True:
                  yield row
                  row = pascal_next(row)


                  def pascal_triangle_up_to(n):
                  return list(itertools.islice(pascal_triangle(), n))



                  Full code:



                  import itertools


                  def pairwise(iterable):
                  a, b = itertools.tee(iterable)
                  next(b, None)
                  return zip(a, b)


                  def double_chuncker(iterable):
                  extended = itertools.chain([0], iterable, [0])
                  return pairwise(extended)


                  def pascal_next(iterable):
                  return list(map(sum, double_chuncker(iterable)))


                  def pascal_triangle():
                  row = [1]
                  while True:
                  yield row
                  row = pascal_next(row)


                  def pascal_triangle_up_to(n):
                  return list(itertools.islice(pascal_triangle(), n))


                  if __name__ == '__main__':
                  # Testing
                  for row in pascal_triangle():
                  print(row, end='')
                  if (input()):
                  break





                  share|improve this answer











                  $endgroup$















                    10












                    10








                    10





                    $begingroup$


                    def chunk_adder(lst):
                    for i in lst:
                    if len(i) == 1:
                    yield i[0]
                    else:
                    yield sum(i)



                    sum can happilly consume iterable of size 1, it can even consume iterable of size 0:



                    >>> sum([1])
                    1
                    >>> sum()
                    0


                    So you can simplify it to:



                    def chunck_adder(iterable):
                    for element in iterable:
                    yield sum(element)


                    Which is simply



                    def chunck_adder(iterable):
                    yield from map(sum, iterable)


                    So you could simplify pascal_next instead:



                    def pascal_next(lst):
                    return list(map(sum, double_chunker(lst)))




                    def double_chunker(lst):
                    leng = len(lst)
                    for i in range(leng):
                    if i == 0:
                    yield [lst[0]]
                    elif i == 1:
                    yield [lst[0], lst[1]]
                    elif i == leng:
                    yield [lst[-1]]
                    else:
                    yield [lst[i-1], lst[i]]
                    yield [lst[-1]]



                    The intent is pretty much the same than the pairwise recipe from itertools. Except you want to yield the first and last element as well.



                    Here you have two possibilities:




                    • either yield them manually:



                      import itertools

                      def double_chunker(lst):
                      if not lst:
                      return
                      a, b = itertools.tee(lst)
                      next(b, None)

                      yield [lst[0]]
                      yield from zip(a, b)
                      yield [lst[-1]]


                      But this forces the argument to be a list, or at least to know if its empty and to implement __getitem__.




                    • or add boundary values to your input so pairwise can work properly:



                      import itertools


                      def pairwise(iterable):
                      a, b = itertools.tee(iterable)
                      next(b, None)
                      return zip(a, b)


                      def double_chuncker(iterable):
                      extended = itertools.chain([0], iterable, [0])
                      return pairwise(extended)


                      Which I recommend because it happily consume any iterable.





                    def pascal_triangle(rows):
                    end = [[1]]
                    for i in range(rows):
                    end.append(pascal_next(end[-1]))
                    return end



                    Instead of relying on the list being constructed, I would explicitly store the current row. I would also turn this into an infinite generator because it really is and maybe provide an helper function for convenience:



                    def pascal_triangle():
                    row = [1]
                    while True:
                    yield row
                    row = pascal_next(row)


                    def pascal_triangle_up_to(n):
                    return list(itertools.islice(pascal_triangle(), n))



                    Full code:



                    import itertools


                    def pairwise(iterable):
                    a, b = itertools.tee(iterable)
                    next(b, None)
                    return zip(a, b)


                    def double_chuncker(iterable):
                    extended = itertools.chain([0], iterable, [0])
                    return pairwise(extended)


                    def pascal_next(iterable):
                    return list(map(sum, double_chuncker(iterable)))


                    def pascal_triangle():
                    row = [1]
                    while True:
                    yield row
                    row = pascal_next(row)


                    def pascal_triangle_up_to(n):
                    return list(itertools.islice(pascal_triangle(), n))


                    if __name__ == '__main__':
                    # Testing
                    for row in pascal_triangle():
                    print(row, end='')
                    if (input()):
                    break





                    share|improve this answer











                    $endgroup$




                    def chunk_adder(lst):
                    for i in lst:
                    if len(i) == 1:
                    yield i[0]
                    else:
                    yield sum(i)



                    sum can happilly consume iterable of size 1, it can even consume iterable of size 0:



                    >>> sum([1])
                    1
                    >>> sum()
                    0


                    So you can simplify it to:



                    def chunck_adder(iterable):
                    for element in iterable:
                    yield sum(element)


                    Which is simply



                    def chunck_adder(iterable):
                    yield from map(sum, iterable)


                    So you could simplify pascal_next instead:



                    def pascal_next(lst):
                    return list(map(sum, double_chunker(lst)))




                    def double_chunker(lst):
                    leng = len(lst)
                    for i in range(leng):
                    if i == 0:
                    yield [lst[0]]
                    elif i == 1:
                    yield [lst[0], lst[1]]
                    elif i == leng:
                    yield [lst[-1]]
                    else:
                    yield [lst[i-1], lst[i]]
                    yield [lst[-1]]



                    The intent is pretty much the same than the pairwise recipe from itertools. Except you want to yield the first and last element as well.



                    Here you have two possibilities:




                    • either yield them manually:



                      import itertools

                      def double_chunker(lst):
                      if not lst:
                      return
                      a, b = itertools.tee(lst)
                      next(b, None)

                      yield [lst[0]]
                      yield from zip(a, b)
                      yield [lst[-1]]


                      But this forces the argument to be a list, or at least to know if its empty and to implement __getitem__.




                    • or add boundary values to your input so pairwise can work properly:



                      import itertools


                      def pairwise(iterable):
                      a, b = itertools.tee(iterable)
                      next(b, None)
                      return zip(a, b)


                      def double_chuncker(iterable):
                      extended = itertools.chain([0], iterable, [0])
                      return pairwise(extended)


                      Which I recommend because it happily consume any iterable.





                    def pascal_triangle(rows):
                    end = [[1]]
                    for i in range(rows):
                    end.append(pascal_next(end[-1]))
                    return end



                    Instead of relying on the list being constructed, I would explicitly store the current row. I would also turn this into an infinite generator because it really is and maybe provide an helper function for convenience:



                    def pascal_triangle():
                    row = [1]
                    while True:
                    yield row
                    row = pascal_next(row)


                    def pascal_triangle_up_to(n):
                    return list(itertools.islice(pascal_triangle(), n))



                    Full code:



                    import itertools


                    def pairwise(iterable):
                    a, b = itertools.tee(iterable)
                    next(b, None)
                    return zip(a, b)


                    def double_chuncker(iterable):
                    extended = itertools.chain([0], iterable, [0])
                    return pairwise(extended)


                    def pascal_next(iterable):
                    return list(map(sum, double_chuncker(iterable)))


                    def pascal_triangle():
                    row = [1]
                    while True:
                    yield row
                    row = pascal_next(row)


                    def pascal_triangle_up_to(n):
                    return list(itertools.islice(pascal_triangle(), n))


                    if __name__ == '__main__':
                    # Testing
                    for row in pascal_triangle():
                    print(row, end='')
                    if (input()):
                    break






                    share|improve this answer














                    share|improve this answer



                    share|improve this answer








                    edited Jan 17 at 13:29

























                    answered Jan 17 at 13:23









                    Mathias EttingerMathias Ettinger

                    24.3k33184




                    24.3k33184























                        5












                        $begingroup$

                        Names



                        I am not fully convinced by the different function names but I have nothing better to suggest for the time being.



                        Style



                        Python has a Style Guide called PEP 8. It is an interesting read. The most significant impact for your code would be to use 4 spaces for each indentation level instead of 2.



                        Simplify double_chunker



                        In double_chunker, the following condition is never true:



                        elif i == leng:
                        yield [lst[-1]]


                        Also, you don't need to handle explicitly the case:



                        elif i == 1:
                        yield [lst[0], lst[1]]


                        as it is just a particular case for [lst[i-1], lst[i]] with i == 1.



                        Simplify chunk_adder



                        In chunk_adder, instead of:



                        if len(i) == 1:
                        yield i[0]
                        else:
                        yield sum(i)


                        We can write:



                        yield sum(i)


                        Then, we could rewrite the function using generator expressions:



                        def chunk_adder(lst):
                        return (sum(i) for i in lst)


                        Then, it looks like the function is not really needed. We could write:



                        def pascal_next(lst):
                        return [sum(i) for i in double_chunker(lst)]



                        At this stage, we have:



                        def double_chunker(lst):
                        for i in range(len(lst)):
                        if i == 0:
                        yield [lst[0]]
                        else:
                        yield [lst[i-1], lst[i]]
                        yield [lst[-1]]


                        def pascal_next(lst):
                        return [sum(i) for i in double_chunker(lst)]

                        def pascal_triangle(rows):
                        end = [[1]]
                        for i in range(rows):
                        end.append(pascal_next(end[-1]))
                        return end


                        print(pascal_triangle(8))


                        More simplification in double_chunker



                        We could handle the case i == 0 before the loop rather than inside the loop. That could lead to a slightly different behavior when the input is an empty list but that case is not handled properly anyway (exception thrown).



                        def double_chunker(lst):
                        yield [lst[0]]
                        for i in range(1, len(lst)):
                        yield [lst[i-1], lst[i]]
                        yield [lst[-1]]


                        Then, it becomes obvious what we want to do: we want to iterate over all pairs of consecutive items in a list which is a problem common enough to find various solutions to it.






                        share|improve this answer









                        $endgroup$

















                          5












                          $begingroup$

                          Names



                          I am not fully convinced by the different function names but I have nothing better to suggest for the time being.



                          Style



                          Python has a Style Guide called PEP 8. It is an interesting read. The most significant impact for your code would be to use 4 spaces for each indentation level instead of 2.



                          Simplify double_chunker



                          In double_chunker, the following condition is never true:



                          elif i == leng:
                          yield [lst[-1]]


                          Also, you don't need to handle explicitly the case:



                          elif i == 1:
                          yield [lst[0], lst[1]]


                          as it is just a particular case for [lst[i-1], lst[i]] with i == 1.



                          Simplify chunk_adder



                          In chunk_adder, instead of:



                          if len(i) == 1:
                          yield i[0]
                          else:
                          yield sum(i)


                          We can write:



                          yield sum(i)


                          Then, we could rewrite the function using generator expressions:



                          def chunk_adder(lst):
                          return (sum(i) for i in lst)


                          Then, it looks like the function is not really needed. We could write:



                          def pascal_next(lst):
                          return [sum(i) for i in double_chunker(lst)]



                          At this stage, we have:



                          def double_chunker(lst):
                          for i in range(len(lst)):
                          if i == 0:
                          yield [lst[0]]
                          else:
                          yield [lst[i-1], lst[i]]
                          yield [lst[-1]]


                          def pascal_next(lst):
                          return [sum(i) for i in double_chunker(lst)]

                          def pascal_triangle(rows):
                          end = [[1]]
                          for i in range(rows):
                          end.append(pascal_next(end[-1]))
                          return end


                          print(pascal_triangle(8))


                          More simplification in double_chunker



                          We could handle the case i == 0 before the loop rather than inside the loop. That could lead to a slightly different behavior when the input is an empty list but that case is not handled properly anyway (exception thrown).



                          def double_chunker(lst):
                          yield [lst[0]]
                          for i in range(1, len(lst)):
                          yield [lst[i-1], lst[i]]
                          yield [lst[-1]]


                          Then, it becomes obvious what we want to do: we want to iterate over all pairs of consecutive items in a list which is a problem common enough to find various solutions to it.






                          share|improve this answer









                          $endgroup$















                            5












                            5








                            5





                            $begingroup$

                            Names



                            I am not fully convinced by the different function names but I have nothing better to suggest for the time being.



                            Style



                            Python has a Style Guide called PEP 8. It is an interesting read. The most significant impact for your code would be to use 4 spaces for each indentation level instead of 2.



                            Simplify double_chunker



                            In double_chunker, the following condition is never true:



                            elif i == leng:
                            yield [lst[-1]]


                            Also, you don't need to handle explicitly the case:



                            elif i == 1:
                            yield [lst[0], lst[1]]


                            as it is just a particular case for [lst[i-1], lst[i]] with i == 1.



                            Simplify chunk_adder



                            In chunk_adder, instead of:



                            if len(i) == 1:
                            yield i[0]
                            else:
                            yield sum(i)


                            We can write:



                            yield sum(i)


                            Then, we could rewrite the function using generator expressions:



                            def chunk_adder(lst):
                            return (sum(i) for i in lst)


                            Then, it looks like the function is not really needed. We could write:



                            def pascal_next(lst):
                            return [sum(i) for i in double_chunker(lst)]



                            At this stage, we have:



                            def double_chunker(lst):
                            for i in range(len(lst)):
                            if i == 0:
                            yield [lst[0]]
                            else:
                            yield [lst[i-1], lst[i]]
                            yield [lst[-1]]


                            def pascal_next(lst):
                            return [sum(i) for i in double_chunker(lst)]

                            def pascal_triangle(rows):
                            end = [[1]]
                            for i in range(rows):
                            end.append(pascal_next(end[-1]))
                            return end


                            print(pascal_triangle(8))


                            More simplification in double_chunker



                            We could handle the case i == 0 before the loop rather than inside the loop. That could lead to a slightly different behavior when the input is an empty list but that case is not handled properly anyway (exception thrown).



                            def double_chunker(lst):
                            yield [lst[0]]
                            for i in range(1, len(lst)):
                            yield [lst[i-1], lst[i]]
                            yield [lst[-1]]


                            Then, it becomes obvious what we want to do: we want to iterate over all pairs of consecutive items in a list which is a problem common enough to find various solutions to it.






                            share|improve this answer









                            $endgroup$



                            Names



                            I am not fully convinced by the different function names but I have nothing better to suggest for the time being.



                            Style



                            Python has a Style Guide called PEP 8. It is an interesting read. The most significant impact for your code would be to use 4 spaces for each indentation level instead of 2.



                            Simplify double_chunker



                            In double_chunker, the following condition is never true:



                            elif i == leng:
                            yield [lst[-1]]


                            Also, you don't need to handle explicitly the case:



                            elif i == 1:
                            yield [lst[0], lst[1]]


                            as it is just a particular case for [lst[i-1], lst[i]] with i == 1.



                            Simplify chunk_adder



                            In chunk_adder, instead of:



                            if len(i) == 1:
                            yield i[0]
                            else:
                            yield sum(i)


                            We can write:



                            yield sum(i)


                            Then, we could rewrite the function using generator expressions:



                            def chunk_adder(lst):
                            return (sum(i) for i in lst)


                            Then, it looks like the function is not really needed. We could write:



                            def pascal_next(lst):
                            return [sum(i) for i in double_chunker(lst)]



                            At this stage, we have:



                            def double_chunker(lst):
                            for i in range(len(lst)):
                            if i == 0:
                            yield [lst[0]]
                            else:
                            yield [lst[i-1], lst[i]]
                            yield [lst[-1]]


                            def pascal_next(lst):
                            return [sum(i) for i in double_chunker(lst)]

                            def pascal_triangle(rows):
                            end = [[1]]
                            for i in range(rows):
                            end.append(pascal_next(end[-1]))
                            return end


                            print(pascal_triangle(8))


                            More simplification in double_chunker



                            We could handle the case i == 0 before the loop rather than inside the loop. That could lead to a slightly different behavior when the input is an empty list but that case is not handled properly anyway (exception thrown).



                            def double_chunker(lst):
                            yield [lst[0]]
                            for i in range(1, len(lst)):
                            yield [lst[i-1], lst[i]]
                            yield [lst[-1]]


                            Then, it becomes obvious what we want to do: we want to iterate over all pairs of consecutive items in a list which is a problem common enough to find various solutions to it.







                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered Jan 17 at 13:22









                            JosayJosay

                            25.7k14087




                            25.7k14087





















                                3












                                $begingroup$


                                Is there any better code practices I should be employing and am not?




                                • The first thing that caught my attention is the missing tests

                                You should implement a few test cases to ensure that after changes the program does still work as intended



                                Both the unittest module or doctest are good Python modules for testing, I have used the unittest as an example



                                class PascalTriangleTest(unittest.TestCase):
                                def test_triangle_0(self):
                                self.assertEqual(
                                pascal_triangle(0),
                                [[1]]
                                )

                                def test_triangle_1(self):
                                self.assertEqual(
                                pascal_triangle(1),
                                [[1], [1, 1]]
                                )

                                def test_triangle_2(self):
                                self.assertEqual(
                                pascal_triangle(2),
                                [[1], [1, 1], [1, 2, 1]]
                                )

                                def test_triangle_3(self):
                                self.assertEqual(
                                pascal_triangle(3),
                                [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
                                )

                                if __name__ == '__main__':
                                unittest.main()


                                • The second one would be the missing docstrings

                                The comments below your code would be a good start to make the docstring for each function.



                                See PEP257, for docstring conventions






                                share|improve this answer









                                $endgroup$

















                                  3












                                  $begingroup$


                                  Is there any better code practices I should be employing and am not?




                                  • The first thing that caught my attention is the missing tests

                                  You should implement a few test cases to ensure that after changes the program does still work as intended



                                  Both the unittest module or doctest are good Python modules for testing, I have used the unittest as an example



                                  class PascalTriangleTest(unittest.TestCase):
                                  def test_triangle_0(self):
                                  self.assertEqual(
                                  pascal_triangle(0),
                                  [[1]]
                                  )

                                  def test_triangle_1(self):
                                  self.assertEqual(
                                  pascal_triangle(1),
                                  [[1], [1, 1]]
                                  )

                                  def test_triangle_2(self):
                                  self.assertEqual(
                                  pascal_triangle(2),
                                  [[1], [1, 1], [1, 2, 1]]
                                  )

                                  def test_triangle_3(self):
                                  self.assertEqual(
                                  pascal_triangle(3),
                                  [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
                                  )

                                  if __name__ == '__main__':
                                  unittest.main()


                                  • The second one would be the missing docstrings

                                  The comments below your code would be a good start to make the docstring for each function.



                                  See PEP257, for docstring conventions






                                  share|improve this answer









                                  $endgroup$















                                    3












                                    3








                                    3





                                    $begingroup$


                                    Is there any better code practices I should be employing and am not?




                                    • The first thing that caught my attention is the missing tests

                                    You should implement a few test cases to ensure that after changes the program does still work as intended



                                    Both the unittest module or doctest are good Python modules for testing, I have used the unittest as an example



                                    class PascalTriangleTest(unittest.TestCase):
                                    def test_triangle_0(self):
                                    self.assertEqual(
                                    pascal_triangle(0),
                                    [[1]]
                                    )

                                    def test_triangle_1(self):
                                    self.assertEqual(
                                    pascal_triangle(1),
                                    [[1], [1, 1]]
                                    )

                                    def test_triangle_2(self):
                                    self.assertEqual(
                                    pascal_triangle(2),
                                    [[1], [1, 1], [1, 2, 1]]
                                    )

                                    def test_triangle_3(self):
                                    self.assertEqual(
                                    pascal_triangle(3),
                                    [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
                                    )

                                    if __name__ == '__main__':
                                    unittest.main()


                                    • The second one would be the missing docstrings

                                    The comments below your code would be a good start to make the docstring for each function.



                                    See PEP257, for docstring conventions






                                    share|improve this answer









                                    $endgroup$




                                    Is there any better code practices I should be employing and am not?




                                    • The first thing that caught my attention is the missing tests

                                    You should implement a few test cases to ensure that after changes the program does still work as intended



                                    Both the unittest module or doctest are good Python modules for testing, I have used the unittest as an example



                                    class PascalTriangleTest(unittest.TestCase):
                                    def test_triangle_0(self):
                                    self.assertEqual(
                                    pascal_triangle(0),
                                    [[1]]
                                    )

                                    def test_triangle_1(self):
                                    self.assertEqual(
                                    pascal_triangle(1),
                                    [[1], [1, 1]]
                                    )

                                    def test_triangle_2(self):
                                    self.assertEqual(
                                    pascal_triangle(2),
                                    [[1], [1, 1], [1, 2, 1]]
                                    )

                                    def test_triangle_3(self):
                                    self.assertEqual(
                                    pascal_triangle(3),
                                    [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
                                    )

                                    if __name__ == '__main__':
                                    unittest.main()


                                    • The second one would be the missing docstrings

                                    The comments below your code would be a good start to make the docstring for each function.



                                    See PEP257, for docstring conventions







                                    share|improve this answer












                                    share|improve this answer



                                    share|improve this answer










                                    answered Jan 17 at 14:19









                                    LudisposedLudisposed

                                    7,80721960




                                    7,80721960





















                                        2












                                        $begingroup$


                                        Is there anything in my program that seems redundant, repetitive, or can be shortened?




                                        The 22 lines of double_chunker, chunk_adder, and pascal_next can be shortened to



                                        def pascal_next(lst):
                                        return [left + right for (left, right) in zip(lst + [0], [0] + lst)]





                                        share|improve this answer









                                        $endgroup$








                                        • 1




                                          $begingroup$
                                          Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                          $endgroup$
                                          – Ludisposed
                                          Jan 17 at 14:47











                                        • $begingroup$
                                          @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                          $endgroup$
                                          – Peter Taylor
                                          Jan 17 at 15:28










                                        • $begingroup$
                                          You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                          $endgroup$
                                          – Graipher
                                          Jan 17 at 15:30















                                        2












                                        $begingroup$


                                        Is there anything in my program that seems redundant, repetitive, or can be shortened?




                                        The 22 lines of double_chunker, chunk_adder, and pascal_next can be shortened to



                                        def pascal_next(lst):
                                        return [left + right for (left, right) in zip(lst + [0], [0] + lst)]





                                        share|improve this answer









                                        $endgroup$








                                        • 1




                                          $begingroup$
                                          Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                          $endgroup$
                                          – Ludisposed
                                          Jan 17 at 14:47











                                        • $begingroup$
                                          @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                          $endgroup$
                                          – Peter Taylor
                                          Jan 17 at 15:28










                                        • $begingroup$
                                          You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                          $endgroup$
                                          – Graipher
                                          Jan 17 at 15:30













                                        2












                                        2








                                        2





                                        $begingroup$


                                        Is there anything in my program that seems redundant, repetitive, or can be shortened?




                                        The 22 lines of double_chunker, chunk_adder, and pascal_next can be shortened to



                                        def pascal_next(lst):
                                        return [left + right for (left, right) in zip(lst + [0], [0] + lst)]





                                        share|improve this answer









                                        $endgroup$




                                        Is there anything in my program that seems redundant, repetitive, or can be shortened?




                                        The 22 lines of double_chunker, chunk_adder, and pascal_next can be shortened to



                                        def pascal_next(lst):
                                        return [left + right for (left, right) in zip(lst + [0], [0] + lst)]






                                        share|improve this answer












                                        share|improve this answer



                                        share|improve this answer










                                        answered Jan 17 at 14:44









                                        Peter TaylorPeter Taylor

                                        16.2k2860




                                        16.2k2860







                                        • 1




                                          $begingroup$
                                          Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                          $endgroup$
                                          – Ludisposed
                                          Jan 17 at 14:47











                                        • $begingroup$
                                          @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                          $endgroup$
                                          – Peter Taylor
                                          Jan 17 at 15:28










                                        • $begingroup$
                                          You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                          $endgroup$
                                          – Graipher
                                          Jan 17 at 15:30












                                        • 1




                                          $begingroup$
                                          Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                          $endgroup$
                                          – Ludisposed
                                          Jan 17 at 14:47











                                        • $begingroup$
                                          @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                          $endgroup$
                                          – Peter Taylor
                                          Jan 17 at 15:28










                                        • $begingroup$
                                          You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                          $endgroup$
                                          – Graipher
                                          Jan 17 at 15:30







                                        1




                                        1




                                        $begingroup$
                                        Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                        $endgroup$
                                        – Ludisposed
                                        Jan 17 at 14:47





                                        $begingroup$
                                        Or return [sum(pair) for pair in zip(lst + [0], [0] + lst)] to make use of the built in sum
                                        $endgroup$
                                        – Ludisposed
                                        Jan 17 at 14:47













                                        $begingroup$
                                        @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                        $endgroup$
                                        – Peter Taylor
                                        Jan 17 at 15:28




                                        $begingroup$
                                        @Ludisposed, I deliberately chose not to do that because I regard it as a pessimisation.
                                        $endgroup$
                                        – Peter Taylor
                                        Jan 17 at 15:28












                                        $begingroup$
                                        You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                        $endgroup$
                                        – Graipher
                                        Jan 17 at 15:30




                                        $begingroup$
                                        You could also omit the parenthesis: [left + right for left, right in zip(lst + [0], [0] + lst)].
                                        $endgroup$
                                        – Graipher
                                        Jan 17 at 15:30

















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