khayyam_triangle.py

# Double Gold Star

# Khayyam Triangle

# The French mathematician, Blaise Pascal, who built a mechanical computer in
# the 17th century, studied a pattern of numbers now commonly known in parts of
# the world as Pascal's Triangle (it was also previously studied by many Indian,
# Chinese, and Persian mathematicians, and is known by different names in other
# parts of the world).

# The pattern is shown below:

#                    1
#                   1 1
#                  1 2 1
#                 1 3 3 1
#                1 4 6 4 1
#                   ...

# Each number is the sum of the number above it to the left and the number above
# it to the right (any missing numbers are counted as 0).

# Define a procedure, triangle(n), that takes a number n as its input, and
# returns a list of the first n rows in the triangle. Each element of the
# returned list should be a list of the numbers at the corresponding row in the
# triangle.

def make_next_row(row):
	result=[]
	prev=0
	for e in row:
		result.append(e+prev)
		prev=e
	result.append(prev)
	return result
def triangle(n):
	result=[]
	current=[1]
	for unused in range(0,n):
		result.append(current)
		current=make_next_row(current)
	return result


#For example:

print triangle(0)
#>>> []

print triangle(1)
#>>> [[1]]

print triangle(2)
#>> [[1], [1, 1]]

print triangle(3)
#>>> [[1], [1, 1], [1, 2, 1]]

print triangle(4)
print triangle(6)
#>>> [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1]]