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18_Khayyam Triangle.py
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18_Khayyam Triangle.py
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# 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 triangle(n):
if n<1:
return []
if n==1:
return [[1]]
else:
list=[]
list+=triangle(n-1)
newlist=[1]
for i in range(1,len(list)):
newlist.append(list[n-2][i-1]+list[n-2][i])
newlist.append(1)
list.append(newlist)
return list
#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(6)
#>>> [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1]]